Linear and nonlinear instability in vertical counter-current laminar gas-liquid flows

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schmidt, Patrick; Lucquiaud, Mathieu; Valluri, Prashant, E-mail: prashant.valluri@ed.ac.uk

We consider the genesis and dynamics of interfacial instability in vertical gas-liquid flows, using as a model the two-dimensional channel flow of a thin falling film sheared by counter-current gas. The methodology is linear stability theory (Orr-Sommerfeld analysis) together with direct numerical simulation of the two-phase flow in the case of nonlinear disturbances. We investigate the influence of two main flow parameters on the interfacial dynamics, namely the film thickness and pressure drop applied to drive the gas stream. To make contact with existing studies in the literature, the effect of various density contrasts is also examined. Energy budget analysesmore » based on the Orr-Sommerfeld theory reveal various coexisting unstable modes (interfacial, shear, internal) in the case of high density contrasts, which results in mode coalescence and mode competition, but only one dynamically relevant unstable interfacial mode for low density contrast. A study of absolute and convective instability for low density contrast shows that the system is absolutely unstable for all but two narrow regions of the investigated parameter space. Direct numerical simulations of the same system (low density contrast) show that linear theory holds up remarkably well upon the onset of large-amplitude waves as well as the existence of weakly nonlinear waves. For high density contrasts, corresponding more closely to an air-water-type system, linear stability theory is also successful at determining the most-dominant features in the interfacial wave dynamics at early-to-intermediate times. Nevertheless, the short waves selected by the linear theory undergo secondary instability and the wave train is no longer regular but rather exhibits chaotic motion. The same linear stability theory predicts when the direction of travel of the waves changes — from downwards to upwards. We outline the practical implications of this change in terms of loading and flooding. The change in direction of the wave propagation is represented graphically in terms of a flow map based on the liquid and gas flow rates and the prediction carries over to the nonlinear regime with only a small deviation.« less

The Hagen-Poiseuille, Plane Couette and Poiseuille Flows Linear Instability and Rogue Waves Excitation Mechanism

NASA Astrophysics Data System (ADS)

Chefranov, Sergey; Chefranov, Alexander

2016-04-01

Linear hydrodynamic stability theory for the Hagen-Poiseuille (HP) flow yields a conclusion of infinitely large threshold Reynolds number, Re, value. This contradiction to the observation data is bypassed using assumption of the HP flow instability having hard type and possible for sufficiently high-amplitude disturbances. HP flow disturbance evolution is considered by nonlinear hydrodynamic stability theory. Similar is the case of the plane Couette (PC) flow. For the plane Poiseuille (PP) flow, linear theory just quantitatively does not agree with experimental data defining the threshold Reynolds number Re= 5772 ( S. A. Orszag, 1971), more than five-fold exceeding however the value observed, Re=1080 (S. J. Davies, C. M. White, 1928). In the present work, we show that the linear stability theory conclusions for the HP and PC on stability for any Reynolds number and evidently too high threshold Reynolds number estimate for the PP flow are related with the traditional use of the disturbance representation assuming the possibility of separation of the longitudinal (along the flow direction) variable from the other spatial variables. We show that if to refuse from this traditional form, conclusions on the linear instability for the HP and PC flows may be obtained for finite Reynolds numbers (for the HP flow, for Re>704, and for the PC flow, for Re>139). Also, we fit the linear stability theory conclusion on the PP flow to the experimental data by getting an estimate of the minimal threshold Reynolds number as Re=1040. We also get agreement of the minimal threshold Reynolds number estimate for PC with the experimental data of S. Bottin, et.al., 1997, where the laminar PC flow stability threshold is Re = 150. Rogue waves excitation mechanism in oppositely directed currents due to the PC flow linear instability is discussed. Results of the new linear hydrodynamic stability theory for the HP, PP, and PC flows are published in the following papers: 1. S.G. Chefranov, A.G. Chefranov, JETP, v.119, No.2, 331, 2014 2. S.G. Chefranov, A.G. Chefranov, Doklady Physics, vol.60, No.7, 327-332, 2015 3. S.G. Chefranov, A. G. Chefranov, arXiv: 1509.08910v1 [physics.flu-dyn] 29 Sep 2015 (accepted to JETP)

The roll-up and merging of coherent structures in shallow mixing layers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lam, M. Y., E-mail: celmy@connect.ust.hk; Ghidaoui, M. S.; Kolyshkin, A. A.

2016-09-15

The current study seeks a fundamental explanation to the development of two-dimensional coherent structures (2DCSs) in shallow mixing layers. A nonlinear numerical model based on the depth-averaged shallow water equations is used to investigate the temporal evolution of shallow mixing layers, where the mapping from temporal to spatial results is made using the velocity at the center of the mixing layers. The flow is periodic in the streamwise direction. Transmissive boundary conditions are used in the cross-stream boundaries to prevent reflections. Numerical results are compared to linear stability analysis, mean-field theory, and secondary stability analysis. Results suggest that the onsetmore » and development of 2DCS in shallow mixing layers are the result of a sequence of instabilities governed by linear theory, mean-field theory, and secondary stability theory. The linear instability of the shearing velocity gradient gives the onset of 2DCS. When the perturbations reach a certain amplitude, the flow field of the perturbations changes from a wavy shape to a vortical (2DCS) structure because of nonlinearity. The development of the vertical 2DCS does not appear to follow weakly nonlinear theory; instead, it follows mean-field theory. After the formation of 2DCS, separate 2DCSs merge to form larger 2DCS. In this way, 2DCSs grow and shallow mixing layers develop and grow in scale. The merging of 2DCS in shallow mixing layers is shown to be caused by the secondary instability of the 2DCS. Eventually 2DCSs are dissipated by bed friction. The sequence of instabilities can cause the upscaling of the turbulent kinetic energy in shallow mixing layers.« less

Slipping and tangential discontinuity instabilities in quasi-one-dimensional planar and cylindrical flows

NASA Astrophysics Data System (ADS)

Kuzelev, M. V.

2017-09-01

An analytical linear theory of instability of an electron beam with a nonuniform directional velocity (slipping instability) against perturbations with wavelengths exceeding the transverse beam size is offered. An analogy with hydrodynamic instabilities of tangential discontinuity of an incompressible liquid flow is drawn. The instability growth rates are calculated for particular cases and in a general form in planar and cylindrical geometries. The stabilizing effect of the external magnetic field is analyzed.

Thermal effects in rapid directional solidification - Linear theory

NASA Technical Reports Server (NTRS)

Huntley, D. A.; Davis, S. H.

1993-01-01

We study the morphological instability of the planar solid/liquid interface for a unidirectionally-solidified dilute binary mixture. We use a model developed by Boettinger et al. (1985, 1986), Aziz (1982), and Jackson et al. (1980), which allows for nonequilibrium effects on the interface through velocity-dependent segregation and attachment kinetics. Two types of instabilities are found in the linear stability analysis: (1) a cellular instability, and (2) an oscillatory instability driven by disequilibrium effects. Merchant and Davis (1990) characterized these instabilities subject to the frozen-temperature approximation (FTA). The present work relaxes the FTA by including the effects of latent heat and the full temperature distribution. Thermal effects slightly postpone the onset of the cellular instability but dramatically postpone the onset of the oscillatory instability; however, the absolute-stability conditions, at which at high speed the cellular and oscillatory instabilities are suppressed, remain unchanged from the FTA.

Theory of electrohydrodynamic instabilities in electrolytic cells

NASA Technical Reports Server (NTRS)

Bruinsma, R.; Alexander, S.

1990-01-01

The paper develops the theory of the hydrodynamic stability of an electrolytic cell as a function of the imposed electric current. A new electrohydrodynamic instability is encountered when the current is forced to exceed the Nernst limit. The convection is driven by the volume force exerted by the electric field on space charges in the electrolyte. This intrinsic instability is found to be easily masked by extrinsic convection sources such as gravity or stirring. A linear stability analysis is performed and a dimensionless number Le is derived whose value determines the convection pattern.

Fluid aspects of electron streaming instability in electron-ion plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jao, C.-S.; Hau, L.-N.; Department of Physics, National Central University, Jhongli, Taiwan

2014-02-15

Electrons streaming in a background electron and ion plasma may lead to the formation of electrostatic solitary wave (ESW) and hole structure which have been observed in various space plasma environments. Past studies on the formation of ESW are mostly based on the particle simulations due to the necessity of incorporating particle's trapping effects. In this study, the fluid aspects and thermodynamics of streaming instabilities in electron-ion plasmas including bi-streaming and bump-on-tail instabilities are addressed based on the comparison between fluid theory and the results from particle-in-cell simulations. The energy closure adopted in the fluid model is the polytropic lawmore » of d(pρ{sup −γ})/dt=0 with γ being a free parameter. Two unstable modes are identified for the bump-on-tail instability and the growth rates as well as the dispersion relation of the streaming instabilities derived from the linear theory are found to be in good agreement with the particle simulations for both bi-streaming and bump-on-tail instabilities. At the nonlinear saturation, 70% of the electrons are trapped inside the potential well for the drift velocity being 20 times of the thermal velocity and the pρ{sup −γ} value is significantly increased. Effects of ion to electron mass ratio on the linear fluid theory and nonlinear simulations are also examined.« less

The Kelvin-Helmholtz instability of boundary-layer plasmas in the kinetic regime

DOE Office of Scientific and Technical Information (OSTI.GOV)

Steinbusch, Benedikt, E-mail: b.steinbusch@fz-juelich.de; Gibbon, Paul, E-mail: p.gibbon@fz-juelich.de; Department of Mathematics, Centre for Mathematical Plasma Astrophysics, Katholieke Universiteit Leuven

2016-05-15

The dynamics of the Kelvin-Helmholtz instability are investigated in the kinetic, high-frequency regime with a novel, two-dimensional, mesh-free tree code. In contrast to earlier studies which focused on specially prepared equilibrium configurations in order to compare with fluid theory, a more naturally occurring plasma-vacuum boundary layer is considered here with relevance to both space plasma and linear plasma devices. Quantitative comparisons of the linear phase are made between the fluid and kinetic models. After establishing the validity of this technique via comparison to linear theory and conventional particle-in-cell simulation for classical benchmark problems, a quantitative analysis of the more complexmore » magnetized plasma-vacuum layer is presented and discussed. It is found that in this scenario, the finite Larmor orbits of the ions result in significant departures from the effective shear velocity and width underlying the instability growth, leading to generally slower development and stronger nonlinear coupling between fast growing short-wavelength modes and longer wavelengths.« less

Scalings of Alfvén-cyclotron and ion Bernstein instabilities on temperature anisotropy of a ring-like velocity distribution in the inner magnetosphere

DOE PAGES

Min, Kyungguk; Liu, Kaijun; Gary, S. Peter

2016-03-18

Here, a ring-like proton velocity distribution with ∂f p(v ⊥)/∂v ⊥>0 and which is sufficiently anisotropic can excite two distinct types of growing modes in the inner magnetosphere: ion Bernstein instabilities with multiple ion cyclotron harmonics and quasi-perpendicular propagation and an Alfvén-cyclotron instability at frequencies below the proton cyclotron frequency and quasi-parallel propagation. Recent particle-in-cell simulations have demonstrated that even if the maximum linear growth rate of the latter instability is smaller than the corresponding growth of the former instability, the saturation levels of the fluctuating magnetic fields can be greater for the Alfvén-cyclotron instability than for the ion Bernsteinmore » instabilities. In this study, linear dispersion theory and two-dimensional particle-in-cell simulations are used to examine scalings of the linear growth rate and saturation level of the two types of growing modes as functions of the temperature anisotropy T ⊥/T || for a general ring-like proton distribution with a fixed ring speed of 2v A, where v A is the Alfvén speed. For the proton distribution parameters chosen, the maximum linear theory growth rate of the Alfvén-cyclotron waves is smaller than that of the fastest-growing Bernstein mode for the wide range of anisotropies (1≤T ⊥/T ||≤7) considered here. Yet the corresponding particle-in-cell simulations yield a higher saturation level of the fluctuating magnetic fields for the Alfvén-cyclotron instability than for the Bernstein modes as long as inline image. Since fast magnetosonic waves with ion Bernstein instability properties observed in the magnetosphere are often not accompanied by electromagnetic ion cyclotron waves, the results of the present study indicate that the ring-like proton distributions responsible for the excitation of these fast magnetosonic waves should not be very anisotropic.« less

Spatial Holmboe instability

NASA Astrophysics Data System (ADS)

Ortiz, Sabine; Chomaz, Jean-Marc; Loiseleux, Thomas

2002-08-01

In mixing-layers between two parallel streams of different densities, shear and gravity effects interplay; buoyancy acts as a restoring force and the Kelvin-Helmholtz mode is known to be stabilized by the stratification. If the density interface is sharp enough, two new instability modes, known as Holmboe modes, appear, propagating in opposite directions. This mechanism has been studied in the temporal instability framework. The present paper analyzes the associated spatial instability problem. It considers, in the Boussinesq approximation, two immiscible inviscid fluids with a piecewise linear broken-line velocity profile. We show how the classical scenario for transition between absolute and convective instability should be modified due to the presence of propagating waves. In the convective region, the spatial theory is relevant and the slowest propagating wave is shown to be the most spatially amplified, as suggested by intuition. Predictions of spatial linear theory are compared with mixing-layer [C. G. Koop and F. K. Browand, J. Fluid Mech. 93, 135 (1979)] and exchange flow [G. Pawlak and L. Armi, J. Fluid Mech. 376, 1 (1999)] experiments. The physical mechanism for Holmboe mode destabilization is analyzed via an asymptotic expansion that predicts the absolute instability domain at large Richardson number.

Bending instability in galactic discs: advocacy of the linear theory

NASA Astrophysics Data System (ADS)

Rodionov, S. A.; Sotnikova, N. Ya.

2013-09-01

We demonstrate that in N-body simulations of isolated disc galaxies, there is numerical vertical heating which slowly increases the vertical velocity dispersion and the disc thickness. Even for models with over a million particles in a disc, this heating can be significant. Such an effect is just the same as in numerical experiments by Sellwood. We also show that in a stellar disc, outside a boxy/peanut bulge, if it presents, the saturation level of the bending instability is rather close to the value predicted by the linear theory. We pay attention to the fact that the bending instability develops and decays very fast, so it cannot play any role in secular vertical heating. However, the bending instability defines the minimal value of the ratio between the vertical and radial velocity dispersions σz/σR ≈ 0.3 (so indirectly the minimal thickness), which stellar discs in real galaxies may have. We demonstrate that observations confirm the last statement.

Whistler and Alfvén Mode Cyclotron Masers in Space

NASA Astrophysics Data System (ADS)

Trakhtengerts, V. Y.; Rycroft, M. J.

2012-10-01

Preface; 1. Introduction; 2. Basic theory of cyclotron masers (CMs); 3. Linear theory of the cyclotron instability (CI); 4. Backward wave oscillator (BWO) regime in CMs; 5. Nonlinear cyclotron wave-particle interactions for a quasi-monochromatic wave; 6. Nonlinear interaction of quasi-monochromatic whistler mode waves with gyroresonant electrons in an in homogeneous plasma; 7. Wavelet amplification in an inhomogeneous plasma; 8. Quasi-linear theory of cyclotron masers; 9. Nonstationary generation regimes, and modulation effects; 10. ELF/VLF noise-like emissions and electrons in the Earth's radiation belts; 11. Generation of discrete ELF/VLF whistler mode emissions; 12. Cyclotron instability of the proton radiation belts; 13. Cyclotron masers elsewhere in the solar system and in laboratory plasma devices; Epilogue; Glossary of terms; List of acronyms; References; Index.

A non-linear theory of the parallel firehose and gyrothermal instabilities in a weakly collisional plasma

NASA Astrophysics Data System (ADS)

Rosin, M. S.; Schekochihin, A. A.; Rincon, F.; Cowley, S. C.

2011-05-01

Weakly collisional magnetized cosmic plasmas have a dynamical tendency to develop pressure anisotropies with respect to the local direction of the magnetic field. These anisotropies trigger plasma instabilities at scales just above the ion Larmor radius ρi and much below the mean free path λmfp. They have growth rates of a fraction of the ion cyclotron frequency, which is much faster than either the global dynamics or even local turbulence. Despite their microscopic nature, these instabilities dramatically modify the transport properties and, therefore, the macroscopic dynamics of the plasma. The non-linear evolution of these instabilities is expected to drive pressure anisotropies towards marginal stability values, controlled by the plasma beta βi. Here this non-linear evolution is worked out in an ab initio kinetic calculation for the simplest analytically tractable example - the parallel (k⊥= 0) firehose instability in a high-beta plasma. An asymptotic theory is constructed, based on a particular physical ordering and leading to a closed non-linear equation for the firehose turbulence. In the non-linear regime, both the analytical theory and the numerical solution predict secular (∝t) growth of magnetic fluctuations. The fluctuations develop a k-3∥ spectrum, extending from scales somewhat larger than ρi to the maximum scale that grows secularly with time (∝t1/2); the relative pressure anisotropy (p⊥-p∥)/p∥ tends to the marginal value -2/βi. The marginal state is achieved via changes in the magnetic field, not particle scattering. When a parallel ion heat flux is present, the parallel firehose mutates into the new gyrothermal instability (GTI), which continues to exist up to firehose-stable values of pressure anisotropy, which can be positive and are limited by the magnitude of the ion heat flux. The non-linear evolution of the GTI also features secular growth of magnetic fluctuations, but the fluctuation spectrum is eventually dominated by modes around a maximal scale ˜ρilT/λmfp, where lT is the scale of the parallel temperature variation. Implications for momentum and heat transport are speculated about. This study is motivated by our interest in the dynamics of galaxy cluster plasmas (which are used as the main astrophysical example), but its relevance to solar wind and accretion flow plasmas is also briefly discussed.

Secular instabilities of Keplerian stellar discs

NASA Astrophysics Data System (ADS)

Kaur, Karamveer; Kazandjian, Mher V.; Sridhar, S.; Touma, Jihad R.

2018-05-01

We present idealized models of a razor-thin, axisymmetric, Keplerian stellar disc around a massive black hole, and study non-axisymmetric secular instabilities in the absence of either counter-rotation or loss cones. These discs are prograde mono-energetic waterbags, whose phase-space distribution functions are constant for orbits within a range of eccentricities (e) and zero outside this range. The linear normal modes of waterbags are composed of sinusoidal disturbances of the edges of distribution function in phase space. Waterbags that include circular orbits (polarcaps) have one stable linear normal mode for each azimuthal wavenumber m. The m = 1 mode always has positive pattern speed and, for polarcaps consisting of orbits with e < 0.9428, only the m = 1 mode has positive pattern speed. Waterbags excluding circular orbits (bands) have two linear normal modes for each m, which can be stable or unstable. We derive analytical expressions for the instability condition, pattern speeds, growth rates, and normal mode structure. Narrow bands are unstable to modes with a wide range in m. Numerical simulations confirm linear theory and follow the non-linear evolution of instabilities. Long-time integration suggests that instabilities of different m grow, interact non-linearly, and relax collisionlessly to a coarse-grained equilibrium with a wide range of eccentricities.

Proton velocity ring-driven instabilities and their dependence on the ring speed: Linear theory

NASA Astrophysics Data System (ADS)

Min, Kyungguk; Liu, Kaijun; Gary, S. Peter

2017-08-01

Linear dispersion theory is used to study the Alfvén-cyclotron, mirror and ion Bernstein instabilities driven by a tenuous (1%) warm proton ring velocity distribution with a ring speed, vr, varying between 2vA and 10vA, where vA is the Alfvén speed. Relatively cool background protons and electrons are assumed. The modeled ring velocity distributions are unstable to both the Alfvén-cyclotron and ion Bernstein instabilities whose maximum growth rates are roughly a linear function of the ring speed. The mirror mode, which has real frequency ωr=0, becomes the fastest growing mode for sufficiently large vr/vA. The mirror and Bernstein instabilities have maximum growth at propagation oblique to the background magnetic field and become more field-aligned with an increasing ring speed. Considering its largest growth rate, the mirror mode, in addition to the Alfvén-cyclotron mode, can cause pitch angle diffusion of the ring protons when the ring speed becomes sufficiently large. Moreover, because the parallel phase speed, v∥ph, becomes sufficiently small relative to vr, the low-frequency Bernstein waves can also aid the pitch angle scattering of the ring protons for large vr. Potential implications of including these two instabilities at oblique propagation on heliospheric pickup ion dynamics are discussed.

Instability of the cored barotropic disc: the linear eigenvalue formulation

NASA Astrophysics Data System (ADS)

Polyachenko, E. V.

2018-05-01

Gaseous rotating razor-thin discs are a testing ground for theories of spiral structure that try to explain appearance and diversity of disc galaxy patterns. These patterns are believed to arise spontaneously under the action of gravitational instability, but calculations of its characteristics in the gas are mostly obscured. The paper suggests a new method for finding the spiral patterns based on an expansion of small amplitude perturbations over Lagrange polynomials in small radial elements. The final matrix equation is extracted from the original hydrodynamical equations without the use of an approximate theory and has a form of the linear algebraic eigenvalue problem. The method is applied to a galactic model with the cored exponential density profile.

Turbulence closure for mixing length theories

NASA Astrophysics Data System (ADS)

Jermyn, Adam S.; Lesaffre, Pierre; Tout, Christopher A.; Chitre, Shashikumar M.

2018-05-01

We present an approach to turbulence closure based on mixing length theory with three-dimensional fluctuations against a two-dimensional background. This model is intended to be rapidly computable for implementation in stellar evolution software and to capture a wide range of relevant phenomena with just a single free parameter, namely the mixing length. We incorporate magnetic, rotational, baroclinic, and buoyancy effects exactly within the formalism of linear growth theories with non-linear decay. We treat differential rotation effects perturbatively in the corotating frame using a novel controlled approximation, which matches the time evolution of the reference frame to arbitrary order. We then implement this model in an efficient open source code and discuss the resulting turbulent stresses and transport coefficients. We demonstrate that this model exhibits convective, baroclinic, and shear instabilities as well as the magnetorotational instability. It also exhibits non-linear saturation behaviour, and we use this to extract the asymptotic scaling of various transport coefficients in physically interesting limits.

Electromagnetic ion instabilities in a cometary environment

NASA Astrophysics Data System (ADS)

Gary, S. P.; Madland, C. D.

1988-01-01

This paper considers the linear theory of electromagnetic ion beam and ion ring-beam instabilities in a homogeneous Vlasov plasma. Propagation parallel or antiparallel to a uniform magnetic field and frequencies at or below the proton cyclotron frequency are considered. For parameters representative of the distant cometary environment, the authors show that instabilities with right-hand polarization in the zero momentum frame have larger linear growth rates than left-hand polarized instabilities at α values up to 90° where α is the angle between the solar wind velocity and the uniform interplanetary magnetic field. If both a proton beam and an oxygen beam are present with α = 0°, two right-hand resonant instabilities may grow; these two modes are distinct and relatively independent of one another for a very wide range of proton/oxygen beam density ratios.

RELATIVISTIC CYCLOTRON INSTABILITY IN ANISOTROPIC PLASMAS

DOE Office of Scientific and Technical Information (OSTI.GOV)

López, Rodrigo A.; Moya, Pablo S.; Muñoz, Víctor

2016-11-20

A sufficiently large temperature anisotropy can sometimes drive various types of electromagnetic plasma micro-instabilities, which can play an important role in the dynamics of relativistic pair plasmas in space, astrophysics, and laboratory environments. Here, we provide a detailed description of the cyclotron instability of parallel propagating electromagnetic waves in relativistic pair plasmas on the basis of a relativistic anisotropic distribution function. Using plasma kinetic theory and particle-in-cell simulations, we study the influence of the relativistic temperature and the temperature anisotropy on the collective and noncollective modes of these plasmas. Growth rates and dispersion curves from the linear theory show amore » good agreement with simulations results.« less

On the persistence of unstable bump-on-tail electron velocity distributions in the earth's foreshock

NASA Technical Reports Server (NTRS)

Klimas, Alexander J.; Fitzenreiter, Richard J.

1988-01-01

This paper presents further evidence for the persistence of bump-on-tail unstable reduced velocity distributions in the earth's electron foreshock, which contradicts the understanding of quasi-linear saturation of the bump-on-tail instability. A modified theory for the saturation of the bump-on-tail instability in the earth's foreshock is proposed to explain the mechanism of this persistence, and the predictions are compared to the results of a numerical simulation of the electron plasma in the foreshock. The results support the thesis that quasi-linear saturation of the bump-on-tail instability is modified in the foreshock, due to the driven nature of the region, so that at saturation the stabilized velocity distribution still appears bump-on-tail unstable to linear plasma analysis.

Artificial ion beam instabilities. I - Linear theory. II - Simulations

NASA Astrophysics Data System (ADS)

Scales, W. A.; Kintner, P. M.

1990-07-01

Some of the important plasma instabilities that result when an artificial ion beam is injected into the ionospheric F region are studied using linear Vlasov theory. The variation in wave spectra at the receiver as the receiver and plasma gun separate perpendicularly to the magnetic field is consistent with a beam density decrease at or near the receiver. At separation distances that are large fractions of the beam gyrodiameter, usually narrow-band waves near the background lower hybrid and H+ gyroharmonic frequencies are measured. These observations are consistent with waves expected to be generated by beam densities on the order of or less than a few percent of the background density. At smaller separation distances, broadband waves are usually observed with frequencies from zero up to and above the lower hybrid frequency. Electrostatic particle simulation studies of the plasma instabilities indicate that the broadband fluidlike lower hybrid instability is the most important for background particle heating. Perpendicular H+ heating is more efficient than perpendicular O+ or parallel electron heating for the drift velocity regime most relevant to past experiments.

Long-wave theory for a new convective instability with exponential growth normal to the wall.

PubMed

Healey, J J

2005-05-15

A linear stability theory is presented for the boundary-layer flow produced by an infinite disc rotating at constant angular velocity in otherwise undisturbed fluid. The theory is developed in the limit of long waves and when the effects of viscosity on the waves can be neglected. This is the parameter regime recently identified by the author in a numerical stability investigation where a curious new type of instability was found in which disturbances propagate and grow exponentially in the direction normal to the disc, (i.e. the growth takes place in a region of zero mean shear). The theory describes the mechanisms controlling the instability, the role and location of critical points, and presents a saddle-point analysis describing the large-time evolution of a wave packet in frames of reference moving normal to the disc. The theory also shows that the previously obtained numerical solutions for numerically large wavelengths do indeed lie in the asymptotic long-wave regime, and so the behaviour and mechanisms described here may apply to a number of cross-flow instability problems.

Dynamical density functional theory analysis of the laning instability in sheared soft matter.

PubMed

Scacchi, A; Archer, A J; Brader, J M

2017-12-01

Using dynamical density functional theory (DDFT) methods we investigate the laning instability of a sheared colloidal suspension. The nonequilibrium ordering at the laning transition is driven by nonaffine particle motion arising from interparticle interactions. Starting from a DDFT which incorporates the nonaffine motion, we perform a linear stability analysis that enables identification of the regions of parameter space where lanes form. We illustrate our general approach by applying it to a simple one-component fluid of soft penetrable particles.

Potential Role of the Mirror and Ion Bernstein Instabilities on the Pickup Ion Dynamics in the Outer Heliosheath: Linear Theory and Hybrid Simulations

NASA Astrophysics Data System (ADS)

Min, K.; Liu, K.; Gary, S. P.

2017-12-01

The main challenge of the secondary ENA mechanism, a theory put forth to explain the IBEX ENA ribbon, is maintaining the stability of the pickup ion velocity distribution before the pickup ions in the outer heliosheath go through two consecutive charge exchanges. The Alfvén/ion-cyclotron instability, which has its maximum growth at propagation parallel to Bo, the background magnetic field, is believed to be the main agent leading to rapid isotropization of the pickup ions. However, recent studies found that this instability can be suppressed when parallel temperatures of the background plasma and the pickup ion ring distribution are comparable, allowing the pickup ion distribution to remain stable for a long period. This paper demonstrates that a pickup ion ring distribution can also drive the mirror and ion Bernstein instabilities which lead to growing modes at propagation oblique to Bo. For idealized proton-electron plasmas where relatively cool background electron and proton populations are represented by isotropic Maxwellian distributions and tenuous (1%) pickup protons are represented by a Maxwellian-ring distribution (assuming a 90˚ pickup angle), linear Vlasov theory predicts unstable mirror and ion Bernstein modes with growth rates comparable to or exceeding that of the Alfvén-cyclotron instability. According to quasilinear theory, interactions with these obliquely-propagating modes can lead to substantial pitch angle scattering of the ring protons. Two-dimensional hybrid (kinetic ions and massless fluid electrons) simulations are carried out to examine the nonlinear consequences of the mirror and Bernstein instabilities. The preliminary simulation results are presented. The study suggests a scenario that the oblique mirror and ion Bernstein modes can be an active agent of the pickup ion isotropization when the condition is such that the Alfvén-cyclotron instability is suppressed.

Measurements in a Transitioning Cone Boundary Layer at Freestream Mach 3.5

NASA Technical Reports Server (NTRS)

King, Rudolph A.; Chou, Amanda; Balakumar, Ponnampalam; Owens, Lewis R.; Kegerise, Michael A.

2016-01-01

An experimental study was conducted in the Supersonic Low-Disturbance Tunnel to investigate naturally-occurring instabilities in a supersonic boundary layer on a 7 deg half- angle cone. All tests were conducted with a nominal freestream Mach number of M(sub infinity) = 3:5, total temperature of T(sub 0) = 299:8 K, and unit Reynolds numbers of Re(sub infinity) x 10(exp -6) = 9:89, 13.85, 21.77, and 25.73 m(exp -1). Instability measurements were acquired under noisy- ow and quiet- ow conditions. Measurements were made to document the freestream and the boundary-layer edge environment, to document the cone baseline flow, and to establish the stability characteristics of the transitioning flow. Pitot pressure and hot-wire boundary- layer measurements were obtained using a model-integrated traverse system. All hot- wire results were single-point measurements and were acquired with a sensor calibrated to mass ux. For the noisy-flow conditions, excellent agreement for the growth rates and mode shapes was achieved between the measured results and linear stability theory (LST). The corresponding N factor at transition from LST is N 3:9. The stability measurements for the quiet-flow conditions were limited to the aft end of the cone. The most unstable first-mode instabilities as predicted by LST were successfully measured, but this unstable first mode was not the dominant instability measured in the boundary layer. Instead, the dominant instabilities were found to be the less-amplified, low-frequency disturbances predicted by linear stability theory, and these instabilities grew according to linear theory. These low-frequency unstable disturbances were initiated by freestream acoustic disturbances through a receptivity process that is believed to occur near the branch I locations of the cone. Under quiet-flow conditions, the boundary layer remained laminar up to the last measurement station for the largest Re1, implying a transition N factor of N greater than 8:5.

Analysis of friction and instability by the centre manifold theory for a non-linear sprag-slip model

NASA Astrophysics Data System (ADS)

Sinou, J.-J.; Thouverez, F.; Jezequel, L.

2003-08-01

This paper presents the research devoted to the study of instability phenomena in non-linear model with a constant brake friction coefficient. Indeed, the impact of unstable oscillations can be catastrophic. It can cause vehicle control problems and component degradation. Accordingly, complex stability analysis is required. This paper outlines stability analysis and centre manifold approach for studying instability problems. To put it more precisely, one considers brake vibrations and more specifically heavy trucks judder where the dynamic characteristics of the whole front axle assembly is concerned, even if the source of judder is located in the brake system. The modelling introduces the sprag-slip mechanism based on dynamic coupling due to buttressing. The non-linearity is expressed as a polynomial with quadratic and cubic terms. This model does not require the use of brake negative coefficient, in order to predict the instability phenomena. Finally, the centre manifold approach is used to obtain equations for the limit cycle amplitudes. The centre manifold theory allows the reduction of the number of equations of the original system in order to obtain a simplified system, without loosing the dynamics of the original system as well as the contributions of non-linear terms. The goal is the study of the stability analysis and the validation of the centre manifold approach for a complex non-linear model by comparing results obtained by solving the full system and by using the centre manifold approach. The brake friction coefficient is used as an unfolding parameter of the fundamental Hopf bifurcation point.

Long-wave instabilities of two interlaced helical vortices

NASA Astrophysics Data System (ADS)

Quaranta, H. U.; Brynjell-Rahkola, M.; Leweke, T.; Henningson, D. S.

2016-09-01

We present a comparison between experimental observations and theoretical predictions concerning long-wave displacement instabilities of the helical vortices in the wake of a two-bladed rotor. Experiments are performed with a small-scale rotor in a water channel, using a set-up that allows the individual triggering of various instability modes at different azimuthal wave numbers, leading to local or global pairing of successive vortex loops. The initial development of the instability and the measured growth rates are in good agreement with the predictions from linear stability theory, based on an approach where the helical vortex system is represented by filaments. At later times, local pairing develops into large-scale distortions of the vortices, whereas for global pairing the non-linear evolution returns the system almost to its initial geometry.

Experiments on the Richtmyer-Meshkov Instability of Incompressible Fluids

NASA Technical Reports Server (NTRS)

Jacobs, J.; Niederhaus, C.

2000-01-01

Richtmyer-Meshkov (R-M) instability occurs when two different density fluids are impulsively accelerated in the direction normal to their nearly planar interface. The instability causes small perturbations on the interface to grow and possibly become turbulent given the proper initial conditions. R-M instability is similar to the Rayleigh-Taylor (R-T) instability, which is generated when the two fluids undergo a constant acceleration. R-M instability is a fundamental fluid instability that is important to fields ranging from astrophysics to high-speed combustion. For example, R-M instability is currently the limiting factor in achieving a net positive yield with inertial confinement fusion. The experiments described here utilize a novel technique that circumvents many of the experimental difficulties previously limiting the study of the R-M instability. A Plexiglas tank contains two unequal density liquids and is gently oscillated horizontally to produce a controlled initial fluid interface shape. The tank is mounted to a sled on a high speed, low friction linear rail system, constraining the main motion to the vertical direction. The sled is released from an initial height and falls vertically until it bounces off of a movable spring, imparting an impulsive acceleration in the upward direction. As the sled travels up and down the rails, the spring retracts out of the way, allowing the instability to evolve in free-fall until impacting a shock absorber at the end of the rails. The impulsive acceleration provided to the system is measured by a piezoelectric accelerometer mounted on the tank, and a capacitive accelerometer measures the low-level drag of the bearings. Planar Laser-Induced Fluorescence is used for flow visualization, which uses an Argon ion laser to illuminate the flow and a CCD camera, mounted to the sled, to capture images of the interface. This experimental study investigates the instability of an interface between incompressible, miscible liquids with an initial sinusoidal perturbation. The amplitude of the disturbance during the experiment is measured and compared to theory. The results show good agreement (within 10%) with linear stability theory up to nondimensional amplitude ka = 0.7 (wavenumber x amplitude). These results hold true for an initial ka (before acceleration) of -0.7 less than ka less than -0.06, while the linear theory was developed for absolute value of ka much less than 1. In addition, a third order weakly nonlinear perturbation theory is shown to be accurate for amplitudes as large as ka = 1.3, even though the interface becomes double-valued at ka = 1.1. As time progresses, the vorticity on the interface concentrates, and the interface spirals around the alternating sign vortex centers to form a mushroom pattern. At higher Reynolds Number (based on circulation), an instability of the vortex cores has been observed. While time limitations of the apparatus prevent determination of a critical Reynolds Number, the lowest Reynolds Number this vortex instability has been observed at is 5000.

Jeans instability of magnetized quantum plasma: Effect of viscosity, rotation and finite Larmor radius corrections

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jain, Shweta, E-mail: jshweta09@gmail.com; Sharma, Prerana; Chhajlani, R. K.

2015-07-31

The Jeans instability of self-gravitating quantum plasma is examined considering the effects of viscosity, finite Larmor radius (FLR) corrections and rotation. The analysis is done by normal mode analysis theory with the help of relevant linearized perturbation equations of the problem. The general dispersion relation is obtained using the quantum magneto hydrodynamic model. The modified condition of Jeans instability is obtained and the numerical calculations have been performed to show the effects of various parameters on the growth rate of Jeans instability.

Linear and nonlinear properties of the ULF waves driven by ring-beam distribution functions

NASA Technical Reports Server (NTRS)

Killen, K.; Omidi, N.; Krauss-Varban, D.; Karimabadi, H.

1995-01-01

The problem of the exitation of obliquely propagating magnetosonic waves which can steepen up (also known as shocklets) is considered. Shocklets have been observed upstream of the Earth's bow shock and at comets Giacobini-Zinner and Grigg-Skjellerup. Linear theory as well as two-dimensional (2-D) hybrid (fluid electrons, particle ions) simulations are used to determine the properties of waves generated by ring-beam velocity distributions in great detail. The effects of both proton and oxygen ring-beams are considered. The study of instabilities excited by a proton ring-beam is relevant to the region upstream of the Earth's bow shock, whereas the oxygen ring-beam corresponds to cometary ions picked up by the solar wind. Linear theory has shown that for a ring-beam, four instabilities are found, one on the nonresonant mode, one on the Alfven mode, and two along the magnetosonic/whistler branch. The relative growth rate of these instabilities is a sensitive function of parameters. Although one of the magnetosonic instabilities has maximum growth along the magnetic field, the other has maximum growth in oblique directions. We have studied the competition of these instabilities in the nonlinear regime using 2-D simulations. As in the linear limit, the nonlinear results are a function of beam density and distribution function. By performing the simulations as both initial value and driven systems, we have found that the outcome of the simulations can vary, suggesting that the latter type simulations is needed to address the observations. A general conclusion of the simulation results is that field-aligned beams do not result in the formation of shocklets, whereas ring-beam distributions can.

Non-linear Frequency Shifts, Mode Couplings, and Decay Instability of Plasma Waves

NASA Astrophysics Data System (ADS)

Affolter, Mathew; Anderegg, F.; Driscoll, C. F.; Valentini, F.

2015-11-01

We present experiments and theory for non-linear plasma wave decay to longer wavelengths, in both the oscillatory coupling and exponential decay regimes. The experiments are conducted on non-neutral plasmas in cylindrical Penning-Malmberg traps, θ-symmetric standing plasma waves have near acoustic dispersion ω (kz) ~kz - αkz2 , discretized by kz =mz (π /Lp) . Large amplitude waves exhibit non-linear frequency shifts δf / f ~A2 and Fourier harmonic content, both of which are increased as the plasma dispersion is reduced. Non-linear coupling rates are measured between large amplitude mz = 2 waves and small amplitude mz = 1 waves, which have a small detuning Δω = 2ω1 -ω2 . At small excitation amplitudes, this detuning causes the mz = 1 mode amplitude to ``bounce'' at rate Δω , with amplitude excursions ΔA1 ~ δn2 /n0 consistent with cold fluid theory and Vlasov simulations. At larger excitation amplitudes, where the non-linear coupling exceeds the dispersion, phase-locked exponential growth of the mz = 1 mode is observed, in qualitative agreement with simple 3-wave instability theory. However, significant variations are observed experimentally, and N-wave theory gives stunningly divergent predictions that depend sensitively on the dispersion-moderated harmonic content. Measurements on higher temperature Langmuir waves and the unusual ``EAW'' (KEEN) waves are being conducted to investigate the effects of wave-particle kinetics on the non-linear coupling rates. Department of Energy Grants DE-SC0002451and DE-SC0008693.

The second-order theory of electromagnetic hot ion beam instabilities. [in interplanetary magnetic field

NASA Technical Reports Server (NTRS)

Gary, S. P.; Tokar, R. L.

1985-01-01

The present investigation is concerned with the application of a second-order theory for electromagnetic instabilities in a collisionless plasma to two modes which resonate with hot ion beams. The application of the theory is strictly limited to the linear growth phase. However, the application of the theory may be extended to obtain a description of the beam at postsaturation if the wave-beam resonance is sufficiently broad in velocity space. Under the considered limitations, it is shown that, as in the cold beam case, the fluctuating fields do not gain appreciable momentum and that the primary exchange of momentum is between the beam and main component.

Global Surrogates for the Upshift of the Critical Threshold in the Gradient for ITG Driven Turbulence

NASA Astrophysics Data System (ADS)

Michoski, Craig; Janhunen, Salomon; Faghihi, Danial; Carey, Varis; Moser, Robert

2017-10-01

The suppression of micro-turbulence and ultimately the inhibition of large-scale instabilities observed in tokamak plasmas is partially characterized by the onset of a global stationary state. This stationary attractor corresponds experimentally to a state of ``marginal stability'' in the plasma. The critical threshold that characterizes the onset in the nonlinear regime is observed both experimentally and numerically to exhibit an upshift relative to the linear theory. That is, the onset in the stationary state is up-shifted from those predicted by the linear theory as a function of the ion temperature gradient R0 /LT . Because the transition to this state with enhanced transport and therefore reduced confinement times is inaccessible to the linear theory, strategies for developing nonlinear reduced physics models to predict the upshift have been ongoing. As a complement to these effort, the principle aim of this work is to establish low-fidelity surrogate models that can be used to predict instability driven loss of confinement using training data from high-fidelity models. DE-SC0008454 and DE-AC02-09CH11466.

Assessing the role of the Kelvin-Helmholtz instability at the QCD cosmological transition

NASA Astrophysics Data System (ADS)

Mourão Roque, V. R. C.; Lugones, G.

2018-03-01

We performed numerical simulations with the PLUTO code in order to analyze the non-linear behavior of the Kelvin-Helmholtz instability in non-magnetized relativistic fluids. The relevance of the instability at the cosmological QCD phase transition was explored using an equation of state based on lattice QCD results with the addition of leptons. The results of the simulations were compared with the theoretical predictions of the linearized theory. For small Mach numbers up to Ms ~ 0.1 we find that both results are in good agreement. However, for higher Mach numbers, non-linear effects are significant. In particular, many initial conditions that look stable according to the linear analysis are shown to be unstable according to the full calculation. Since according to lattice calculations the cosmological QCD transition is a smooth crossover, violent fluid motions are not expected. Thus, in order to assess the role of the Kelvin-Helmholtz instability at the QCD epoch, we focus on simulations with low shear velocity and use monochromatic as well as random perturbations to trigger the instability. We find that the Kelvin-Helmholtz instability can strongly amplify turbulence in the primordial plasma and as a consequence it may increase the amount of primordial gravitational radiation. Such turbulence may be relevant for the evolution of the Universe at later stages and may have an impact in the stochastic gravitational wave background.

Elastic Instability of Slender Rods in Steady Shear Flow Yields Positive First Normal Stress Differences

NASA Astrophysics Data System (ADS)

Becker, Leif E.; Shelley, Michael J.

2000-11-01

First normal stress differences in shear flow are a fundamental property of Non-Newtonian fluids. Experiments involving dilute suspensions of slender fibers exhibit a sharp transition to non-zero normal stress differences beyond a critical shear rate, but existing continuum theories for rigid rods predict neither this transition nor the corresponding magnitude of this effect. We present the first conclusive evidence that elastic instabilities are predominantly responsible for observed deviations from the dilute suspension theory of rigid rods. Our analysis is based on slender body theory and the equilibrium equations of elastica. A straight slender body executing its Jeffery orbit in Couette flow is subject to axial fluid forcing, alternating between compression and tension. We present a stability analysis showing that elastic instabilities are possible for strong flows. Simulations give the fully non-linear evolution of this shape instability, and show that flexibility of the fibers alone is sufficient to cause both shear-thinning and significant first normal stress differences.

The initial instability and finite-amplitude stability of alternate bars in straight channels

USGS Publications Warehouse

Nelson, J.M.

1990-01-01

The initial instability and fully developed stability of alternate bars in straight channels are investigated using linearized and nonlinear analyses. The fundamental instability leading to these features is identified through a linear stability analysis of the equations governing the flow and sediment transport fields. This instability is explained in terms of topographically induced steering of the flow and the associated pattern of erosion and deposition on the bed. While the linear theory is useful for examining the instability mechanism, this approach is shown to yield relatively little information about well-developed alternate bars and, specifically, the linear analysis is shown to yield poor predictions of the fully developed bar wavelength. A fully nonlinear approach is presented that permits computation of the evolution of these bed features from an initial perturbation to their fully developed morphology. This analysis indicates that there is typically substantial elongation of the bar wavelength during the evolution process, a result that is consistent with observations of bar development in flumes and natural channels. The nonlinear approach demonstrates that the eventual stability of these features is a result of the interplay between topographic steering effects, secondary flow production as a result of streamline curvature, and gravitationally induced modifications of sediment fluxes over a sloping bed. ?? 1990.

Kinetic-MHD simulations of gyroresonance instability driven by CR pressure anisotropy

NASA Astrophysics Data System (ADS)

Lebiga, O.; Santos-Lima, R.; Yan, H.

2018-05-01

The transport of cosmic rays (CRs) is crucial for the understanding of almost all high-energy phenomena. Both pre-existing large-scale magnetohydrodynamic (MHD) turbulence and locally generated turbulence through plasma instabilities are important for the CR propagation in astrophysical media. The potential role of the resonant instability triggered by CR pressure anisotropy to regulate the parallel spatial diffusion of low-energy CRs (≲100 GeV) in the interstellar and intracluster medium of galaxies has been shown in previous theoretical works. This work aims to study the gyroresonance instability via direct numerical simulations, in order to access quantitatively the wave-particle scattering rates. For this, we employ a 1D PIC-MHD code to follow the growth and saturation of the gyroresonance instability. We extract from the simulations the pitch-angle diffusion coefficient Dμμ produced by the instability during the linear and saturation phases, and a very good agreement (within a factor of 3) is found with the values predicted by the quasi-linear theory (QLT). Our results support the applicability of the QLT for modelling the scattering of low-energy CRs by the gyroresonance instability in the complex interplay between this instability and the large-scale MHD turbulence.

Quasi-linear regime of gravitational instability: Implication to density-velocity relation

NASA Technical Reports Server (NTRS)

Shandarin, Sergei F.

1993-01-01

The well known linear relation between density and peculiar velocity distributions is a powerful tool for studying the large-scale structure in the Universe. Potentially it can test the gravitational instability theory and measure Omega. At present it is used in both ways: the velocity is reconstructed, provided the density is given, and vice versa. Reconstructing the density from the velocity field usually makes use of the Zel'dovich approximation. However, the standard linear approximation in Eulerian space is used when the velocity is reconstructed from the density distribution. I show that the linearized Zel'dovich approximation, in other words the linear approximation in the Lagrangian space, is more accurate for reconstructing velocity. In principle, a simple iteration technique can recover both the density and velocity distributions in Lagrangian space, but its practical application may need an additional study.

On the instability of a three-dimensional attachment-line boundary layer - Weakly nonlinear theory and a numerical approach

NASA Technical Reports Server (NTRS)

Hall, P.; Malik, M. R.

1986-01-01

The instability of a three-dimensional attachment-line boundary layer is considered in the nonlinear regime. Using weakly nonlinear theory, it is found that, apart from a small interval near the (linear) critical Reynolds number, finite-amplitude solutions bifurcate subcritically from the upper branch of the neutral curve. The time-dependent Navier-Stokes equations for the attachment-line flow have been solved using a Fourier-Chebyshev spectral method and the subcritical instability is found at wavenumbers that correspond to the upper branch. Both the theory and the numerical calculations show the existence of supercritical finite-amplitude (equilibrium) states near the lower branch which explains why the observed flow exhibits a preference for the lower branch modes. The effect of blowing and suction on nonlinear stability of the attachment-line boundary layer is also investigated.

On the instability of a 3-dimensional attachment line boundary layer: Weakly nonlinear theory and a numerical approach

NASA Technical Reports Server (NTRS)

Hall, P.; Malik, M. R.

1984-01-01

The instability of a three dimensional attachment line boundary layer is considered in the nonlinear regime. Using weakly nonlinear theory, it is found that, apart from a small interval near the (linear) critical Reynolds number, finite amplitude solutions bifurcate subcritically from the upper branch of the neutral curve. The time dependent Navier-Stokes equations for the attachment line flow have been solved using a Fourier-Chebyshev spectral method and the subcritical instability is found at wavenumbers that correspond to the upper branch. Both the theory and the numerical calculations show the existence of supercritical finite amplitude (equilibrium) states near the lower branch which explains why the observed flow exhibits a preference for the lower branch modes. The effect of blowing and suction on nonlinear stability of the attachment line boundary layer is also investigated.

Two-dimensional Nonlinear Simulations of Temperature-anisotropy Instabilities with a Proton-alpha Drift

NASA Astrophysics Data System (ADS)

Markovskii, S. A.; Chandran, Benjamin D. G.; Vasquez, Bernard J.

2018-04-01

We present two-dimensional hybrid simulations of proton-cyclotron and mirror instabilities in a proton-alpha plasma with particle-in-cell ions and a neutralizing electron fluid. The instabilities are driven by the protons with temperature perpendicular to the background magnetic field larger than the parallel temperature. The alpha particles with initially isotropic temperature have a nonzero drift speed with respect to the protons. The minor ions are known to influence the relative effect of the proton-cyclotron and mirror instabilities. In this paper, we show that the mirror mode can dominate the power spectrum at the nonlinear stage even if its linear growth rate is significantly lower than that of the proton-cyclotron mode. The proton-cyclotron instability combined with the alpha-proton drift is a possible cause of the nonzero magnetic helicity observed in the solar wind for fluctuations propagating nearly parallel to the magnetic field. Our simulations generally confirm this concept but reveal a complex helicity spectrum that is not anticipated from the linear theory of the instability.

Direct Numerical Simulation of Transition Due to Traveling Crossflow Vortices

NASA Technical Reports Server (NTRS)

Li, Fei; Choudhari, Meelan M.; Duan, Lian

2016-01-01

Previous simulations of laminar breakdown mechanisms associated with stationary crossflow instability over a realistic swept-wing configuration are extended to investigate the alternate scenario of transition due to secondary instability of traveling crossflow modes. Earlier analyses based on secondary instability theory and parabolized stability equations have shown that this alternate scenario is viable when the initial amplitude of the most amplified mode of the traveling crossflow instability is greater than approximately 0.03 times the initial amplitude of the most amplified stationary mode. The linear growth predictions based on the secondary instability theory and parabolized stability equations agree well with the direct numerical simulation. Nonlinear effects are initially stabilizing but subsequently lead to a rapid growth followed by the onset of transition when the amplitude of the secondary disturbance exceeds a threshold value. Similar to the breakdown of stationary vortices, the transition zone is rather short and the boundary layer becomes completely turbulent across a distance of less than 15 times the boundary layer thickness at the completion of transition.

Collisionless kinetic theory of oblique tearing instabilities

DOE PAGES

Baalrud, S. D.; Bhattacharjee, A.; Daughton, W.

2018-02-15

The linear dispersion relation for collisionless kinetic tearing instabilities is calculated for the Harris equilibrium. In contrast to the conventional 2D geometry, which considers only modes at the center of the current sheet, modes can span the current sheet in 3D. Modes at each resonant surface have a unique angle with respect to the guide field direction. Both kinetic simulations and numerical eigenmode solutions of the linearized Vlasov-Maxwell equations have recently revealed that standard analytic theories vastly overestimate the growth rate of oblique modes. In this paper, we find that this stabilization is associated with the density-gradient-driven diamagnetic drift. Themore » analytic theories miss this drift stabilization because the inner tearing layer broadens at oblique angles sufficiently far that the assumption of scale separation between the inner and outer regions of boundary-layer theory breaks down. The dispersion relation obtained by numerically solving a single second order differential equation is found to approximately capture the drift stabilization predicted by solutions of the full integro-differential eigenvalue problem. Finally, a simple analytic estimate for the stability criterion is provided.« less

Collisionless kinetic theory of oblique tearing instabilities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Baalrud, S. D.; Bhattacharjee, A.; Daughton, W.

The linear dispersion relation for collisionless kinetic tearing instabilities is calculated for the Harris equilibrium. In contrast to the conventional 2D geometry, which considers only modes at the center of the current sheet, modes can span the current sheet in 3D. Modes at each resonant surface have a unique angle with respect to the guide field direction. Both kinetic simulations and numerical eigenmode solutions of the linearized Vlasov-Maxwell equations have recently revealed that standard analytic theories vastly overestimate the growth rate of oblique modes. In this paper, we find that this stabilization is associated with the density-gradient-driven diamagnetic drift. Themore » analytic theories miss this drift stabilization because the inner tearing layer broadens at oblique angles sufficiently far that the assumption of scale separation between the inner and outer regions of boundary-layer theory breaks down. The dispersion relation obtained by numerically solving a single second order differential equation is found to approximately capture the drift stabilization predicted by solutions of the full integro-differential eigenvalue problem. Finally, a simple analytic estimate for the stability criterion is provided.« less

Collisionless kinetic theory of oblique tearing instabilities

NASA Astrophysics Data System (ADS)

Baalrud, S. D.; Bhattacharjee, A.; Daughton, W.

2018-02-01

The linear dispersion relation for collisionless kinetic tearing instabilities is calculated for the Harris equilibrium. In contrast to the conventional 2D geometry, which considers only modes at the center of the current sheet, modes can span the current sheet in 3D. Modes at each resonant surface have a unique angle with respect to the guide field direction. Both kinetic simulations and numerical eigenmode solutions of the linearized Vlasov-Maxwell equations have recently revealed that standard analytic theories vastly overestimate the growth rate of oblique modes. We find that this stabilization is associated with the density-gradient-driven diamagnetic drift. The analytic theories miss this drift stabilization because the inner tearing layer broadens at oblique angles sufficiently far that the assumption of scale separation between the inner and outer regions of boundary-layer theory breaks down. The dispersion relation obtained by numerically solving a single second order differential equation is found to approximately capture the drift stabilization predicted by solutions of the full integro-differential eigenvalue problem. A simple analytic estimate for the stability criterion is provided.

Comparison of intense electrostatic waves near f/sub UHR/ with linear instability theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kurth, W.S.; Frank, L.A.; Gurnett, D.A.

1979-06-01

Intense electrostatic waves beyond the plasmapause have recently been identified at frequencies near the upper hybrid resonance frequency. In addition, the waves occur within a band at an odd, half-harmonic of the local electron gyrofrequency. These bands of electrostatic turbulence are among the most intense waves detected within the earth's magnetosphere. Measurements obtained with the ISEE 1 plasma wave receiver show that the intense waves appear to be intensifications of an electrostatic cyclotron harmonic band near the upper hybrid resonance frequency. A straightforward explanation of intense waves at the upper hybrid resonance frequency exists in the electrostatic multi-cyclotron emission theory.more » For a broad range of plasma parameters nonconvective instability or large spatial growth rates occur within the cyclotron band encompassing the cold upper hybrid frequency. Comparison of spatial growth rate spectra with measured wave spectra shows that there is excellent qualitative agreement between the linear theory and the observed wave characteristics.« less

Application of non-linear dynamics to the characterization of cardiac electrical instability

NASA Technical Reports Server (NTRS)

Kaplan, D. T.; Cohen, R. J.

1987-01-01

Beat-to-beat alternation in the morphology of the ECG has been previously observed in hearts susceptible to fibrillation. In addition, fibrillation has been characterized by some as a chaotic state. Period doubling phenomena, such as alternation, and the onset of chaos have been connected by non-linear dynamical systems theory. In this paper, we describe the use of a technique from nonlinear dynamics theory, the construction of a first return nap, to assess the susceptibility to fibrillation threshhold in canine experiments.

Linear Rayleigh-Taylor instability in an accelerated Newtonian fluid with finite width

NASA Astrophysics Data System (ADS)

Piriz, S. A.; Piriz, A. R.; Tahir, N. A.

2018-04-01

The linear theory of Rayleigh-Taylor instability is developed for the case of a viscous fluid layer accelerated by a semi-infinite viscous fluid, considering that the top interface is a free surface. Effects of the surface tensions at both interfaces are taken into account. When viscous effects dominate on surface tensions, an interplay of two mechanisms determines opposite behaviors of the instability growth rate with the thickness of the heavy layer for an Atwood number AT=1 and for sufficiently small values of AT. In the former case, viscosity is a less effective stabilizing mechanism for the thinnest layers. However, the finite thickness of the heavy layer enhances its viscous effects that, in general, prevail on the viscous effects of the semi-infinite medium.

Mirror Instability: Quasi-linear Effects

NASA Astrophysics Data System (ADS)

Hellinger, P.; Travnicek, P. M.; Passot, T.; Sulem, P.; Kuznetsov, E. A.

2008-12-01

Nonlinear properties of the mirror instability are investigated by direct integration of the quasi-linear diffusion equation [Shapiro and Shevchenko, 1964] near threshold. The simulation results are compared to the results of standard hybrid simulations [Califano et al., 2008] and discussed in the context of the nonlinear dynamical model by Kuznetsov et al. [2007]. References: Califano, F., P. Hellinger, E. Kuznetsov, T. Passot, P. L. Sulem, and P. M. Travnicek (2008), Nonlinear mirror mode dynamics: Simulations and modeling, J. Geophys. Res., 113, A08219, doi:10.1029/2007JA012898. Kuznetsov, E., T. Passot and P. L. Sulem (2007), Dynamical model for nonlinear mirror modes near threshold, Phys. Rev. Lett., 98, 235003 . Shapiro, V. D., and V. I. Shevchenko (1964), Quasilinear theory of instability of a plasma with an anisotropic ion velocity distribution, Sov. JETP, 18, 1109.

Nonlinear study of the parallel velocity/tearing instability using an implicit, nonlinear resistive MHD solver

NASA Astrophysics Data System (ADS)

Chacon, L.; Finn, J. M.; Knoll, D. A.

2000-10-01

Recently, a new parallel velocity instability has been found.(J. M. Finn, Phys. Plasmas), 2, 12 (1995) This mode is a tearing mode driven unstable by curvature effects and sound wave coupling in the presence of parallel velocity shear. Under such conditions, linear theory predicts that tearing instabilities will grow even in situations in which the classical tearing mode is stable. This could then be a viable seed mechanism for the neoclassical tearing mode, and hence a non-linear study is of interest. Here, the linear and non-linear stages of this instability are explored using a fully implicit, fully nonlinear 2D reduced resistive MHD code,(L. Chacon et al), ``Implicit, Jacobian-free Newton-Krylov 2D reduced resistive MHD nonlinear solver,'' submitted to J. Comput. Phys. (2000) including viscosity and particle transport effects. The nonlinear implicit time integration is performed using the Newton-Raphson iterative algorithm. Krylov iterative techniques are employed for the required algebraic matrix inversions, implemented Jacobian-free (i.e., without ever forming and storing the Jacobian matrix), and preconditioned with a ``physics-based'' preconditioner. Nonlinear results indicate that, for large total plasma beta and large parallel velocity shear, the instability results in the generation of large poloidal shear flows and large magnetic islands even in regimes when the classical tearing mode is absolutely stable. For small viscosity, the time asymptotic state can be turbulent.

Solar Wind Proton Temperature Anisotropy: Linear Theory and WIND/SWE Observations

NASA Technical Reports Server (NTRS)

Hellinger, P.; Travnicek, P.; Kasper, J. C.; Lazarus, A. J.

2006-01-01

We present a comparison between WIND/SWE observations (Kasper et al., 2006) of beta parallel to p and T perpendicular to p/T parallel to p (where beta parallel to p is the proton parallel beta and T perpendicular to p and T parallel to p are the perpendicular and parallel proton are the perpendicular and parallel proton temperatures, respectively; here parallel and perpendicular indicate directions with respect to the ambient magnetic field) and predictions of the Vlasov linear theory. In the slow solar wind, the observed proton temperature anisotropy seems to be constrained by oblique instabilities, by the mirror one and the oblique fire hose, contrary to the results of the linear theory which predicts a dominance of the proton cyclotron instability and the parallel fire hose. The fast solar wind core protons exhibit an anticorrelation between beta parallel to c and T perpendicular to c/T parallel to c (where beta parallel to c is the core proton parallel beta and T perpendicular to c and T parallel to c are the perpendicular and parallel core proton temperatures, respectively) similar to that observed in the HELIOS data (Marsch et al., 2004).

Simulation studies of plasma waves in the electron foreshock - The transition from reactive to kinetic instability

NASA Technical Reports Server (NTRS)

Dum, C. T.

1990-01-01

Particle simulation experiments were used to analyze the electron beam-plasma instability. It is shown that there is a transition from the reactive state of the electron beam-plasma instability to the kinetic instability of Langmuir waves. Quantitative tests, which include an evaluation of the dispersion relation for the evolving non-Maxwellian beam distribution, show that a quasi-linear theory describes the onset of this transition and applies again fully to the kinetic stage. This stage is practically identical to the late stage seen in simulations of plasma waves in the electron foreshock described by Dum (1990).

Saturation of the magnetorotational instability at large Elsasser number

NASA Astrophysics Data System (ADS)

Jamroz, B.; Julien, K.; Knobloch, E.

2008-09-01

The magnetorotational instability is investigated within the shearing box approximation in the large Elsasser number regime. In this regime, which is of fundamental importance to astrophysical accretion disk theory, shear is the dominant source of energy, but the instability itself requires the presence of a weaker vertical magnetic field. Dissipative effects are weaker still but not negligible. The regime explored retains the condition that (viscous and ohmic) dissipative forces do not play a role in the leading order linear instability mechanism. However, they are sufficiently large to permit a nonlinear feedback mechanism whereby the turbulent stresses generated by the MRI act on and modify the local background shear in the angular velocity profile. To date this response has been omitted in shearing box simulations and is captured by a reduced pde model derived here from the global MHD fluid equations using multiscale asymptotic perturbation theory. Results from numerical simulations of the reduced pde model indicate a linear phase of exponential growth followed by a nonlinear adjustment to algebraic growth and decay in the fluctuating quantities. Remarkably, the velocity and magnetic field correlations associated with these algebraic growth and decay laws conspire to achieve saturation of the angular momentum transport. The inclusion of subdominant ohmic dissipation arrests the algebraic growth of the fluctuations on a longer, dissipative time scale.

Saturation of the Magnetorotational Instability at Large Elssaser Number

NASA Astrophysics Data System (ADS)

Julien, Keith; Jamroz, Benjamin; Knobloch, Edgar

2009-11-01

The MRI is believed to play an important role in accretion disk physics in extracting angular momentum from the disk and allowing accretion to take place. The instability is investigated within the shearing box approximation under conditions of fundamental importance to astrophysical accretion disk theory. The shear is taken to be the dominant source of energy, but the instability itself requires the presence of a weaker vertical magnetic field. Dissipative effects are suffiently weak that the Elsasser number is large. Thus dissipative forces do not play a role in the leading order linear instability mechanism. However, they are sufficiently large to permit a nonlinear feedback mechanism whereby the turbulent stresses generated by the MRI act on and modify the local background shear in the angular velocity profile. To date this response has been omitted in shearing box simulations and is captured by a reduced pde model derived from the global MHD fluid equations using multiscale asymptotic perturbation theory. Results from simulations of the model indicate a linear phase of exponential growth followed by a nonlinear adjustment to algebraic growth and decay in the fluctuating quantities. Remarkably, the velocity and magnetic field correlations associated with these growth and decay laws conspire to achieve saturation of angular momentum transport.

A new method for the prediction of combustion instability

NASA Astrophysics Data System (ADS)

Flanagan, Steven Meville

This dissertation presents a new approach to the prediction of combustion instability in solid rocket motors. Previous attempts at developing computational tools to solve this problem have been largely unsuccessful, showing very poor agreement with experimental results and having little or no predictive capability. This is due primarily to deficiencies in the linear stability theory upon which these efforts have been based. Recent advances in linear instability theory by Flandro have demonstrated the importance of including unsteady rotational effects, previously considered negligible. Previous versions of the theory also neglected corrections to the unsteady flow field of the first order in the mean flow Mach number. This research explores the stability implications of extending the solution to include these corrections. Also, the corrected linear stability theory based upon a rotational unsteady flow field extended to first order in mean flow Mach number has been implemented in two computer programs developed for the Macintosh platform. A quasi one-dimensional version of the program has been developed which is based upon an approximate solution to the cavity acoustics problem. The three-dimensional program applies Greens's Function Discretization (GFD) to the solution for the acoustic mode shapes and frequency. GFD is a recently developed numerical method for finding fully three dimensional solutions for this class of problems. The analysis of complex motor geometries, previously a tedious and time consuming task, has also been greatly simplified through the development of a drawing package designed specifically to facilitate the specification of typical motor geometries. The combination of the drawing package, improved acoustic solutions, and new analysis, results in a tool which is capable of producing more accurate and meaningful predictions than have been possible in the past.

Particle trapping: A key requisite of structure formation and stability of Vlasov–Poisson plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schamel, Hans, E-mail: hans.schamel@uni-bayreuth.de

2015-04-15

Particle trapping is shown to control the existence of undamped coherent structures in Vlasov–Poisson plasmas and thereby affects the onset of plasma instability beyond the realm of linear Landau theory.

Electron-acoustic Instability Simulated By Modified Zakharov Equations

NASA Astrophysics Data System (ADS)

Jásenský, V.; Fiala, V.; Vána, O.; Trávnícek, P.; Hellinger, P.

We present non-linear equations describing processes in plasma when electron - acoustic waves are excited. These waves are present for instance in the vicinity of Earth's bow shock and in the polar ionosphere. Frequently they are excited by an elec- tron beam in a plasma with two electron populations, a cold and hot one. We derive modified Zakharov equations from kinetic theory for such a case together with numer- ical method for solving of this type of equations. Bispectral analysis is used to show which non-linear wave processes are of importance in course of the instability. Finally, we compare these results with similar simulations using Vlasov approach.

Highly compact neutron stars in scalar-tensor theories of gravity: Spontaneous scalarization versus gravitational collapse

NASA Astrophysics Data System (ADS)

Mendes, Raissa F. P.; Ortiz, Néstor

2016-06-01

Scalar-tensor theories of gravity are extensions of general relativity (GR) including an extra, nonminimally coupled scalar degree of freedom. A wide class of these theories, albeit indistinguishable from GR in the weak field regime, predicts a radically different phenomenology for neutron stars, due to a nonperturbative, strong-field effect referred to as spontaneous scalarization. This effect is known to occur in theories where the effective linear coupling β0 between the scalar and matter fields is sufficiently negative, i.e. β0≲-4.35 , and has been strongly constrained by pulsar timing observations. In the test-field approximation, spontaneous scalarization manifests itself as a tachyonic-like instability. Recently, it was argued that, in theories where β0>0 , a similar instability would be triggered by sufficiently compact neutron stars obeying realistic equations of state. In this work we investigate the end state of this instability for some representative coupling functions with β0>0 . This is done both through an energy balance analysis of the existing equilibrium configurations, and by numerically determining the nonlinear Cauchy development of unstable initial data. We find that, contrary to the β0<0 case, the final state of the instability is highly sensitive to the details of the coupling function, varying from gravitational collapse to spontaneous scalarization. In particular, we show, for the first time, that spontaneous scalarization can happen in theories with β0>0 , which could give rise to novel astrophysical tests of the theory of gravity.

Instability in dynamic fracture

NASA Astrophysics Data System (ADS)

Fineberg, J.; Marder, M.

1999-05-01

The fracture of brittle amorphous materials is an especially challenging problem, because the way a large object shatters is intimately tied to details of cohesion at microscopic scales. This subject has been plagued by conceptual puzzles, and to make matters worse, experiments seemed to contradict the most firmly established theories. In this review, we will show that the theory and experiments fit within a coherent picture where dynamic instabilities of a crack tip play a crucial role. To accomplish this task, we first summarize the central results of linear elastic dynamic fracture mechanics, an elegant and powerful description of crack motion from the continuum perspective. We point out that this theory is unable to make predictions without additional input, information that must come either from experiment, or from other types of theories. We then proceed to discuss some of the most important experimental observations, and the methods that were used to obtain the them. Once the flux of energy to a crack tip passes a critical value, the crack becomes unstable, and it propagates in increasingly complicated ways. As a result, the crack cannot travel as quickly as theory had supposed, fracture surfaces become rough, it begins to branch and radiate sound, and the energy cost for crack motion increases considerably. All these phenomena are perfectly consistent with the continuum theory, but are not described by it. Therefore, we close the review with an account of theoretical and numerical work that attempts to explain the instabilities. Currently, the experimental understanding of crack tip instabilities in brittle amorphous materials is fairly detailed. We also have a detailed theoretical understanding of crack tip instabilities in crystals, reproducing qualitatively many features of the experiments, while numerical work is beginning to make the missing connections between experiment and theory.

Electromagnetic Electron Cyclotron Instability in the Solar Wind

NASA Astrophysics Data System (ADS)

Lazar, M.; Yoon, P. H.; López, R. A.; Moya, P. S.

2018-01-01

The abundant reports on the existence of electromagnetic high-frequency fluctuations in space plasmas have increased the expectations that theoretical modeling may help understand their origins and implications (e.g., kinetic instabilities and dissipation). This paper presents an extended quasi-linear approach of the electromagnetic electron cyclotron instability in conditions typical for the solar wind, where the anisotropic electrons (T⊥>T∥) exhibit a dual distribution combining a bi-Maxwellian core and bi-Kappa halo. Involving both the core and halo populations, the instability is triggered by the cumulative effects of these components, mainly depending of their anisotropies. The instability is not very sensitive to the shape of halo distribution function conditioned in this case by the power index κ. This result seems to be a direct consequence of the low density of electron halo, which is assumed more dilute than the core component in conformity with the observations in the ecliptic. Quasi-linear time evolutions predicted by the theory are confirmed by the particle-in-cell simulations, which also suggest possible explanations for the inherent differences determined by theoretical constraints. These results provide premises for an advanced methodology to characterize, realistically, the electromagnetic electron cyclotron instability and its implication in the solar wind.

Analysis of Instabilities in Non-Axisymmetric Hypersonic Boundary Layers Over Cones

NASA Technical Reports Server (NTRS)

Li, Fei; Choudhari, Meelan M.; Chang, Chau-Lyan; White, Jeffery A.

2010-01-01

Hypersonic flows over circular cones constitute one of the most important generic configurations for fundamental aerodynamic and aerothermodynamic studies. In this paper, numerical computations are carried out for Mach 6 flows over a 7-degree half-angle cone with two different flow incidence angles and a compression cone with a large concave curvature. Instability wave and transition-related flow physics are investigated using a series of advanced stability methods ranging from conventional linear stability theory (LST) and a higher-fidelity linear and nonlinear parabolized stability equations (PSE), to the 2D eigenvalue analysis based on partial differential equations. Computed N factor distribution pertinent to various instability mechanisms over the cone surface provides initial assessments of possible transition fronts and a guide to corresponding disturbance characteristics such as frequency and azimuthal wave numbers. It is also shown that strong secondary instability that eventually leads to transition to turbulence can be simulated very efficiently using a combination of advanced stability methods described above.

Explore Stochastic Instabilities of Periodic Points by Transition Path Theory

NASA Astrophysics Data System (ADS)

Cao, Yu; Lin, Ling; Zhou, Xiang

2016-06-01

We consider the noise-induced transitions from a linearly stable periodic orbit consisting of T periodic points in randomly perturbed discrete logistic map. Traditional large deviation theory and asymptotic analysis at small noise limit cannot distinguish the quantitative difference in noise-induced stochastic instabilities among the T periodic points. To attack this problem, we generalize the transition path theory to the discrete-time continuous-space stochastic process. In our first criterion to quantify the relative instability among T periodic points, we use the distribution of the last passage location related to the transitions from the whole periodic orbit to a prescribed disjoint set. This distribution is related to individual contributions to the transition rate from each periodic points. The second criterion is based on the competency of the transition paths associated with each periodic point. Both criteria utilize the reactive probability current in the transition path theory. Our numerical results for the logistic map reveal the transition mechanism of escaping from the stable periodic orbit and identify which periodic point is more prone to lose stability so as to make successful transitions under random perturbations.

Nonaxisymmetric Dynamic Instabilities of Rotating Polytropes. II. Torques, Bars, and Mode Saturation with Applications to Protostars and Fizzlers

NASA Astrophysics Data System (ADS)

Imamura, James N.; Durisen, Richard H.; Pickett, Brian K.

2000-01-01

Dynamic nonaxisymmetric instabilities in rapidly rotating stars and protostars have a range of potential applications in astrophysics, including implications for binary formation during protostellar cloud collapse and for the possibility of aborted collapse to neutron star densities at late stages of stellar evolution (``fizzlers''). We have recently presented detailed linear analyses for polytropes of the most dynamically unstable global modes, the barlike modes. These produce bar distortions in the regions near the rotation axis but have trailing spiral arms toward the equator. In this paper, we use our linear eigenfunctions to predict the early nonlinear behavior of the dynamic instability and compare these ``quasi-linear'' predictions with several fully nonlinear hydrodynamics simulations. The comparisons demonstrate that the nonlinear saturation of the barlike instability is due to the self-interaction gravitational torques between the growing central bar and the spiral arms, where angular momentum is transferred outward from bar to arms. We also find a previously unsuspected resonance condition that accurately predicts the mass of the bar regions in our own simulations and in those published by other researchers. The quasi-linear theory makes other accurate predictions about consequences of instability, including properties of possible end-state bars and increases in central density, which can be large under some conditions. We discuss in some detail the application of our results to binary formation during protostellar collapse and to the formation of massive rotating black holes.

Transition from convective to absolute Raman instability via the longitudinal relativistic effect by using Vlasov-Maxwell simulations

NASA Astrophysics Data System (ADS)

Wang, Q.; Liu, Z. J.; Zheng, C. Y.; Xiao, C. Z.; Feng, Q. S.; Zhang, H. C.; He, X. T.

2018-01-01

The longitudinal relativistic effect on stimulated Raman backscattering (SRBS) is investigated by using one-dimensional (1D) Vlasov-Maxwell simulations. Using a short backscattered light seed pulse with a very small amplitude, the linear gain spectra of SRBS in the strongly convective regime is presented by combining the relativistic and non-relativistic 1D Vlasov-Maxwell simulations, which is in agreement with the steady-state linear theory. More interestingly, by considering transition from convective to absolute instability due to electron trapping, we successfully predict the critical duration of the seed which can just trigger the kinetic inflation of the excited SRBS after the seed leaves the simulation box. The critical duration in the relativistic case is much shorter than that in the nonrelativistic case, which indicates that the kinetic inflation more easily occurs in the relativistic case than in the nonrelativistic case. In the weakly convective regime, the transition from convective to absolute instability for SRBS can directly occur in the linear regime due to the longitudinal relativistic modification. For the same pump, our simulations first demonstrate that the SRBS excited by a short and small seed pulse is a convective instability in the nonrelativistic case but becomes an absolute instability due to the decrease of the linear Landau damping from the longitudinal relativistic modification in the relativistic case. In more detail, the growth rate of the backscattered light is also in excellent agreement with theoretical prediction.

Nonlinear stability of solar type 3 radio bursts. 1: Theory

NASA Technical Reports Server (NTRS)

Smith, R. A.; Goldstein, M. L.; Papadopoulos, K.

1978-01-01

A theory of the excitation of solar type 3 bursts is presented. Electrons initially unstable to the linear bump-in-tail instability are shown to rapidly amplify Langmuir waves to energy densities characteristic of strong turbulence. The three-dimensional equations which describe the strong coupling (wave-wave) interactions are derived. For parameters characteristic of the interplanetary medium the equations reduce to one dimension. In this case, the oscillating two stream instability (OTSI) is the dominant nonlinear instability, and is stablized through the production of nonlinear ion density fluctuations that efficiently scatter Langmuir waves out of resonance with the electron beam. An analytical model of the electron distribution function is also developed which is used to estimate the total energy losses suffered by the electron beam as it propagates from the solar corona to 1 A.U. and beyond.

Absolute instability of the Gaussian wake profile

NASA Technical Reports Server (NTRS)

Hultgren, Lennart S.; Aggarwal, Arun K.

1987-01-01

Linear parallel-flow stability theory has been used to investigate the effect of viscosity on the local absolute instability of a family of wake profiles with a Gaussian velocity distribution. The type of local instability, i.e., convective or absolute, is determined by the location of a branch-point singularity with zero group velocity of the complex dispersion relation for the instability waves. The effects of viscosity were found to be weak for values of the wake Reynolds number, based on the center-line velocity defect and the wake half-width, larger than about 400. Absolute instability occurs only for sufficiently large values of the center-line wake defect. The critical value of this parameter increases with decreasing wake Reynolds number, thereby indicating a shrinking region of absolute instability with decreasing wake Reynolds number. If backflow is not allowed, absolute instability does not occur for wake Reynolds numbers smaller than about 38.

Perturbations of linear delay differential equations at the verge of instability.

PubMed

Lingala, N; Namachchivaya, N Sri

2016-06-01

The characteristic equation for a linear delay differential equation (DDE) has countably infinite roots on the complex plane. This paper considers linear DDEs that are on the verge of instability, i.e., a pair of roots of the characteristic equation lies on the imaginary axis of the complex plane and all other roots have negative real parts. It is shown that when small noise perturbations are present, the probability distribution of the dynamics can be approximated by the probability distribution of a certain one-dimensional stochastic differential equation (SDE) without delay. This is advantageous because equations without delay are easier to simulate and one-dimensional SDEs are analytically tractable. When the perturbations are also linear, it is shown that the stability depends on a specific complex number. The theory is applied to study oscillators with delayed feedback. Some errors in other articles that use multiscale approach are pointed out.

Vertical Structure of Heat and Momentum Transport in the Urban Surface Layer

NASA Astrophysics Data System (ADS)

Hrisko, J.; Ramamurthy, P.

2017-12-01

Vertical transport of heat and momentum during convective periods is investigated in the urban surface layer using eddy covariance measurements at 5 levels. The Obukhov length is used to divide the dataset into distinct stability regimes: weakly unstable, unstable and very unstable. Our preliminary analysis indicates critical differences in the transport of heat and momentum as the instability increases. Particularly, during periods of increased instability the vertical heat flux deviates from surface layer similarity theory. Further analysis of primary quadrant sweeps and ejections also indicate deviations from the theory, alluding that ejections dominate during convective periods for heat transport, but equally contribute with sweeps for momentum transport. The transport efficiencies of momentum at all 5 levels uniformly decreases as the instability increases, in stark contrast the heat transport efficiencies increase non-linearly as the instability increases. Collectively, these results demonstrate the breakdown of similarity theory during convective periods, and reaffirm that revised and improved methods for characterizing heat and momentum transport in urban areas is needed. These implications could ultimately advance weather prediction and estimation of scalar transport for urban areas susceptible to weather hazards and large amounts of pollution.

Most-Critical Transient Disturbances in an Incompressible Flat-Plate Boundary Layer

NASA Astrophysics Data System (ADS)

Monschke, Jason; White, Edward

2015-11-01

Transient growth is a linear disturbance growth mechanism that plays a key role in roughness-induced boundary-layer transition. It occurs when superposed stable, non-orthogonal continuous spectrum modes experience algebraic disturbance growth followed by exponential decay. Algebraic disturbance growth can modify the basic state making it susceptible to secondary instabilities rapidly leading to transition. Optimal disturbance theory was developed to model the most-dangerous disturbances. However, evidence suggests roughness-induced transient growth is sub-optimal yet leads to transition earlier than optimal theory suggests. This research computes initial disturbances most unstable to secondary instabilities to further develop the applicability of transient growth theory to surface roughness. The main approach is using nonlinear adjoint optimization with solutions of the parabolized Navier-Stokes and BiGlobal stability equations. Two objective functions were considered: disturbance kinetic energy growth and sinuous instability growth rate. The first objective function was used as validation of the optimization method. Counter-rotating streamwise vortices located low in the boundary layer maximize the sinuous instability growth rate. The authors would like to acknowledge NASA and the AFOSR for funding this work through AFOSR Grant FA9550-09-1-0341.

Cross-field Current Instability for Substorm Expansions

NASA Technical Reports Server (NTRS)

Lui, Anthony

1997-01-01

The funding provided by the above-referenced NASA grant has enabled us: (1) to investigate the quasi-linear evolution of the IWI [Lui et al., 1993] and that of the generalized MTSI/IWI [Yoon and Lui, 1993], (2) to carry out the linear analysis of the LHDI to elucidate the difference between it and the MTSI/PM instability [Yoon et al., 1994], (3) to conduct some preliminary nonlocal analyses of the MTSI [Lui et al., 1995] and the IWI [Yoon and Lui, 1996] modes, (4) to study low-frequency shear-driven instability and its nonlinear evolution, which might compete with the CCI [Yoon et al., 1996], and (5) to study the evolution of current sheet during late substorm growth phase by means of 2-D Hall-MHD simulation in order to obtain a better understanding of the current sheet equilibrium crucial for CCI theory [Yoon and Lui, 1997].

Non-linear tides in a homogeneous rotating planet or star: global modes and elliptical instability

NASA Astrophysics Data System (ADS)

Barker, Adrian J.; Braviner, Harry J.; Ogilvie, Gordon I.

2016-06-01

We revisit the global modes and instabilities of homogeneous rotating ellipsoidal fluid masses, which are the simplest global models of rotationally and tidally deformed gaseous planets or stars. The tidal flow in a short-period planet may be unstable to the elliptical instability, a hydrodynamic instability that can drive tidal evolution. We perform a global (and local WKB) analysis to study this instability using the elegant formalism of Lebovitz & Lifschitz. We survey the parameter space of global instabilities with harmonic orders ℓ ≤ 5, for planets with spins that are purely aligned (prograde) or anti-aligned (retrograde) with their orbits. In general, the instability has a much larger growth rate if the planetary spin and orbit are anti-aligned rather than aligned. We have identified a violent instability for anti-aligned spins outside of the usual frequency range for the elliptical instability (when n/Ω ≲ -1, where n and Ω are the orbital and spin angular frequencies, respectively) if the tidal amplitude is sufficiently large. We also explore the instability in a rigid ellipsoidal container, which is found to be quantitatively similar to that with a realistic free surface. Finally, we study the effect of rotation and tidal deformation on mode frequencies. We find that larger rotation rates and larger tidal deformations both decrease the frequencies of the prograde sectoral surface gravity modes. This increases the prospect of their tidal excitation, potentially enhancing the tidal response over expectations from linear theory. In a companion paper, we use our results to interpret global simulations of the elliptical instability.

Long-Wavelength Rupturing Instability in Surface-Tension-Driven Benard Convection

NASA Technical Reports Server (NTRS)

Swift, J. B.; Hook, Stephen J. Van; Becerril, Ricardo; McCormick, W. D.; Swinney, H. L.; Schatz, Michael F.

1999-01-01

A liquid layer with a free upper surface and heated from below is subject to thermocapillary-induced convective instabilities. We use very thin liquid layers (0.01 cm) to significantly reduce buoyancy effects and simulate Marangoni convection in microgravity. We observe thermocapillary-driven convection in two qualitatively different modes, short-wavelength Benard hexagonal convection cells and a long-wavelength interfacial rupturing mode. We focus on the long-wavelength mode and present experimental observations and theoretical analyses of the long-wavelength instability. Depending on the depths and thermal conductivities of the liquid and the gas above it, the interface can rupture downwards and form a dry spot or rupture upwards and form a high spot. Linear stability theory gives good agreement to the experimental measurements of onset as long as sidewall effects are taken into account. Nonlinear theory correctly predicts the subcritical nature of the bifurcation and the selection between the dry spot and high spots.

Stabilization of Hypersonic Boundary Layers by Linear and Nonlinear Optimal Perturbations

NASA Technical Reports Server (NTRS)

Paredes, Pedro; Choudhari, Meelan M.; Li, Fei

2017-01-01

The effect of stationary, finite-amplitude, linear and nonlinear optimal perturbations on the modal disturbance growth in a Mach 6 axisymmetric flow over a 7 deg. half-angle cone with 0:126 mm nose radius and 0:305 m length is investigated. The freestream parameters (M = 6, Re(exp 1) = 18 x 10(exp. 6) /m) are selected to match the flow conditions of a previous experiment in the VKI H3 hypersonic tunnel. Plane-marching parabolized stability equations are used in conjunction with a partial-differential equation based planar eigenvalue analysis to characterize the boundary layer instability in the presence of azimuthally periodic streaks. The streaks are observed to stabilize nominally planar Mack mode instabilities, although oblique Mack mode and first-mode disturbances are destabilized. Experimentally measured transition onset in the absence of any streaks correlates with an amplification factor of N = 6 for the planar Mack modes. For high enough streak amplitudes, the transition threshold of N = 6 is not reached by the Mack mode instabilities within the length of the cone; however, subharmonic first-mode instabilities, which are destabilized by the presence of the streaks, do reach N = 6 near the end of the cone. The highest stabilization is observed at streak amplitudes of approximately 20 percent of the freestream velocity. Because the use of initial disturbance profiles based on linear optimal growth theory may yield suboptimal control in the context of nonlinear streaks, the computational predictions are extended to nonlinear optimal growth theory. Results show that by using nonlinearly optimal perturbation leads to slightly enhanced stabilization of plane Mack mode disturbances as well as reduced destabilization of subharmonic first-mode disturbances.

Theory of Collisional Two-Stream Plasma Instabilities in the Solar Chromosphere

NASA Astrophysics Data System (ADS)

Madsen, Chad Allen; Dimant, Yakov; Oppenheim, Meers; Fontenla, Juan

2014-06-01

The solar chromosphere experiences intense heating just above its temperature minimum. The heating increases the electron temperature in this region by over 2000 K. Furthermore, it exhibits little time variation and appears widespread across the solar disk. Although semi-empirical models, UV continuum observations, and line emission measurements confirm the existence of the heating, its source remains unexplained. Potential heating sources such as acoustic shocks, resistive dissipation, and magnetic reconnection via nanoflares fail to account for the intensity, persistence, and ubiquity of the heating. Fontenla (2005) suggested turbulence from a collisional two-stream plasma instability known as the Farley-Buneman instability (FBI) could contribute significantly to the heating. This instability is known to heat the plasma of the E-region ionosphere which bears many similarities to the chromospheric plasma. However, the ionospheric theory of the FBI does not account for the diverse ion species found in the solar chromosphere. This work develops a new collisional, two-stream instability theory appropriate for the chromospheric plasma environment using a linear fluid analysis to derive a new dispersion relationship and critical E x B drift velocity required to trigger the instability. Using a 1D, non-local thermodynamic equilibrium, radiative transfer model and careful estimates of collision rates and magnetic field strengths, we calculate the trigger velocities necessary to induce the instability throughout the chromosphere. Trigger velocities as low as 4 km s^-1 are found near the temperature minimum, well below the local neutral acoustic speed in that region. From this, we expect the instability to occur frequently, converting kinetic energy contained in neutral convective flows from the photosphere into thermal energy via turbulence. This could contribute significantly to chromospheric heating and explain its persistent and ubiquitous nature.

Singular growth shapes in turbulent field theories

NASA Astrophysics Data System (ADS)

Conrado, Claudine V.; Bohr, Tomas

1994-05-01

In this work we study deterministic, turbulent partial differential equations (the Kuramoto-Sivashinsky equation and generalizations) with initial conditions which are nonzero only in a small region. We demonstrate that the asymptotic state has a well-defined growth shape, which can be determined by the combination of nonlinear growth velocities, and front propagation governed by the linear instabilities. We show that the growth shapes are, in general, singular and that a new type of instability occurs when the growth shape becomes discontinuous.

Regularization of Grad’s 13 -Moment-Equations in Kinetic Gas Theory

DTIC Science & Technology

2011-01-01

variant of the moment method has been proposed by Eu (1980) and is used, e.g., in Myong (2001). Recently, a maximum- entropy 10-moment system has been used...small amplitude linear waves, the R13 system is linearly stable in time for all modes and wave lengths. The instability of the Burnett system indicates...Boltzmann equation. Related to the problem of global hyperbolicity is the questions of the existence of an entropy law for the R13 system . In the linear

Interface coupling and growth rate measurements in multilayer Rayleigh-Taylor instabilities

NASA Astrophysics Data System (ADS)

Adkins, Raymond; Shelton, Emily M.; Renoult, Marie-Charlotte; Carles, Pierre; Rosenblatt, Charles

2017-06-01

Magnetic levitation was used to measure the growth rate Σ vs wave vector k of a Rayleigh-Taylor instability in a three-layer fluid system, a crucial step in the elucidation of interface coupling in finite-layer instabilities. For a three-layer (low-high-low density) system, the unstable mode growth rate decreases as both the height h of the middle layer and k are reduced, consistent with an interface coupling ∝e-k h . The ratios of the three-layer to the established two-layer growth rates are in good agreement with those of classic linear stability theory, which has long resisted verification in that configuration.

Mass-induced instability of SAdS black hole in Einstein-Ricci cubic gravity

NASA Astrophysics Data System (ADS)

Myung, Yun Soo

2018-05-01

We perform the stability analysis of Schwarzschild-AdS (SAdS) black hole in the Einstein-Ricci cubic gravity. It shows that the Ricci tensor perturbations exhibit unstable modes for small black holes. We call this the mass-induced instability of SAdS black hole because the instability of small black holes arises from the massiveness in the linearized Einstein-Ricci cubic gravity, but not a feature of higher-order derivative theory giving ghost states. Also, we point out that the correlated stability conjecture holds for the SAdS black hole by computing the Wald entropy of SAdS black hole in Einstein-Ricci cubic gravity.

On the stimulated Raman sidescattering in inhomogeneous plasmas: revisit of linear theory and three-dimensional particle-in-cell simulations

NASA Astrophysics Data System (ADS)

Xiao, C. Z.; Zhuo, H. B.; Yin, Y.; Liu, Z. J.; Zheng, C. Y.; Zhao, Y.; He, X. T.

2018-02-01

Stimulated Raman sidescattering (SRSS) in inhomogeneous plasma is comprehensively revisited on both theoretical and numerical aspects due to the increasing concern of its detriments to inertial confinement fusion. Firstly, two linear mechanisms of finite beam width and collisional effects that could suppress SRSS are investigated theoretically. Thresholds for the eigenmode and wave packet in a finite-width beam are derived as a supplement to the theory proposed by Mostrom and Kaufman (1979 Phys. Rev. Lett. 42 644). Collisional absorption of SRSS is efficient at high-density plasma and high-Z material, otherwise, it allows emission of sidescattering. Secondly, we have performed the first three-dimensional particle-in-cell simulations in the context of SRSS to investigate its linear and nonlinear effects. Simulation results are qualitatively agreed with the linear theory. SRSS with the maximum growth gain is excited at various densities, grows to an amplitude that is comparable with the pump laser, and evolutes to lower densities with a large angle of emergence. Competitions between SRSS and other parametric instabilities such as stimulated Raman backscattering, two-plasmon decay, and stimulated Brillouin scattering are discussed. These interaction processes are determined by gains, occurrence sites, scattering geometries of each instability, and will affect subsequent evolutions. Nonlinear effects of self-focusing and azimuthal magnetic field generation are observed to be accompanied with SRSS. In addition, it is found that SRSS is insensitive to ion motion, collision (low-Z material), and electron temperature.

The multi-species Farley-Buneman instability in the solar chromosphere

DOE Office of Scientific and Technical Information (OSTI.GOV)

Madsen, Chad A.; Dimant, Yakov S.; Oppenheim, Meers M.

2014-03-10

Empirical models of the solar chromosphere show intense electron heating immediately above its temperature minimum. Mechanisms such as resistive dissipation and shock waves appear insufficient to account for the persistence and uniformity of this heating as inferred from both UV lines and continuum measurements. This paper further develops the theory of the Farley-Buneman instability (FBI) which could contribute substantially to this heating. It expands upon the single-ion theory presented by Fontenla by developing a multiple-ion-species approach that better models the diverse, metal-dominated ion plasma of the solar chromosphere. This analysis generates a linear dispersion relationship that predicts the critical electronmore » drift velocity needed to trigger the instability. Using careful estimates of collision frequencies and a one-dimensional, semi-empirical model of the chromosphere, this new theory predicts that the instability may be triggered by velocities as low as 4 km s{sup -1}, well below the neutral acoustic speed. In the Earth's ionosphere, the FBI occurs frequently in situations where the instability trigger speed significantly exceeds the neutral acoustic speed. From this, we expect neutral flows rising from the photosphere to have enough energy to easily create electric fields and electron Hall drifts with sufficient amplitude to make the FBI common in the chromosphere. If so, this process will provide a mechanism to convert neutral flow and turbulence energy into electron thermal energy in the quiet Sun.« less

The Multi-species Farley-Buneman Instability in the Solar Chromosphere

NASA Astrophysics Data System (ADS)

Madsen, Chad A.; Dimant, Yakov S.; Oppenheim, Meers M.; Fontenla, Juan M.

2014-03-01

Empirical models of the solar chromosphere show intense electron heating immediately above its temperature minimum. Mechanisms such as resistive dissipation and shock waves appear insufficient to account for the persistence and uniformity of this heating as inferred from both UV lines and continuum measurements. This paper further develops the theory of the Farley-Buneman instability (FBI) which could contribute substantially to this heating. It expands upon the single-ion theory presented by Fontenla by developing a multiple-ion-species approach that better models the diverse, metal-dominated ion plasma of the solar chromosphere. This analysis generates a linear dispersion relationship that predicts the critical electron drift velocity needed to trigger the instability. Using careful estimates of collision frequencies and a one-dimensional, semi-empirical model of the chromosphere, this new theory predicts that the instability may be triggered by velocities as low as 4 km s-1, well below the neutral acoustic speed. In the Earth's ionosphere, the FBI occurs frequently in situations where the instability trigger speed significantly exceeds the neutral acoustic speed. From this, we expect neutral flows rising from the photosphere to have enough energy to easily create electric fields and electron Hall drifts with sufficient amplitude to make the FBI common in the chromosphere. If so, this process will provide a mechanism to convert neutral flow and turbulence energy into electron thermal energy in the quiet Sun.

Zonostrophic instability driven by discrete particle noise

DOE Office of Scientific and Technical Information (OSTI.GOV)

St-Onge, D. A.; Krommes, J. A.

The consequences of discrete particle noise for a system possessing a possibly unstable collective mode are discussed. It is argued that a zonostrophic instability (of homogeneous turbulence to the formation of zonal flows) occurs just below the threshold for linear instability. The scenario provides a new interpretation of the random forcing that is ubiquitously invoked in stochastic models such as the second-order cumulant expansion or stochastic structural instability theory; neither intrinsic turbulence nor coupling to extrinsic turbulence is required. A representative calculation of the zonostrophic neutral curve is made for a simple two-field model of toroidal ion-temperature-gradient-driven modes. To themore » extent that the damping of zonal flows is controlled by the ion-ion collision rate, the point of zonostrophic instability is independent of that rate. Published by AIP Publishing.« less

Zonostrophic instability driven by discrete particle noise

DOE PAGES

St-Onge, D. A.; Krommes, J. A.

2017-04-01

The consequences of discrete particle noise for a system possessing a possibly unstable collective mode are discussed. It is argued that a zonostrophic instability (of homogeneous turbulence to the formation of zonal flows) occurs just below the threshold for linear instability. The scenario provides a new interpretation of the random forcing that is ubiquitously invoked in stochastic models such as the second-order cumulant expansion or stochastic structural instability theory; neither intrinsic turbulence nor coupling to extrinsic turbulence is required. A representative calculation of the zonostrophic neutral curve is made for a simple two-field model of toroidal ion-temperature-gradient-driven modes. To themore » extent that the damping of zonal flows is controlled by the ion-ion collision rate, the point of zonostrophic instability is independent of that rate. Published by AIP Publishing.« less

Onset of Darrieus-Landau Instability in Expanding Flames

NASA Astrophysics Data System (ADS)

Mohan, Shikhar; Matalon, Moshe

2017-11-01

The effect of small amplitude perturbations on the propagation of circular flames in unconfined domains is investigated, computationally and analytically, within the context of the hydrodynamic theory. The flame, treated as a surface of density discontinuity separating fresh combustible mixture from the burnt gas, propagates at a speed dependent upon local curvature and hydrodynamic strain. For mixtures with Lewis numbers above criticality, thermodiffusive effects have stabilizing influences which largely affect the flame at small radii. The amplitude of these disturbances initially decay and only begin to grow once a critical radius is reached. This instability is hydrodynamic in nature and is a consequence of thermal expansion. Through linear stability analysis, predictions of critical flame radius at the onset of instability are obtained as functions of Markstein length and thermal expansion coefficients. The flame evolution is also examined numerically where the motion of the interface is tracked via a level-set method. Consistent with linear stability results, simulations show the flame initially remaining stable and the existence of a particular mode that will be first to grow and later determine the cellular structure observed experimentally at the onset of instability.

Instability of elliptic liquid jets: Temporal linear stability theory and experimental analysis

NASA Astrophysics Data System (ADS)

Amini, Ghobad; Lv, Yu; Dolatabadi, Ali; Ihme, Matthias

2014-11-01

The instability dynamics of inviscid liquid jets issuing from elliptical orifices is studied, and effects of the surrounding gas and the liquid surface tension on the stability behavior are investigated. A dispersion relation for the zeroth azimuthal (axisymmetric) instability mode is derived. Consistency of the analysis is confirmed by demonstrating that these equations reduce to the well-known dispersion equations for the limiting cases of round and planar jets. It is shown that the effect of the ellipticity is to increase the growth rate over a large range of wavenumbers in comparison to those of a circular jet. For higher Weber numbers, at which capillary forces have a stabilizing effect, the growth rate decreases with increasing ellipticity. Similar to circular and planar jets, increasing the density ratio between gas and liquid increases the growth of disturbances significantly. These theoretical investigations are complemented by experiments to validate the local linear stability results. Comparisons of predicted growth rates with measurements over a range of jet ellipticities confirm that the theoretical model provides a quantitatively accurate description of the instability dynamics in the Rayleigh and first wind-induced regimes.

Collective stimulated Brillouin backscatter

NASA Astrophysics Data System (ADS)

Lushnikov, Pavel; Rose, Harvey

2007-11-01

We develop the statistical theory of linear collective stimulated Brillouin backscatter (CBSBS) in spatially and temporally incoherent laser beam. Instability is collective because it does not depend on the dynamics of isolated hot spots (speckles) of laser intensity, but rather depends on averaged laser beam intensity, optic f/#, and laser coherence time, Tc. CBSBS has a much larger threshold than a classical coherent beam's in long-scale-length high temperature plasma. It is a novel regime in which Tc is too large for applicability of well-known statistical theories (RPA) but Tc must be small enough to suppress single speckle processes such as self-focusing. Even if laser Tc is too large for a priori applicability of our theory, collective forward SBS^1, perhaps enhanced by high Z dopant, and its resultant self-induced Tc reduction, may regain the CBSBS regime. We identified convective and absolute CBSBS regimes. The threshold of convective instability is inside the typical parameter region of NIF designs. Well above incoherent threshold, the coherent instability growth rate is recovered. ^1 P.M. Lushnikov and H.A. Rose, Plasma Physics and Controlled Fusion, 48, 1501 (2006).

Effect of wave localization on plasma instabilities

NASA Astrophysics Data System (ADS)

Levedahl, William Kirk

1987-10-01

The Anderson model of wave localization in random media is involved to study the effect of solar wind density turbulence on plasma processes associated with the solar type III radio burst. ISEE-3 satellite data indicate that a possible model for the type III process is the parametric decay of Langmuir waves excited by solar flare electron streams into daughter electromagnetic and ion acoustic waves. The threshold for this instability, however, is much higher than observed Langmuir wave levels because of rapid wave convection of the transverse electromagnetic daughter wave in the case where the solar wind is assumed homogeneous. Langmuir and transverse waves near critical density satisfy the Ioffe-Reigel criteria for wave localization in the solar wind with observed density fluctuations -1 percent. Numerical simulations of wave propagation in random media confirm the localization length predictions of Escande and Souillard for stationary density fluctations. For mobile density fluctuations localized wave packets spread at the propagation velocity of the density fluctuations rather than the group velocity of the waves. Computer simulations using a linearized hybrid code show that an electron beam will excite localized Langmuir waves in a plasma with density turbulence. An action principle approach is used to develop a theory of non-linear wave processes when waves are localized. A theory of resonant particles diffusion by localized waves is developed to explain the saturation of the beam-plasma instability. It is argued that localization of electromagnetic waves will allow the instability threshold to be exceeded for the parametric decay discussed above.

Neighborhood, Family and Individual Influences on School Physical Victimization

PubMed Central

Brooks-Gunn, Jeanne

2013-01-01

Few studies on the correlates of school violence include school and neighborhood influences. We use ecological systems theory and social disorganization theory to simultaneously incorporate neighborhood (e.g., concentrated poverty, residential instability, and immigrant concentration), school, family, and individual predictors of physical school victimization longitudinally among a large socio-economically and ethnically diverse (49% Hispanic; 34% African American) sample of 6 and 9 year olds (49% female) from the Project on Human Development in Chicago Neighborhoods (PHDCN). These children were followed up at Wave II at ages 8 and 11 (n=1425). Results of Hierarchical Generalized Linear Models reveal neighborhood residential instability increases school victimization net of family and individual correlates. Furthermore, cross-level interactions were also supported where residential family mobility has a stronger risk influence in areas of high residential instability. Also, the influence of residential family mobility is decreased in areas with higher levels of immigrant concentration. We also found cross-context connections where parent-to-child aggression in the home is connected to a higher risk of victimization at school. The role of neighborhood and family residential instability on victimization warrants further research. PMID:23263822

Graviton mass or cosmological constant?

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gabadadze, Gregory; Gruzinov, Andrei

2005-12-15

To describe a massive graviton in 4D Minkowski space-time one introduces a quadratic term in the Lagrangian. This term, however, can lead to a readjustment or instability of the background instead of describing a massive graviton on flat space. We show that for all local 4D Lorentz-invariant mass terms Minkowski space is unstable. The instability can develop in a time scale that is many orders of magnitude shorter than the inverse graviton mass. We start with the Pauli-Fierz (PF) term that is the only local mass term with no ghosts in the linearized approximation. We show that nonlinear completions ofmore » the PF Lagrangian give rise to instability of Minkowski space. We continue with the mass terms that are not of a PF type. Although these models are known to have ghosts in the linearized approximations, nonlinear interactions can lead to background change in which the ghosts are eliminated. In the latter case, however, the graviton perturbations on the new background are not massive. We argue that a consistent theory of a massive graviton on flat space can be formulated in theories with extra dimensions. They require an infinite number of fields or nonlocal description from a 4D point of view.« less

Proton-driven electromagnetic instabilities in high-speed solar wind streams

NASA Technical Reports Server (NTRS)

Abraham-Shrauner, B.; Asbridge, J. R.; Bame, S. J.; Feldman, W. C.

1979-01-01

Electromagnetic instabilities of the field-aligned, right-hand circularly polarized magnetosonic wave and the left-hand circularly polarized Alfven wave driven by two drifted proton components are analyzed for model parameters determined from Imp 7 solar wind proton data measured during high-speed flow conditions. Growth rates calculated using bi-Lorentzian forms for the main and beam proton as well as core and halo electron velocity distributions do not differ significantly from those calculated using bi-Maxwellian forms. Using distribution parameters determined from 17 measured proton spectra, we show that considering the uncertainties the magnetosonic wave may be linearly stable and the Alfven wave is linearly unstable. Because proton velocity distribution function shapes are observed to persist for times long compared to the proton gyroperiod, the latter result suggests that linear stability theory fails for proton-driven ion cyclotron waves in the high-speed solar wind.

Simulation and analysis of chemical release in the ionosphere

NASA Astrophysics Data System (ADS)

Gao, Jing-Fan; Guo, Li-Xin; Xu, Zheng-Wen; Zhao, Hai-Sheng; Feng, Jie

2018-05-01

Ionospheric inhomogeneous plasma produced by single point chemical release has simple space-time structure, and cannot impact radio wave frequencies higher than Very High Frequency (VHF) band. In order to produce more complicated ionospheric plasma perturbation structure and trigger instabilities phenomena, multiple-point chemical release scheme is presented in this paper. The effects of chemical release on low latitude ionospheric plasma are estimated by linear instability growth rate theory that high growth rate represents high irregularities, ionospheric scintillation occurrence probability and high scintillation intension in scintillation duration. The amplitude scintillations and the phase scintillations of 150 MHz, 400 MHz, and 1000 MHz are calculated based on the theory of multiple phase screen (MPS), when they propagate through the disturbed area.

Radiating Instabilities of Internal Inertio-gravity Waves

NASA Astrophysics Data System (ADS)

Kwasniok, F.; Schmitz, G.

The vertical radiation of local convective and shear instabilities of internal inertio- gravity waves is examined within linear stability theory. A steady, plane-parallel Boussinesq flow with vertical profiles of horizontal velocity and static stability re- sembling an internal inertio-gravity wave packet without mean vertical shear is used as dynamical framework. The influence of primary-wave frequency and amplitude as well as orientation and horizontal wavenumber of the instability on vertical radi- ation is discussed. Considerable radiation occurs at small to intermediate instability wavenumbers for basic state gravity waves with high to intermediate frequencies and moderately convectively supercritical amplitudes. Radiation is then strongest when the horizontal wavevector of the instability is aligned parallel to the horizontal wavevector of the basic state gravity wave. These radiating modes are essentially formed by shear instability. Modes of convective instability, that occur at large instability wavenum- bers or strongly convectively supercritical amplitudes, as well as modes at convec- tively subcritical amplitudes are nonradiating, trapped in the region of instability. The radiation of an instability is found to be related to the existence of critical levels, a radiating mode being characterized by the absence of critical levels outside the region of instability of the primary wave.

Experimental Study of the Richtmyer-Meshkov Instability of Incompressible Fluids

NASA Technical Reports Server (NTRS)

Niederhaus, Charles; Jacobs, Jeffrey W.

2002-01-01

The Richtmyer-Meshkov instability of a low Atwood number, miscible, two-liquid system is investigated experimentally. The initially stratified fluids are contained within a rectangular tank mounted to a sled that rides on a vertical set of rails. The instability is generated by dropping the sled onto a coil spring, producing a nearly impulsive upward acceleration. The subsequent freefall that occurs as the container travels upward and then downward on the rails allows the instability to evolve in the absence of gravity. The interface separating the two liquids initially has a well-defined, sinusoidal perturbation that quickly inverts and then grows in amplitude after undergoing the impulsive acceleration. Disturbance amplitudes are measured and compared to theoretical predictions. Linear stability theory gives excellent agreement with the measured initial growth rate, a(sub 0), for single-mode perturbations with the predicted amplitudes differing by less than 10% from experimental measurements up to a nondimensional time ka(sub 0)t = 0.7, where k is the wavenumber. Linear stability theory also provides excellent agreement for the individual mode amplitudes of multi-mode initial perturbations up until the interface becomes multi-valued. Comparison with previously published weakly nonlinear single-mode models shows good agreement up to ka(sub 0)t = 3, while published nonlinear single-mode models provide good agreement up to ka(sub 0)t = 30. The effects of Reynolds number on the vortex core evolution and overall growth rate of the interface are also investigated. Measurements of the overall amplitude are found to be unaffected by the Reynolds number for the range of values studied here. However, experiments carried out at lower values of Reynolds numbers were found to have decreased vortex core rotation rates. In addition, an instability in the vortex cores is observed.

Rayleigh-Taylor instability in accelerated elastic-solid slabs

NASA Astrophysics Data System (ADS)

Piriz, S. A.; Piriz, A. R.; Tahir, N. A.

2017-12-01

We develop the linear theory for the asymptotic growth of the incompressible Rayleigh-Taylor instability of an accelerated solid slab of density ρ2, shear modulus G , and thickness h , placed over a semi-infinite ideal fluid of density ρ1<ρ2 . It extends previous results for Atwood number AT=1 [B. J. Plohr and D. H. Sharp, Z. Angew. Math. Phys. 49, 786 (1998), 10.1007/s000330050121] to arbitrary values of AT and unveil the singular feature of an instability threshold below which the slab is stable for any perturbation wavelength. As a consequence, an accelerated elastic-solid slab is stable if ρ2g h /G ≤2 (1 -AT) /AT .

Linear-stability theory of thermocapillary convection in a model of float-zone crystal growth

NASA Technical Reports Server (NTRS)

Neitzel, G. P.; Chang, K.-T.; Jankowski, D. F.; Mittelmann, H. D.

1992-01-01

Linear-stability theory has been applied to a basic state of thermocapillary convection in a model half-zone to determine values of the Marangoni number above which instability is guaranteed. The basic state must be determined numerically since the half-zone is of finite, O(1) aspect ratio with two-dimensional flow and temperature fields. This, in turn, means that the governing equations for disturbance quantities will remain partial differential equations. The disturbance equations are treated by a staggered-grid discretization scheme. Results are presented for a variety of parameters of interest in the problem, including both terrestrial and microgravity cases.

Fully compressible solutions for early stage Richtmyer–Meshkov instability

DOE PAGES

Margolin, Len G.; Reisner, Jon Michael

2016-10-27

Here, we will consider the effects of compressibility and viscosity on the early dynamics of the Richtmyer–Meshkov instability (RMI). In particular, we will combine theory, scaling, and high resolution simulation of RMI to probe the details of the initial compression and the subsequent viscous damping as a shock interacts with a density discontinuity. We will propose a refinement of the classic 1D model for the linear regime of RMI that, for small initial perturbation wavelengths, more accurately reproduces the 2D dynamics of a fully resolved numerical simulation.

Return current instability driven by a temperature gradient in ICF plasmas

DOE PAGES

Rozmus, W.; Brantov, A. V.; Sherlock, M.; ...

2017-10-12

Here, hot plasmas with strong temperature gradients in inertial confinement fusion (ICF) experiments are examined for ion acoustic instabilities produced by electron heat flow. The return current instability (RCI) due to a neutralizing current of cold electrons arising in response to a large electron heat flux has been considered. First, the linear threshold and growth rates are derived in the nonlocal regime of thermal transport. They are compared with the results of Vlasov-Fokker-Planck (VFP) simulations in one spatial dimension. Very good agreement has been found between kinetic VFP simulations and the linear theory of the RCI. A quasi-stationary state ofmore » ion acoustic turbulence produced by the RCI is achieved in the VFP simulations. Saturation of the RCI involves heating of ions in the tail of the ion distribution function and convection of the enhanced ion acoustic fluctuations from the unstable region of the plasma. Further evolution of the ion acoustic turbulence and its effects on absorption and transport are also discussed.« less

Return current instability driven by a temperature gradient in ICF plasmas

NASA Astrophysics Data System (ADS)

Rozmus, W.; Brantov, A. V.; Sherlock, M.; Bychenkov, V. Yu

2018-01-01

Hot plasmas with strong temperature gradients in inertial confinement fusion experiments are examined for ion acoustic instabilities produced by electron heat flow. The return current instability (RCI) due to a neutralizing current of cold electrons arising in response to a large electron heat flux has been considered. First, the linear threshold and growth rates are derived in the non-local regime of thermal transport. They are compared with the results of Vlasov-Fokker-Planck (VFP) simulations in one spatial dimension. Very good agreement has been found between kinetic VFP simulations and the linear theory of the RCI. A quasi-stationary state of ion acoustic turbulence (IAT) produced by the RCI is achieved in the VFP simulations. Saturation of the RCI involves heating of ions in the tail of the ion distribution function and convection of the enhanced ion acoustic fluctuations from the unstable region of the plasma. Further evolution of the IAT and its effects on absorption and transport are also discussed.

Direct Numerical Simulation of Transition in a Swept-Wing Boundary Layer

NASA Technical Reports Server (NTRS)

Duan, Lian; Choudhari, Meelan M.; Li, Fei

2013-01-01

Direct numerical simulation (DNS) is performed to examine laminar to turbulent transition due to high-frequency secondary instability of stationary crossflow vortices in a subsonic swept-wing boundary layer for a realistic natural-laminar-flow airfoil configuration. The secondary instability is introduced via inflow forcing derived from a two-dimensional, partial-differential-equation based eigenvalue computation; and the mode selected for forcing corresponds to the most amplified secondary instability mode which, in this case, derives a majority of its growth from energy production mechanisms associated with the wall-normal shear of the stationary basic state. Both the growth of the secondary instability wave and the resulting onset of laminar-turbulent transition are captured within the DNS computations. The growth of the secondary instability wave in the DNS solution compares well with linear secondary instability theory when the amplitude is small; the linear growth is followed by a region of reduced growth resulting from nonlinear effects before an explosive onset of laminar breakdown to turbulence. The peak fluctuations are concentrated near the boundary layer edge during the initial stage of transition, but rapidly propagates towards the surface during the process of laminar breakdown. Both time-averaged statistics and flow visualization based on the DNS reveal a sawtooth transition pattern that is analogous to previously documented surface flow visualizations of transition due to stationary crossflow instability. The memory of the stationary crossflow vortex is found to persist through the transition zone and well beyond the location of the maximum skin friction.

Rayleigh-Taylor and Richtmyer-Meshkov Instabilities in Turbulent Regime

NASA Astrophysics Data System (ADS)

Dimonte, G.

1998-11-01

The Rayleigh-Taylor instability (RTI) and its shock driven analog, the Richtmyer-Meshkov instability (RMI), affect a wide variety of important phenomena from sub-terrainian to astrophysical environments. The ``fluids" are equally varied from plasmas and magnetic fields to elastic-plastic solids. In most applications, the instabilities occur with a complex acceleration history and evolve to a highly nonlinear state, making the theoretical description formidable. We will link the fluid and plasma regimes while describing the theoretical issues and basic experiments in different venues to isolate key physics issues. RMI experiments on the Nova laser investigate the affects of compressibility with strong radiatively driven shocks (Mach > 10) in near solid density plasmas of sub-millimeter scale. The growth of single sinusoidal and random 3-D perturbations are measured using backlit radiography. RTI experiments with the Linear Electric Motor (LEM) are conducted with a variety of acceleration (<< 10^4 m/s^2) histories and fluids of 10 cm scale. Turbulent RTI experiments with high Reynolds number liquids show self-similar growth which is characterized with laser induced fluorescence. LEM experiments with an elastic-plastic material (yogurt) exhibit a critical wavelength and amplitude for instability. The experimental results will be compared with linear and nonlinear theories and hydrodynamic simulations.

The response of multidegree-of-freedom systems with quadratic non-linearities to a harmonic parametric resonance

NASA Astrophysics Data System (ADS)

Nayfeh, A. H.

1983-09-01

An analysis is presented of the response of multidegree-of-freedom systems with quadratic non-linearities to a harmonic parametric excitation in the presence of an internal resonance of the combination type ω3 ≈ ω2 + ω1, where the ωn are the linear natural frequencies of the systems. In the case of a fundamental resonance of the third mode (i.e., Ω ≈ω 3, where Ω is the frequency of the excitation), one can identify two critical values ζ 1 and ζ 2, where ζ 2 ⩾ ζ 1, of the amplitude F of the excitation. The value F = ζ2 corresponds to the transition from stable to unstable solutions. When F < ζ1, the motion decays to zero according to both linear and non-linear theories. When F > ζ2, the motion grows exponentially with time according to the linear theory but the non-linearity limits the motion to a finite amplitude steady state. The amplitude of the third mode, which is directly excited, is independent of F, whereas the amplitudes of the first and second modes, which are indirectly excited through the internal resonance, are functions of F. When ζ1 ⩽ F ⩽ ζ2, the motion decays or achieves a finite amplitude steady state depending on the initial conditions according to the non-linear theory, whereas it decays to zero according to the linear theory. This is an example of subcritical instability. In the case of a fundamental resonance of either the first or second mode, the trivial response is the only possible steady state. When F ⩽ ζ2, the motion decays to zero according to both linear and non-linear theories. When F > ζ2, the motion grows exponentially with time according to the linear theory but it is aperiodic according to the non-linear theory. Experiments are being planned to check these theoretical results.

Regularization of instabilities in gravity theories

NASA Astrophysics Data System (ADS)

Ramazanoǧlu, Fethi M.

2018-01-01

We investigate instabilities and their regularization in theories of gravitation. Instabilities can be beneficial since their growth often leads to prominent observable signatures, which makes them especially relevant to relatively low signal-to-noise ratio measurements such as gravitational wave detections. An indefinitely growing instability usually renders a theory unphysical; hence, a desirable instability should also come with underlying physical machinery that stops the growth at finite values, i.e., regularization mechanisms. The prototypical gravity theory that presents such an instability is the spontaneous scalarization phenomena of scalar-tensor theories, which feature a tachyonic instability. We identify the regularization mechanisms in this theory and show that they can be utilized to regularize other instabilities as well. Namely, we present theories in which spontaneous growth is triggered by a ghost rather than a tachyon and numerically calculate stationary solutions of scalarized neutron stars in these theories. We speculate on the possibility of regularizing known divergent instabilities in certain gravity theories using our findings and discuss alternative theories of gravitation in which regularized instabilities may be present. Even though we study many specific examples, our main point is the recognition of regularized instabilities as a common theme and unifying mechanism in a vast array of gravity theories.

Large-scale galaxy flow from a non-gravitational impulse

NASA Technical Reports Server (NTRS)

Hogan, Craig J.; Kaiser, Nick

1989-01-01

A theory is presented describing linear perturbations of an expanding universe containing multiple, independently perturbed, collisionless, gravitationally coupled constituents. Solutions are found in the limit where one initially unperturbed component dominates the total density. The theory is applied to perturbations generated by a nongravitational process in one or more of the light components, as would occur in explosive or radiation-pressure-instability theories of galaxy formation. The apparent dynamical density parameter and correlations between density and velocity amplitude for various populations, are evaluated as a function of cosmic scale factor.

Global Instability on Laminar Separation Bubbles-Revisited

NASA Technical Reports Server (NTRS)

Theofilis, Vassilis; Rodriquez, Daniel; Smith, Douglas

2010-01-01

In the last 3 years, global linear instability of LSB has been revisited, using state-of-the-art hardware and algorithms. Eigenspectra of LSB flows have been understood and classified in branches of known and newly-discovered eigenmodes. Major achievements: World-largest numerical solutions of global eigenvalue problems are routinely performed. Key aerodynamic phenomena have been explained via critical point theory, applied to our global mode results. Theoretical foundation for control of LSB flows has been laid. Global mode of LSB at the origin of observable phenomena. U-separation on semi-infinite plate. Stall cells on (stalled) airfoil. Receptivity/Sensitivity/AFC feasible (practical?) via: Adjoint EVP solution. Direct/adjoint coupling (the Crete connection). Minor effect of compressibility on global instability in the subsonic compressible regime. Global instability analysis of LSB in realistic supersonic flows apparently quite some way down the horizon.

Modulational instability in a PT-symmetric vector nonlinear Schrödinger system

NASA Astrophysics Data System (ADS)

Cole, J. T.; Makris, K. G.; Musslimani, Z. H.; Christodoulides, D. N.; Rotter, S.

2016-12-01

A class of exact multi-component constant intensity solutions to a vector nonlinear Schrödinger (NLS) system in the presence of an external PT-symmetric complex potential is constructed. This type of uniform wave pattern displays a non-trivial phase whose spatial dependence is induced by the lattice structure. In this regard, light can propagate without scattering while retaining its original form despite the presence of inhomogeneous gain and loss. These constant-intensity continuous waves are then used to perform a modulational instability analysis in the presence of both non-hermitian media and cubic nonlinearity. A linear stability eigenvalue problem is formulated that governs the dynamical evolution of the periodic perturbation and its spectrum is numerically determined using Fourier-Floquet-Bloch theory. In the self-focusing case, we identify an intensity threshold above which the constant-intensity modes are modulationally unstable for any Floquet-Bloch momentum belonging to the first Brillouin zone. The picture in the self-defocusing case is different. Contrary to the bulk vector case, where instability develops only when the waves are strongly coupled, here an instability occurs in the strong and weak coupling regimes. The linear stability results are supplemented with direct (nonlinear) numerical simulations.

Effect of wave localization on plasma instabilities. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Levedahl, William Kirk

1987-01-01

The Anderson model of wave localization in random media is involved to study the effect of solar wind density turbulence on plasma processes associated with the solar type III radio burst. ISEE-3 satellite data indicate that a possible model for the type III process is the parametric decay of Langmuir waves excited by solar flare electron streams into daughter electromagnetic and ion acoustic waves. The threshold for this instability, however, is much higher than observed Langmuir wave levels because of rapid wave convection of the transverse electromagnetic daughter wave in the case where the solar wind is assumed homogeneous. Langmuir and transverse waves near critical density satisfy the Ioffe-Reigel criteria for wave localization in the solar wind with observed density fluctuations -1 percent. Numerical simulations of wave propagation in random media confirm the localization length predictions of Escande and Souillard for stationary density fluctations. For mobile density fluctuations localized wave packets spread at the propagation velocity of the density fluctuations rather than the group velocity of the waves. Computer simulations using a linearized hybrid code show that an electron beam will excite localized Langmuir waves in a plasma with density turbulence. An action principle approach is used to develop a theory of non-linear wave processes when waves are localized. A theory of resonant particles diffusion by localized waves is developed to explain the saturation of the beam-plasma instability. It is argued that localization of electromagnetic waves will allow the instability threshold to be exceeded for the parametric decay discussed above.

Multigrid direct numerical simulation of the whole process of flow transition in 3-D boundary layers

NASA Technical Reports Server (NTRS)

Liu, Chaoqun; Liu, Zhining

1993-01-01

A new technology was developed in this study which provides a successful numerical simulation of the whole process of flow transition in 3-D boundary layers, including linear growth, secondary instability, breakdown, and transition at relatively low CPU cost. Most other spatial numerical simulations require high CPU cost and blow up at the stage of flow breakdown. A fourth-order finite difference scheme on stretched and staggered grids, a fully implicit time marching technique, a semi-coarsening multigrid based on the so-called approximate line-box relaxation, and a buffer domain for the outflow boundary conditions were all used for high-order accuracy, good stability, and fast convergence. A new fine-coarse-fine grid mapping technique was developed to keep the code running after the laminar flow breaks down. The computational results are in good agreement with linear stability theory, secondary instability theory, and some experiments. The cost for a typical case with 162 x 34 x 34 grid is around 2 CRAY-YMP CPU hours for 10 T-S periods.

Modulational instability of finite-amplitude, circularly polarized Alfven waves

NASA Technical Reports Server (NTRS)

Derby, N. F., Jr.

1978-01-01

The simple theory of the decay instability of Alfven waves is strictly applicable only to a small-amplitude parent wave in a low-beta plasma, but, if the parent wave is circularly polarized, it is possible to analyze the situation without either of these restrictions. Results show that a large-amplitude circularly polarized wave is unstable with respect to decay into three waves, one longitudinal and one transverse wave propagating parallel to the parent wave and one transverse wave propagating antiparallel. The transverse decay products appear at frequencies which are the sum and difference of the frequencies of the parent wave and the longitudinal wave. The decay products are not familiar MHD modes except in the limit of small beta and small amplitude of the parent wave, in which case the decay products are a forward-propagating sound wave and a backward-propagating circularly polarized wave. In this limit the other transverse wave disappears. The effect of finite beta is to reduce the linear growth rate of the instability from the value suggested by the simple theory. Possible applications of these results to the theory of the solar wind are briefly touched upon.

Fire Hose Instability in the Multiple Magnetic Reconnection

NASA Astrophysics Data System (ADS)

Alexandrova, A.; Retino, A.; Divin, A. V.; Le Contel, O.; Matteini, L.; Breuillard, H.; Deca, J.; Catapano, F.; Cozzani, G.; Nakamura, R.; Panov, E. V.; Voros, Z.

2017-12-01

We present observations of multiple reconnection in the Earth's magnetotail. In particular, we observe an ion temperature anisotropy characterized by large temperature along the magnetic field, between the two active X-lines. The anisotropy is associated with right-hand polarized waves at frequencies lower than the ion cyclotron frequency and propagating obliquely to the background magnetic field. We show that the observed anisotropy and the wave properties are consistent with linear kinetic theory of fire hose instability. The observations are in agreement with the particle-in-cell simulations of multiple reconnection. The results suggest that the fire hose instability can develop during multiple reconnection as a consequence of the ion parallel anisotropy that is produced by counter-streaming ions trapped between the X-lines.

Theory of the corrugation instability of a piston-driven shock wave.

PubMed

Bates, J W

2015-01-01

We analyze the two-dimensional stability of a shock wave driven by a steadily moving corrugated piston in an inviscid fluid with an arbitrary equation of state. For h≤-1 or h>h(c), where h is the D'yakov parameter and h(c) is the Kontorovich limit, we find that small perturbations on the shock front are unstable and grow--at first quadratically and later linearly--with time. Such instabilities are associated with nonequilibrium fluid states and imply a nonunique solution to the hydrodynamic equations. The above criteria are consistent with instability limits observed in shock-tube experiments involving ionizing and dissociating gases and may have important implications for driven shocks in laser-fusion, astrophysical, and/or detonation studies.

Charge instabilities due to local charge conjugation symmetry in /2+1 dimensions

NASA Astrophysics Data System (ADS)

Bais, F. A.; Striet, J.

2003-08-01

Alice electrodynamics (AED) is a theory of electrodynamics in which charge conjugation is a local gauge symmetry. In this paper we investigate a charge instability in alice electrodynamics in 2+1 dimensions due to this local charge conjugation. The instability manifests itself through the creation of a pair of alice fluxes. The final state is one in which the charge is completely delocalized, i.e., it is carried as cheshire charge by the flux pair that gets infinitely separated. We determine the decay rate in terms of the parameters of the model. The relation of this phenomenon with other salient features of 2-dimensional compact QED, such as linear confinement due to instantons/monopoles, is discussed.

Effect of Compliant Walls on Secondary Instabilities in Boundary-Layer Transition

NASA Technical Reports Server (NTRS)

Joslin, Ronald D.; Morris, Philip J.

1991-01-01

For aerodynamic and hydrodynamic vehicles, it is highly desirable to reduce drag and noise levels. A reduction in drag leads to fuel savings. In particular for submersible vehicles, a decrease in noise levels inhibits detection. A suggested means to obtain these reduction goals is by delaying the transition from laminar to turbulent flow in external boundary layers. For hydrodynamic applications, a passive device which shows promise for transition delays is the compliant coating. In previous studies with a simple mechanical model representing the compliant wall, coatings were found that provided transition delays as predicted from the semi-empirical e(sup n) method. Those studies were concerned with the linear stage of transition where the instability of concern is referred to as the primary instability. For the flat-plate boundary layer, the Tollmien-Schlichting (TS) wave is the primary instability. In one of those studies, it was shown that three-dimensional (3-D) primary instabilities, or oblique waves, could dominate transition over the coatings considered. From the primary instability, the stretching and tilting of vorticity in the shear flow leads to a secondary instability mechanism. This has been theoretical described by Herbert based on Floquet theory. In the present study, Herbert's theory is used to predict the development of secondary instabilities over isotropic and non-isotropic compliant walls. Since oblique waves may be dominant over compliant walls, a secondary theory extention is made to allow for these 3-D primary instabilities. The effect of variations in primary amplitude, spanwise wavenumber, and Reynolds number on the secondary instabilities are examined. As in the rigid wall case, over compliant walls the subharmonic mode of secondary instability dominates for low-amplitude primary disturbances. Both isotropic and non-isotropic compliant walls lead to reduced secondary growth rates compared to the rigid wall results. For high frequencies, the non-isotropic wall suppresses the amplification of the secondary instabilities, while instabilities over the isotropic wall may grow with an explosive rate similar to the rigid wall results. For the more important lower frequencies, both isotropic and non-isotropic compliant walls suppress the amplification of secondary instabilities compared to the rigid wall results. The twofold major discovery and demonstration of the present investigation are: (1) the use of passive devices, such as compliant walls, can lead to significant reductions in the secondary instability growth rates and amplification; (2) suppressing the primary growth rates and subsequent amplification enable delays in the growth of the explosive secondary instability mechanism.

Acceleration and stability of a high-current ion beam in induction fields

NASA Astrophysics Data System (ADS)

Karas', V. I.; Manuilenko, O. V.; Tarakanov, V. P.; Federovskaya, O. V.

2013-03-01

A one-dimensional nonlinear analytic theory of the filamentation instability of a high-current ion beam is formulated. The results of 2.5-dimensional numerical particle-in-cell simulations of acceleration and stability of an annular compensated ion beam (CIB) in a linear induction particle accelerator are presented. It is shown that additional transverse injection of electron beams in magnetically insulated gaps (cusps) improves the quality of the ion-beam distribution function and provides uniform beam acceleration along the accelerator. The CIB filamentation instability in both the presence and the absence of an external magnetic field is considered.

Non-linear boundary-layer receptivity due to distributed surface roughness

NASA Technical Reports Server (NTRS)

Amer, Tahani Reffet

1995-01-01

The process by which a laminar boundary layer internalizes the external disturbances in the form of instability waves is known as boundary-layer receptivity. The objective of the present research was to determine the effect of acoustic excitation on boundary-layer receptivity for a flat plate with distributed variable-amplitude surface roughness through measurements with a hot-wire probe. Tollmien-Schlichting mode shapes due to surface roughness receptivity have also been determined, analyzed, and shown to be in agreement with theory and other experimental work. It has been shown that there is a linear relationship between the surface roughness and receptivity for certain roughness configurations with constant roughness wavelength. In addition, strong non-linear receptivity effects exist for certain surface roughness configurations over a band where the surface roughness and T-S wavelength are matched. The results from the present experiment follow the trends predicted by theory and other experimental work for linear receptivity. In addition, the results show the existence of non-linear receptivity effects for certain combinations of surface roughness elements.

Linear theory of plasma Čerenkov masers

NASA Astrophysics Data System (ADS)

Birau, M.

1996-11-01

A different theoretical model of Čerenkov instability in the linear amplification regime of plasma Čerenkov masers is developed. The model assumes a cold relativistic annular electron beam propagating through a column of cold dense plasma, the two bodies being immersed in an infinite magnetic guiding field inside a perfect cylindrical waveguide. In order to simplify the calculations, a radial rectangular distribution of plasma and beam density is assumed and only azimuthal symmetric modes are under investigation. The model's difference consists of taking into account the whole plasma and beam electromagnetic structures in the interpretation of the Čerenkov instability. This model leads to alternative results such as the possibility of emission at several frequencies. In addition, the electric field is calculated taking into account its radial phase dependence, so that a map of the field in the interaction region can be presented.

Experimental study of the laminar-turbulent transition of a concave wall in a parallel flow

NASA Technical Reports Server (NTRS)

Bippes, H.

1978-01-01

The instability of the laminar boundary layer flow along a concave wall was studied. Observations of these three-dimensional boundary layer phenomena were made using the hydrogen-bubble visualization technique. With the application of stereo-photogrammetric methods in the air-water system it was possible to investigate the flow processes qualitatively and quantitatively. In the case of a concave wall of sufficient curvature, a primary instability occurs first in the form of Goertler vortices with wave lengths depending upon the boundary layer thickness and the wall curvature. At the onset the amplification rate is in agreement with the linear theory. Later, during the non-linear amplification stage, periodic spanwise vorticity concentrations develop in the low velocity region between the longitudinal vortices. Then a meandering motion of the longitudinal vortex streets subsequently ensues, leading to turbulence.

Instability of a shear layer between multicomponent fluids at supercritical pressure

NASA Astrophysics Data System (ADS)

Fu, Qing-fei; Zhang, Yun-xiao; Mo, Chao-jie; Yang, Li-jun

2018-04-01

The temporal instability of a thin shear layer lying between streams of two components of fluids has been studied. The effects of density profile of the layer on the instability behavior were mainly considered. The detailed density profile was obtained through Linear Gradient Theory. The eigenvalue problem was calculated, and the temporal instability curves were obtained for the thermodynamic parameters, e.g. pressure and temperature. The results show that, increase of pressure leads to the increase of the maximum growth rate. However, increasing pressure has opposite effects on the disturbances with small and large wave length. The increase of temperature causes the decrease of disturbance growth rate. The instability behavior of the shear layers was determined mainly by the interval between the inflections of the velocity and density profiles, and the maximum density gradient. The total effects, determined by coupling density stratification, and interval between the inflections of the velocity and density profiles, were quite distinct for different ranges of temperature and pressure.

Electromagnetic ion beam instabilities - Growth at cyclotron harmonic wave numbers

NASA Technical Reports Server (NTRS)

Smith, Charles W.; Gary, S. Peter

1987-01-01

The linear theory of electromagnetic ion beam instabilities for arbitrary angles of propagation is studied, with an emphasis on the conditions necessary to generate unstable modes at low harmonics of the ion cyclotron resonance condition. The present results extend the analysis of Smith et al. (1985). That paper considered only the plasma parameters at a time during which harmonic wave modes were observed in the earth's foreshock. The parameters of that paper are used as the basis of parametric variations here to establish the range of beam properties which may give rise to observable harmonic spectra. It is shown that the growth rates of both left-hand and right-hand cyclotron harmonic instabilities are enhanced by an increase in the beam temperature anisotropy and/or the beam speed. Decreases in the beam density and/or the core-ion beta reduce the overall growth of the cyclotron harmonic instabilities but favor the growth of these modes over the growth of the nonresonant instability and thereby enhance the observability of the harmonics.

Generalized Brans-Dicke theories

DOE Office of Scientific and Technical Information (OSTI.GOV)

De Felice, Antonio; Tsujikawa, Shinji, E-mail: defelice@rs.kagu.tus.ac.jp, E-mail: shinji@rs.kagu.tus.ac.jp

2010-07-01

In Brans-Dicke theory a non-linear self interaction of a scalar field φ allows a possibility of realizing the late-time cosmic acceleration, while recovering the General Relativistic behavior at early cosmological epochs. We extend this to more general modified gravitational theories in which a de Sitter solution for dark energy exists without using a field potential. We derive a condition for the stability of the de Sitter point and study the background cosmological dynamics of such theories. We also restrict the allowed region of model parameters from the demand for the avoidance of ghosts and instabilities. A peculiar evolution of themore » field propagation speed allows us to distinguish those theories from the ΛCDM model.« less

Simulation of Nonlinear Instabilities in an Attachment-Line Boundary Layer

NASA Technical Reports Server (NTRS)

Joslin, Ronald D.

1996-01-01

The linear and the nonlinear stability of disturbances that propagate along the attachment line of a three-dimensional boundary layer is considered. The spatially evolving disturbances in the boundary layer are computed by direct numerical simulation (DNS) of the unsteady, incompressible Navier-Stokes equations. Disturbances are introduced either by forcing at the in ow or by applying suction and blowing at the wall. Quasi-parallel linear stability theory and a nonparallel theory yield notably different stability characteristics for disturbances near the critical Reynolds number; the DNS results con rm the latter theory. Previously, a weakly nonlinear theory and computations revealed a high wave-number region of subcritical disturbance growth. More recent computations have failed to achieve this subcritical growth. The present computational results indicate the presence of subcritically growing disturbances; the results support the weakly nonlinear theory. Furthermore, an explanation is provided for the previous theoretical and computational discrepancy. In addition, the present results demonstrate that steady suction can be used to stabilize disturbances that otherwise grow subcritically along the attachment line.

Stability, intermittency and universal Thorpe length distribution in a laboratory turbulent stratified shear flow

DOE Office of Scientific and Technical Information (OSTI.GOV)

Odier, Philippe; Ecke, Robert E.

Stratified shear flows occur in many geophysical contexts, from oceanic overflows and river estuaries to wind-driven thermocline layers. In this study, we explore a turbulent wall-bounded shear flow of lighter miscible fluid into a quiescent fluid of higher density with a range of Richardson numbersmore » $$0.05\\lesssim Ri\\lesssim 1$$. In order to find a stability parameter that allows close comparison with linear theory and with idealized experiments and numerics, we investigate different definitions of$Ri$$. We find that a gradient Richardson number defined on fluid interface sections where there is no overturning at or adjacent to the maximum density gradient position provides an excellent stability parameter, which captures the Miles–Howard linear stability criterion. For small $$Ri$$ the flow exhibits robust Kelvin–Helmholtz instability, whereas for larger $$Ri$$ interfacial overturning is more intermittent with less frequent Kelvin–Helmholtz events and emerging Holmboe wave instability consistent with a thicker velocity layer compared with the density layer. We compute the perturbed fraction of interface as a quantitative measure of the flow intermittency, which is approximately 1 for the smallest $$Ri$$ but decreases rapidly as $$Ri$ increases, consistent with linear theory. For the perturbed regions, we use the Thorpe scale to characterize the overturning properties of these flows. The probability distribution of the non-zero Thorpe length yields a universal exponential form, suggesting that much of the overturning results from increasingly intermittent Kelvin–Helmholtz instability events. Finally, the distribution of turbulent kinetic energy, conditioned on the intermittency fraction, has a similar form, suggesting an explanation for the universal scaling collapse of the Thorpe length distribution.« less

Stability, intermittency and universal Thorpe length distribution in a laboratory turbulent stratified shear flow

DOE PAGES

Odier, Philippe; Ecke, Robert E.

2017-02-21

Stratified shear flows occur in many geophysical contexts, from oceanic overflows and river estuaries to wind-driven thermocline layers. In this study, we explore a turbulent wall-bounded shear flow of lighter miscible fluid into a quiescent fluid of higher density with a range of Richardson numbersmore » $$0.05\\lesssim Ri\\lesssim 1$$. In order to find a stability parameter that allows close comparison with linear theory and with idealized experiments and numerics, we investigate different definitions of$Ri$$. We find that a gradient Richardson number defined on fluid interface sections where there is no overturning at or adjacent to the maximum density gradient position provides an excellent stability parameter, which captures the Miles–Howard linear stability criterion. For small $$Ri$$ the flow exhibits robust Kelvin–Helmholtz instability, whereas for larger $$Ri$$ interfacial overturning is more intermittent with less frequent Kelvin–Helmholtz events and emerging Holmboe wave instability consistent with a thicker velocity layer compared with the density layer. We compute the perturbed fraction of interface as a quantitative measure of the flow intermittency, which is approximately 1 for the smallest $$Ri$$ but decreases rapidly as $$Ri$ increases, consistent with linear theory. For the perturbed regions, we use the Thorpe scale to characterize the overturning properties of these flows. The probability distribution of the non-zero Thorpe length yields a universal exponential form, suggesting that much of the overturning results from increasingly intermittent Kelvin–Helmholtz instability events. Finally, the distribution of turbulent kinetic energy, conditioned on the intermittency fraction, has a similar form, suggesting an explanation for the universal scaling collapse of the Thorpe length distribution.« less

Probes, Moons, and Kinetic Plasma Wakes

NASA Astrophysics Data System (ADS)

Hutchinson, I. H.; Malaspina, D.; Zhou, C.

2017-10-01

Nonmagnetic objects as varied as probes in tokamaks or moons in space give rise to flowing plasma wakes in which strong distortions of the ion and electron velocity distributions cause electrostatic instabilities. Non-linear phenomena such as electron holes are then produced. Historic probe theory largely ignores the resulting unstable character of the wake, but since we can now simulate computationally the non-linear wake phenomena, a timely challenge is to reassess the influence of these instabilities both on probe measurements and on the wakes themselves. Because the electron instability wavelengths are very short (typically a few Debye-lengths), controlled laboratory experiments face serious challenges in diagnosing them. That is one reason why they have long been neglected as an influence in probe interpretation. Space-craft plasma observations, by contrast, easily obtain sub-Debye-length resolution, but have difficulty with larger-scale reconstruction of the plasma spatial variation. In addition to surveying our developing understanding of wakes in magnetized plasmas, ongoing analysis of Artemis data concerning electron holes observed in the solar-wind lunar wake will be featured. Work partially supported by NASA Grant NNX16AG82G.

Transient Modeling of Hybrid Rocket Low Frequency Instabilities

NASA Technical Reports Server (NTRS)

Karabeyoglu, M. Arif; DeZilwa, Shane; Cantwell, Brian; Zilliac, Greg

2003-01-01

A comprehensive dynamic model of a hybrid rocket has been developed in order to understand and predict the transient behavior including instabilities. A linearized version of the transient model predicted the low-frequency chamber pressure oscillations that are commonly observed in hybrids. The source of the instabilities is based on a complex coupling of thermal transients in the solid fuel, wall heat transfer blocking due to fuel regression rate and the transients in the boundary layer that forms on the fuel surface. The oscillation frequencies predicted by the linearized theory are in very good agreement with 43 motor test results obtained from the hybrid propulsion literature. The motor test results used in the comparison cover a very wide spectrum of parameters including: 1) four separate research and development programs, 2) three different oxidizers (LOX, GOX, N2O), 3) a wide range of motor dimensions (i.e. from 5 inch diameter to 72 inch diameter) and operating conditions and 4) several fuel formulations. A simple universal scaling formula for the frequency of the primary oscillation mode is suggested.

Analysis of Thermo-Diffusive Cellular Instabilities in Continuum Combustion Fronts

NASA Astrophysics Data System (ADS)

Azizi, Hossein; Gurevich, Sebastian; Provatas, Nikolas; Department of Physics, Centre Physics of Materials Team

We explore numerically the morphological patterns of thermo-diffusive instabilities in combustion fronts with a continuum solid fuel source, within a range of Lewis numbers, focusing on the cellular regime. Cellular and dendritic instabilities are found at low Lewis numbers. These are studied using a dynamic adaptive mesh refinement technique that allows very large computational domains, thus allowing us to reduce finite size effects that can affect or even preclude the emergence of these patterns. The distinct types of dynamics found in the vicinity of the critical Lewis number. These types of dynamics are classified as ``quasi-linear'' and characterized by low amplitude cells that may be strongly affected by the mode selection mechanism and growth prescribed by the linear theory. Below this range of Lewis number, highly non-linear effects become prominent and large amplitude, complex cellular and seaweed dendritic morphologies emerge. The cellular patterns simulated in this work are similar to those observed in experiments of flame propagation over a bed of nano-aluminum powder burning with a counter-flowing oxidizer conducted by Malchi et al. It is noteworthy that the physical dimension of our computational domain is roughly close to their experimental setup. This work was supported by a Canadian Space Agency Class Grant ''Percolating Reactive Waves in Particulate Suspensions''. We thank Compute Canada for computing resources.

Ion cyclotron emission studies: Retrospects and prospects

DOE PAGES

Gorelenkov, N. N.

2016-06-05

Ion cyclotron emission (ICE) studies emerged in part from the papers by A.B. Mikhailovskii published in the 1970s. Among the discussed subjects were electromagnetic compressional Alfv,nic cyclotron instabilities with the linear growth rate similar ~ √(n α/n e) driven by fusion products, -particles which draw a lot of attention to energetic particle physics. The theory of ICE excited by energetic particles was significantly advanced at the end of the 20th century motivated by first DT experiments on TFTR and subsequent JET experimental studies which we highlight. Recently ICE theory was advanced by detailed theoretical and experimental studies on spherical torusmore » (ST) fusion devices where the instability signals previously indistinguishable in high aspect ratio tokamaks due to high toroidal magnetic field became the subjects of experiments. Finally, we discuss prospects of ICE theory applications for future burning plasma (BP) experiments such as those to be conducted in ITER device in France, where neutron and gamma rays escaping the plasma create extremely challenging conditions fusion alpha particle diagnostics.« less

Ion cyclotron emission studies: Retrospects and prospects

NASA Astrophysics Data System (ADS)

Gorelenkov, N. N.

2016-05-01

Ion cyclotron emission (ICE) studies emerged in part from the papers by A.B. Mikhailovskii published in the 1970s. Among the discussed subjects were electromagnetic compressional Alfvénic cyclotron instabilities with the linear growth rate √ {n_α /n_e } driven by fusion products, -particles which draw a lot of attention to energetic particle physics. The theory of ICE excited by energetic particles was significantly advanced at the end of the 20th century motivated by first DT experiments on TFTR and subsequent JET experimental studies which we highlight. More recently ICE theory was advanced by detailed theoretical and experimental studies on spherical torus (ST) fusion devices where the instability signals previously indistinguishable in high aspect ratio tokamaks due to high toroidal magnetic field became the subjects of experiments. We discuss further prospects of ICE theory applications for future burning plasma (BP) experiments such as those to be conducted in ITER device in France, where neutron and gamma rays escaping the plasma create extremely challenging conditions fusion alpha particle diagnostics.

Rarefaction-driven Rayleigh–Taylor instability. Part 1. Diffuse-interface linear stability measurements and theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Morgan, R. V.; Likhachev, O. A.; Jacobs, J. W.

Theory and experiments are reported that explore the behaviour of the Rayleigh–Taylor instability initiated with a diffuse interface. Experiments are performed in which an interface between two gases of differing density is made unstable by acceleration generated by a rarefaction wave. Well-controlled, diffuse, two-dimensional and three-dimensional, single-mode perturbations are generated by oscillating the gases either side to side, or vertically for the three-dimensional perturbations. The puncturing of a diaphragm separating a vacuum tank beneath the test section generates a rarefaction wave that travels upwards and accelerates the interface downwards. This rarefaction wave generates a large, but non-constant, acceleration of the order ofmore » $$1000g_{0}$$, where$$g_{0}$$is the acceleration due to gravity. Initial interface thicknesses are measured using a Rayleigh scattering diagnostic and the instability is visualized using planar laser-induced Mie scattering. Growth rates agree well with theoretical values, and with the inviscid, dynamic diffusion model of Duffet al. (Phys. Fluids, vol. 5, 1962, pp. 417–425) when diffusion thickness is accounted for, and the acceleration is weighted using inviscid Rayleigh–Taylor theory. The linear stability formulation of Chandrasekhar (Proc. Camb. Phil. Soc., vol. 51, 1955, pp. 162–178) is solved numerically with an error function diffusion profile using the Riccati method. This technique exhibits good agreement with the dynamic diffusion model of Duffet al. for small wavenumbers, but produces larger growth rates for large-wavenumber perturbations. Asymptotic analysis shows a$$1/k^{2}$$decay in growth rates as$$k\\rightarrow \\infty$$for large-wavenumber perturbations.« less

Rarefaction-driven Rayleigh–Taylor instability. Part 1. Diffuse-interface linear stability measurements and theory

DOE PAGES

Morgan, R. V.; Likhachev, O. A.; Jacobs, J. W.

2016-02-15

Theory and experiments are reported that explore the behaviour of the Rayleigh–Taylor instability initiated with a diffuse interface. Experiments are performed in which an interface between two gases of differing density is made unstable by acceleration generated by a rarefaction wave. Well-controlled, diffuse, two-dimensional and three-dimensional, single-mode perturbations are generated by oscillating the gases either side to side, or vertically for the three-dimensional perturbations. The puncturing of a diaphragm separating a vacuum tank beneath the test section generates a rarefaction wave that travels upwards and accelerates the interface downwards. This rarefaction wave generates a large, but non-constant, acceleration of the order ofmore » $$1000g_{0}$$, where$$g_{0}$$is the acceleration due to gravity. Initial interface thicknesses are measured using a Rayleigh scattering diagnostic and the instability is visualized using planar laser-induced Mie scattering. Growth rates agree well with theoretical values, and with the inviscid, dynamic diffusion model of Duffet al. (Phys. Fluids, vol. 5, 1962, pp. 417–425) when diffusion thickness is accounted for, and the acceleration is weighted using inviscid Rayleigh–Taylor theory. The linear stability formulation of Chandrasekhar (Proc. Camb. Phil. Soc., vol. 51, 1955, pp. 162–178) is solved numerically with an error function diffusion profile using the Riccati method. This technique exhibits good agreement with the dynamic diffusion model of Duffet al. for small wavenumbers, but produces larger growth rates for large-wavenumber perturbations. Asymptotic analysis shows a$$1/k^{2}$$decay in growth rates as$$k\\rightarrow \\infty$$for large-wavenumber perturbations.« less

Multidimensional electron beam-plasma instabilities in the relativistic regime

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bret, A.; Gremillet, L.; Dieckmann, M. E.

2010-12-15

The interest in relativistic beam-plasma instabilities has been greatly rejuvenated over the past two decades by novel concepts in laboratory and space plasmas. Recent advances in this long-standing field are here reviewed from both theoretical and numerical points of view. The primary focus is on the two-dimensional spectrum of unstable electromagnetic waves growing within relativistic, unmagnetized, and uniform electron beam-plasma systems. Although the goal is to provide a unified picture of all instability classes at play, emphasis is put on the potentially dominant waves propagating obliquely to the beam direction, which have received little attention over the years. First, themore » basic derivation of the general dielectric function of a kinetic relativistic plasma is recalled. Next, an overview of two-dimensional unstable spectra associated with various beam-plasma distribution functions is given. Both cold-fluid and kinetic linear theory results are reported, the latter being based on waterbag and Maxwell-Juettner model distributions. The main properties of the competing modes (developing parallel, transverse, and oblique to the beam) are given, and their respective region of dominance in the system parameter space is explained. Later sections address particle-in-cell numerical simulations and the nonlinear evolution of multidimensional beam-plasma systems. The elementary structures generated by the various instability classes are first discussed in the case of reduced-geometry systems. Validation of linear theory is then illustrated in detail for large-scale systems, as is the multistaged character of the nonlinear phase. Finally, a collection of closely related beam-plasma problems involving additional physical effects is presented, and worthwhile directions of future research are outlined.« less

Crossflow Instability on a Wedge-Cone at Mach 3.5

NASA Technical Reports Server (NTRS)

Beeler, George B.; Wilkinson, Stephen P.; Balakumar, P.; McDaniel, Keith S.

2012-01-01

As a follow-on activity to the HyBoLT flight experiment, a six degree half angle wedge-cone model at zero angle of attack has been employed to experimentally and computationally study the boundary layer crossflow instability at Mach 3.5 under low disturbance freestream conditions. Computed meanflow and linear stability analysis results are presented along with corresponding experimental Pitot probe data. Using a model-mounted probe survey apparatus, data acquired to date show a well defined stationary crossflow vortex pattern on the flat wedge surface. This effort paves the way for additional detailed, calibrated flow field measurements of the crossflow instability, both stationary and traveling modes, and transition-to-turbulence under quiet flow conditions as a means of validating existing stability theory and providing a foundation for dynamic flight instrumentation development.

A cosmic ray driven instability

NASA Technical Reports Server (NTRS)

Dorfi, E. A.; Drury, L. O.

1985-01-01

The interaction between energetic charged particles and thermal plasma which forms the basis of diffusive shock acceleration leads also to interesting dynamical phenomena. For a compressional mode propagating in a system with homogeneous energetic particle pressure it is well known that friction with the energetic particles leads to damping. The linear theory of this effect has been analyzed in detail by Ptuskin. Not so obvious is that a non-uniform energetic particle pressure can addition amplify compressional disturbances. If the pressure gradient is sufficiently steep this growth can dominate the frictional damping and lead to an instability. It is important to not that this effect results from the collective nature of the interaction between the energetic particles and the gas and is not connected with the Parker instability, nor with the resonant amplification of Alfven waves.

The nonlinear interaction of Tollmien-Schlichting waves and Taylor-Goertler vortices in curved channel flows

NASA Technical Reports Server (NTRS)

Hall, P.; Smith, F. T.

1987-01-01

It is known that a viscous fluid flow with curved streamlines can support both Tollmien-Schlichting and Taylor-Goertler instabilities. In a situation where both modes are possible on the basis of linear theory a nonlinear theory must be used to determine the effect of the interaction of the instabilities. The details of this interaction are of practical importance because of its possible catastrophic effects on mechanisms used for laminar flow control. This interaction is studied in the context of fully developed flows in curved channels. A part form technical differences associated with boundary layer growth the structures of the instabilities in this flow are very similar to those in the practically more important external boundary layer situation. The interaction is shown to have two distinct phases depending on the size of the disturbances. At very low amplitudes two oblique Tollmein-Schlichting waves interact with a Goertler vortex in such a manner that the amplitudes become infinite at a finite time. This type of interaction is described by ordinary differential amplitude equations with quadratic nonlinearities.

A Reduced Model for the Magnetorotational Instability

NASA Astrophysics Data System (ADS)

Jamroz, Ben; Julien, Keith; Knobloch, Edgar

2008-11-01

The magnetorotational instability is investigated within the shearing box approximation in the large Elsasser number regime. In this regime, which is of fundamental importance to astrophysical accretion disk theory, shear is the dominant source of energy, but the instability itself requires the presence of a weaker vertical magnetic field. Dissipative effects are weaker still. However, they are sufficiently large to permit a nonlinear feedback mechanism whereby the turbulent stresses generated by the MRI act on and modify the local background shear in the angular velocity profile. To date this response has been omitted in shearing box simulations and is captured by a reduced pde model derived here from the global MHD fluid equations using multiscale asymptotic perturbation theory. Results from numerical simulations of the reduced pde model indicate a linear phase of exponential growth followed by a nonlinear adjustment to algebraic growth and decay in the fluctuating quantities. Remarkably, the velocity and magnetic field correlations associated with these algebraic growth and decay laws conspire to achieve saturation of the angular momentum transport. The inclusion of subdominant ohmic dissipation arrests the algebraic growth of the fluctuations on a longer, dissipative time scale.

Development of the electrothermal instability from resistive inclusions

NASA Astrophysics Data System (ADS)

Yu, Edmund; Awe, T. J.; Bauer, B. S.; Yates, K. C.; Yelton, W. G.; Hutchinson, T. M.; Fuelling, S.; McKenzie, B. B.; Peterson, K. J.

2016-10-01

The magneto Rayleigh-Taylor (MRT) instability limits the performance of all magnetically imploded systems. In the case of compressing metal liners, as in the magnetized liner inertial fusion concept, a dominant seed for MRT is believed to be the electrothermal instability (ETI). Here, linear theory predicts the most unstable mode manifests as horizontal (i.e. perpendicular to current flow) bands of heated and expanded metal. However, how do such bands, known as striations, actually develop from a smooth metal surface? Recent experiments on ETI evolution, performed at the University of Nevada, Reno, provide a possible answer: pre-shot characterization of aluminum rods show numerous resistive inclusions, several microns in diameter and distributed throughout the rod. In this work, we use 3D MHD simulation and analytic theory to explore how current redistribution around these isolated inclusions, combined with ETI, can lead to rapid formation of the global striation structures. Later in time, striations expand and form density perturbations much larger than the initial inclusion size. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the National Nuclear Security Administration under DE-AC04-94AL85000.

Experimental investigation of Rayleigh Taylor instability in elastic-plastic materials

NASA Astrophysics Data System (ADS)

Haley, Aaron Alan; Banerjee, Arindam

2010-11-01

The interface of an elastic-plastic plate accelerated by a fluid of lower density is Rayleigh Taylor (RT) unstable, the growth being mitigated by the mechanical strength of the plate. The instability is observed when metal plates are accelerated by high explosives, in explosive welding, and in volcanic island formation due to the strength of the inner crust. In contrast to the classical case involving Newtonian fluids, RT instability in accelerated solids is not well understood. The difficulties for constructing a theory for the linear growth phase in solids is essentially due to the character of elastic-plastic constitutive properties which has a nonlinear dependence on the magnitude of the rate of deformation. Experimental investigation of the phenomena is difficult due to the exceedingly small time scales (in high energy density experiments) and large measurement uncertainties of material properties. We performed experiments on our Two-Wheel facility to study the linear stage of the incompressible RT instability in elastic-plastic materials (yogurt) whose properties were well characterized. Rotation of the wheels imparted a constant centrifugal acceleration on the material interface that was cut with a small sinusoidal ripple. The controlled initial conditions and precise acceleration amplitudes are levied to investigate transition from elastic to plastic deformation and allow accurate and detailed measurements of flow properties.

Black hole perturbations in vector-tensor theories: the odd-mode analysis

NASA Astrophysics Data System (ADS)

Kase, Ryotaro; Minamitsuji, Masato; Tsujikawa, Shinji; Zhang, Ying-li

2018-02-01

In generalized Proca theories with vector-field derivative couplings, a bunch of hairy black hole solutions have been derived on a static and spherically symmetric background. In this paper, we formulate the odd-parity black hole perturbations in generalized Proca theories by expanding the corresponding action up to second order and investigate whether or not black holes with vector hair suffer ghost or Laplacian instabilities. We show that the models with cubic couplings G3(X), where X=‑AμAμ/2 with a vector field Aμ, do not provide any additional stability condition as in General Relativity. On the other hand, the exact charged stealth Schwarzschild solution with a nonvanishing longitudinal vector component A1, which originates from the coupling to the Einstein tensor GμνAμ Aν equivalent to the quartic coupling G4(X) containing a linear function of X, is unstable in the vicinity of the event horizon. The same instability problem also persists for hairy black holes arising from general quartic power-law couplings G4(X) ⊃ β4 Xn with the nonvanishing A1, while the other branch with A1=0 can be consistent with conditions for the absence of ghost and Laplacian instabilities. We also discuss the case of other exact and numerical black hole solutions associated with intrinsic vector-field derivative couplings and show that there exists a wide range of parameter spaces in which the solutions suffer neither ghost nor Laplacian instabilities against odd-parity perturbations.

1985 Particle Accelerator Conference: Accelerator Engineering and Technology, 11th, Vancouver, Canada, May 13-16, 1985, Proceedings

NASA Astrophysics Data System (ADS)

Strathdee, A.

1985-10-01

The topics discussed are related to high-energy accelerators and colliders, particle sources and electrostatic accelerators, controls, instrumentation and feedback, beam dynamics, low- and intermediate-energy circular accelerators and rings, RF and other acceleration systems, beam injection, extraction and transport, operations and safety, linear accelerators, applications of accelerators, radiation sources, superconducting supercolliders, new acceleration techniques, superconducting components, cryogenics, and vacuum. Accelerator and storage ring control systems are considered along with linear and nonlinear orbit theory, transverse and longitudinal instabilities and cures, beam cooling, injection and extraction orbit theory, high current dynamics, general beam dynamics, and medical and radioisotope applications. Attention is given to superconducting RF structures, magnet technology, superconducting magnets, and physics opportunities with relativistic heavy ion accelerators.

Exact near-onset analysis of the spin-density-wave instability in ferromagnetic superconductors: The linearly polarized state

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hu, C.

1984-09-01

Using an approach similar to Abvikosov's theory of the vortex state near H/sub c/2, we have performed an exact, near-onset analysis of a spin-density-wave instability leading to the ''linearly polarized state'' of Greenside et al. in ferromagnetic superconductors. The approach is based on a generalized Ginzburg-Landau theory for such materials, as formulated by Blount and Varma. Two models have been considered. In the (..cap alpha..,..beta..) model, where the bulk magnetic energy is taken to be (1/2)..cap alpha../sub m/M/sup 2/+(1/4)..beta../sub m/M/sup 4/, we find the transition to be second order, and obtain explicit formulas for various physical quantities to leading ordermore » in the deviation from onset. We have also rigorously analyzed the most favored spatial structure just below onset, among all possibilities allowed by the instability, and have concluded that a plane-wave-like structure is favored in a physical limit considered. In the (..cap alpha..,..gamma..) model, where the bulk magnetic energy is taken to be (1/2)..cap alpha../sub m/M/sup 2/+(1/6)..gamma../sub m/M/sup 6/ as is supported by recent experiments for ErRh/sub 4/B/sub 4/, we find the transition to be first order. This approach is then confined to an unphysical branch, which does not permit us to calculate various physical quantities on the physical branch.« less

Summer Study Program in Geophysical Fluid Dynamics, The Woods Hole Oceanographic Institution. Baroclinic Instability and Ocean Fronts.

DTIC Science & Technology

1983-11-01

spectrum of the linear stability theory has multiple roots with zero real parts. Then the general forms of the amplitude equations may be found for given...76 Dynamical Generation of Eastern Boundary Currents George eronis. .......................... 77 ..Amplitude Equations Edward...Associated Countercurrent. Benoit Cushman-Roisin ....... .................... ... 103 Turbulently Generated Eastern Boundary Currents Roger L. Hughes

Parametric Decay Instability and Dissipation of Low-frequency Alfvén Waves in Low-beta Turbulent Plasmas

NASA Astrophysics Data System (ADS)

Fu, Xiangrong; Li, Hui; Guo, Fan; Li, Xiaocan; Roytershteyn, Vadim

2018-03-01

Evolution of the parametric decay instability (PDI) of a circularly polarized Alfvén wave in a turbulent low-beta plasma background is investigated using 3D hybrid simulations. It is shown that the turbulence reduces the growth rate of PDI as compared to the linear theory predictions, but PDI can still exist. Interestingly, the damping rate of the ion acoustic mode (as the product of PDI) is also reduced as compared to the linear Vlasov predictions. Nonetheless, significant heating of ions in the direction parallel to the background magnetic field is observed due to resonant Landau damping of the ion acoustic waves. In low-beta turbulent plasmas, PDI can provide an important channel for energy dissipation of low-frequency Alfvén waves at a scale much larger than the ion kinetic scales, different from the traditional turbulence dissipation models.

The two-dimensional instability of an incompressible vortex in a tube with energy-absorbent walls

NASA Astrophysics Data System (ADS)

Broadbent, E. G.; Moore, D. W.

1994-07-01

We have previously shown that a Rankine vortex in a compressible fluid is unstable to a perturbation in cross section, e.g. to a slightly eccentric ellipse. This result is surprising, because compressibility leads to a loss of energy from the perturbed vortex by acoustic radiation. An explanation, valid for small swirl Mach numbers, was provided by Kop'ev and Leont'ev. For small Mach numbers the flow in the neighborhood of the vortex can be treated as incompressible, from which it follows that the kinetic energy is greater for the circular vortex than for any other nearby shape. Thus the loss of energy by acoustic radiation will result in increasing departures from a circular cross section. We assert here that the instability is not inherently acoustic, but that any mechanism which can remove energy will result in instability. To support our contention, we examine the Rankine vortex in a concentric circular tube which has compliant walls. Linear theory first establishes that the instability exists in this case and an approximate theory for a small region of vorticity shows that the distortion increases indefinitely. This is confirmed, without the restriction on size, by a numerical solution of the integro-differential equation based on contour dynamics.

The Stability and Interfacial Motion of Multi-layer Radial Porous Media and Hele-Shaw Flows

NASA Astrophysics Data System (ADS)

Gin, Craig; Daripa, Prabir

2017-11-01

In this talk, we will discuss viscous fingering instabilities of multi-layer immiscible porous media flows within the Hele-Shaw model in a radial flow geometry. We study the motion of the interfaces for flows with both constant and variable viscosity fluids. We consider the effects of using a variable injection rate on multi-layer flows. We also present a numerical approach to simulating the interface motion within linear theory using the method of eigenfunction expansion. We compare these results with fully non-linear simulations.

Optical solitons, explicit solutions and modulation instability analysis with second-order spatio-temporal dispersion

NASA Astrophysics Data System (ADS)

Inc, Mustafa; Isa Aliyu, Aliyu; Yusuf, Abdullahi; Baleanu, Dumitru

2017-12-01

This paper obtains the dark, bright, dark-bright or combined optical and singular solitons to the nonlinear Schrödinger equation (NLSE) with group velocity dispersion coefficient and second-order spatio-temporal dispersion coefficient, which arises in photonics and waveguide optics and in optical fibers. The integration algorithm is the sine-Gordon equation method (SGEM). Furthermore, the explicit solutions of the equation are derived by considering the power series solutions (PSS) theory and the convergence of the solutions is guaranteed. Lastly, the modulation instability analysis (MI) is studied based on the standard linear-stability analysis and the MI gain spectrum is obtained.

Stability of a jet in confined pressure-driven biphasic flows at low reynolds numbers.

PubMed

Guillot, Pierre; Colin, Annie; Utada, Andrew S; Ajdari, Armand

2007-09-07

Motivated by its importance for microfluidic applications, we study the stability of jets formed by pressure-driven concentric biphasic flows in cylindrical capillaries. The specificity of this variant of the classical Rayleigh-Plateau instability is the role of the geometry which imposes confinement and Poiseuille flow profiles. We experimentally evidence a transition between situations where the flow takes the form of a jet and regimes where drops are produced. We describe this as the transition from convective to absolute instability, within a simple linear analysis using lubrication theory for flows at low Reynolds number, and reach remarkable agreement with the data.

Instabilities in rapid solidification of multi-component alloys

NASA Astrophysics Data System (ADS)

Altieri, Anthony L.; Davis, Stephen H.

2017-10-01

Rapid solidification of multi-component liquids occurs in many modern applications such as additive manufacturing. In the present work the interface departures from equilibrium consist of the segregation coefficient and liquidus slope depending on front speed, the one-sided, frozen-temperature approximation, and the alloy behaving as the superposition of individual components. Linear-stability theory is applied, showing that the cellular and oscillatory instabilities of the binary case are modified. The addition of components tends to destabilize the interface while the addition of a single large-diffusivity material can entirely suppress the oscillatory mode. Multiple minima in the neutral curve for the cellular mode occur.

Nonlinear Development and Secondary Instability of Traveling Crossflow Vortices

NASA Technical Reports Server (NTRS)

Li, Fei; Choudhari, Meelan M.; Duan, Lian; Chang, Chau-Lyan

2014-01-01

Transition research under NASA's Aeronautical Sciences Project seeks to develop a validated set of variable fidelity prediction tools with known strengths and limitations, so as to enable "sufficiently" accurate transition prediction and practical transition control for future vehicle concepts. This paper builds upon prior effort targeting the laminar breakdown mechanisms associated with stationary crossflow instability over a swept-wing configuration relevant to subsonic aircraft with laminar flow technology. Specifically, transition via secondary instability of traveling crossflow modes is investigated as an alternate scenario for transition. Results show that, for the parameter range investigated herein, secondary instability of traveling crossflow modes becomes insignificant in relation to the secondary instability of the stationary modes when the relative initial amplitudes of the traveling crossflow instability are lower than those of the stationary modes by approximately two orders of magnitudes or more. Linear growth predictions based on the secondary instability theory are found to agree well with those based on PSE and DNS, with the most significant discrepancies being limited to spatial regions of relatively weak secondary growth, i.e., regions where the primary disturbance amplitudes are smaller in comparison to its peak amplitude. Nonlinear effects on secondary instability evolution is also investigated and found to be initially stabilizing, prior to breakdown.

Interplay between protons and electrons in a firehose-unstable plasma: Particle-in-cell simulations

NASA Astrophysics Data System (ADS)

Bourdin, Philippe-A.; Maneva, Yana

2017-04-01

Kinetic plasma instabilities originating from unstable, non-Maxwellian shapes of the velocity distribution functions serve as internal degrees of freedom in plasma dynamics, and play an important role near solar current sheets and in solar wind plasmas. In the presence of strong temperature anisotropy (different thermal spreads in the velocity space with respect to the mean magnetic field), plasmas are unstable either to the firehose mode or to the mirror mode in the case of predominant parallel and perpendicular temperatures, respectively. The growth rates of these instabilities and their thresholds depend on plasma properties, such as the temperature anisotropy and the plasma beta. The physics of the temperature anisotropy-driven instabilities becomes even more diverse for various shapes of velocity distribution functions and the particle species of interest. Recent studies based on a linear instability analysis show an interplay in the firehose instability between protons and electrons when the both types of particle species are prone to unstable velocity distribution functions and their instability thresholds. In this work we perform for the first time 3D nonlinear PIC (particle-in-cell) numerical simulations to test for the linear-theory prediction of the simultaneous proton-electron firehose instability. The simulation setup allows us not only to evaluate the growth rate of each firehose instability, but also to track its nonlinear evolution and the related wave-particle interactions such as the pitch-angle scattering or saturation effects. The specialty of our simulation is that the magnetic and electric fields have a low numerical noise level by setting a sufficiently large number of super-particles into the simulation box and enhancing the statistical significance of the velocity distribution functions. We use the iPIC3D code with fully periodic boundaries under various conditions of the electron-to-proton mass ratio, which gives insight into the instability interplay at the intermediate electron-proton and on the scaling of our results towards more realistic particle settings.

On the buckling of elastic rings by external confinement.

PubMed

Hazel, Andrew L; Mullin, Tom

2017-05-13

We report the results of an experimental and numerical investigation into the buckling of thin elastic rings confined within containers of circular or regular polygonal cross section. The rings float on the surface of water held in the container and controlled removal of the fluid increases the confinement of the ring. The increased compressive forces can cause the ring to buckle into a variety of shapes. For the circular container, finite perturbations are required to induce buckling, whereas in polygonal containers the buckling occurs through a linear instability that is closely related to the canonical Euler column buckling. A model based on Kirchhoff-Love beam theory is developed and solved numerically, showing good agreement with the experiments and revealing that in polygons increasing the number of sides means that buckling occurs at reduced levels of confinement.This article is part of the themed issue 'Patterning through instabilities in complex media: theory and applications.' © 2017 The Author(s).

Supersonic jet noise generated by large scale instabilities

NASA Technical Reports Server (NTRS)

Seiner, J. M.; Mclaughlin, D. K.; Liu, C. H.

1982-01-01

The role of large scale wavelike structures as the major mechanism for supersonic jet noise emission is examined. With the use of aerodynamic and acoustic data for low Reynolds number, supersonic jets at and below 70 thousand comparisons are made with flow fluctuation and acoustic measurements in high Reynolds number, supersonic jets. These comparisons show that a similar physical mechanism governs the generation of sound emitted in he principal noise direction. These experimental data are further compared with a linear instability theory whose prediction for the axial location of peak wave amplitude agrees satisfactorily with measured phased averaged flow fluctuation data in the low Reynolds number jets. The agreement between theory and experiment in the high Reynolds number flow differs as to the axial location for peak flow fluctuations and predicts an apparent origin for sound emission far upstream of the measured acoustic data.

On the stability of soliton and hairy black hole solutions of 𝔰𝔲(N) Einstein-Yang-Mills theory with a negative cosmological constant

NASA Astrophysics Data System (ADS)

Baxter, J. Erik; Winstanley, Elizabeth

2016-02-01

We investigate the stability of spherically symmetric, purely magnetic, soliton and black hole solutions of four-dimensional 𝔰𝔲(N) Einstein-Yang-Mills theory with a negative cosmological constant Λ. These solutions are described by N - 1 magnetic gauge field functions ωj. We consider linear, spherically symmetric, perturbations of these solutions. The perturbations decouple into two sectors, known as the sphaleronic and gravitational sectors. For any N, there are no instabilities in the sphaleronic sector if all the magnetic gauge field functions ωj have no zeros and satisfy a set of N - 1 inequalities. In the gravitational sector, we prove that there are solutions which have no instabilities in a neighbourhood of stable embedded 𝔰𝔲(2) solutions, provided the magnitude of the cosmological constant |" separators=" Λ | is sufficiently large.

On the buckling of elastic rings by external confinement

PubMed Central

Hazel, Andrew L.

2017-01-01

We report the results of an experimental and numerical investigation into the buckling of thin elastic rings confined within containers of circular or regular polygonal cross section. The rings float on the surface of water held in the container and controlled removal of the fluid increases the confinement of the ring. The increased compressive forces can cause the ring to buckle into a variety of shapes. For the circular container, finite perturbations are required to induce buckling, whereas in polygonal containers the buckling occurs through a linear instability that is closely related to the canonical Euler column buckling. A model based on Kirchhoff–Love beam theory is developed and solved numerically, showing good agreement with the experiments and revealing that in polygons increasing the number of sides means that buckling occurs at reduced levels of confinement. This article is part of the themed issue ‘Patterning through instabilities in complex media: theory and applications.’ PMID:28373386

Navier-Stokes simulation of the crossflow instability in swept-wing flows

NASA Technical Reports Server (NTRS)

Reed, Helen L.

1989-01-01

The computational modeling of the transition process characteristic of flows over swept wings are described. Specifically, the crossflow instability and crossflow/T-S wave interactions are analyzed through the numerical solution of the full three-dimensional Navier-Stokes equations including unsteadiness, curvature, and sweep. This approach is chosen because of the complexity of the problem and because it appears that linear stability theory is insufficient to explain the discrepancies between different experiments and between theory and experiments. The leading edge region of a swept wing is considered in a three-dimensional spatial simulation with random disturbances as the initial conditions. The work has been closely coordinated with the experimental program of Professor William Saric, examining the same problem. Comparisons with NASA flight test data and the experiments at Arizona State University were a necessary and an important integral part of this work.

Particle in cell simulation of instabilities in space and astrophysical plasmas

NASA Astrophysics Data System (ADS)

Tonge, John William

Several plasma instabilities relevant to space physics are investigated using the parallel PIC plasma simulation code P3arsec. This thesis addresses electrostatic micro-instabilities relevant to ion ring distributions, proceeds to electromagnetic micro-instabilities pertinent to streaming plasmas, and then to the stability of a plasma held in the field of a current rod. The physical relevance of each of these instabilities is discussed, a phenomenological description is given, and analytic and simulation results are presented and compared. Instability of a magnetized plasma with a portion of the ions in a velocity ring distribution around the magnetic field is investigated using simulation and analytic theory. The physics of this distribution is relevant to solar flares, x-ray emission by comets, and pulsars. Physical parameters, including the mass ratio, are near those of a solar flare in the simulation. The simulation and analytic results show agreement in the linear regime. In the nonlinear stage the simulation shows highly accelerated electrons in agreement with the observed spectrum of x-rays emitted by solar flares. A mildly relativistic streaming electron positron plasma with no ambient magnetic field is known to be unstable to electrostatic (two-stream/beam instability) and purely electromagnetic (Weibel) modes. This instability is relevant to highly energetic interstellar phenomena, including pulsars, supernova remnants, and the early universe. It is also important for experiments in which relativistic beams penetrate a background plasma, as in fast ignitor scenarios. Cold analytic theory is presented and compared to simulations. There is good agreement in the regime where cold theory applies. The simulation and theory shows that to properly characterize the instability, directions parallel and perpendicular to propagation of the beams must be considered. A residual magnetic field is observed which may be of astro-physical significance. The stability of a plasma in the magnetic field of a current rod is investigated for various temperature and density profiles. Such a plasma obeys similar physics to a plasma in a dipole magnetic field, while the current rod is much easier to analyze theoretically and realize in simulations. The stability properties of a plasma confined in a dipole field are important for understanding a variety of space phenomena and the Levitated Dipole eXperiment (LDX). Simple energy principle calculations and simulations with a variety of temperature and density profiles show that the plasma is stable to interchange for pressure profiles ∝ r-10/3. The simulations also show that the density profile will be stationary as long as density ∝ r -2 even though the temperature profile may not be stable.

Eikonal instability of Gauss-Bonnet-(anti-)-de Sitter black holes

NASA Astrophysics Data System (ADS)

Konoplya, R. A.; Zhidenko, A.

2017-05-01

Here we have shown that asymptotically anti-de Sitter (AdS) black holes in the Einstein-Gauss-Bonnet (GB) theory are unstable under linear perturbations of space-time in some region of parameters. This (eikonal) instability develops at high multipole numbers. We found the exact parametric regions of the eikonal instability and extended this consideration to asymptotically flat and de Sitter cases. The approach to the threshold of instability is driven by purely imaginary quasinormal modes, which are similar to those found recently in Grozdanov, Kaplis, and Starinets, [J. High Energy Phys. 07 (2016) 151, 10.1007/JHEP07(2016)151] for the higher curvature corrected black hole with the planar horizon. The found instability may indicate limits of holographic applicability of the GB-AdS backgrounds. Recently, through the analysis of critical behavior in AdS space-time in the presence of the Gauss-Bonnet term, it was shown [Deppe et al, Phys. Rev. Lett. 114, 071102 (2015), 10.1103/PhysRevLett.114.071102], that, if the total energy content of the AdS space-time is small, then no black holes can be formed with mass less than some critical value. A similar mass gap was also found when considering collapse of mass shells in asymptotically flat Gauss-Bonnet theories [Frolov, Phys. Rev. Lett. 115, 051102 (2015), 10.1103/PhysRevLett.115.051102]. The found instability of all sufficiently small Einstein-Gauss-Bonnet-AdS, dS and asymptotically flat black holes may explain the existing mass gaps in their formation.

Experimental Observation of Nonlinear Mode Coupling In the Ablative Rayleigh-Taylor Instability on the NIF

NASA Astrophysics Data System (ADS)

Martinez, David

2015-11-01

We investigate on the National Ignition Facility (NIF) the ablative Rayleigh-Taylor (RT) instability in the transition from linear to highly nonlinear regimes. This work is part of the Discovery Science Program on NIF and of particular importance to indirect-drive inertial confinement fusion (ICF) where careful attention to the form of the rise to final peak drive is calculated to prevent the RT instability from shredding the ablator in-flight and leading to ablator mixing into the cold fuel. The growth of the ablative RT instability was investigated using a planar plastic foil with pre-imposed two-dimensional broadband modulations and diagnosed using x-ray radiography. The foil was accelerated for 12ns by the x-ray drive created in a gas-filled Au radiation cavity with a radiative temperature plateau at 175 eV. The dependence on initial conditions was investigated by systematically changing the modulation amplitude, ablator material and the modulation pattern. For each of these cases bubble mergers were observed and the nonlinear evolution of the RT instability showed insensitivity to the initial conditions. This experiment provides critical data needed to validate current theories on the ablative RT instability for indirect drive that relies on the ablative stabilization of short-scale modulations for ICF ignition. This paper will compare the experimental data to the current nonlinear theories. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract DE-AC52-07NA27344. Lawrence Livermore National Security, LLC.

The analysis of harmonic generation coefficients in the ablative Rayleigh-Taylor instability

NASA Astrophysics Data System (ADS)

Lu, Yan; Fan, Zhengfeng; Lu, Xinpei; Ye, Wenhua; Zou, Changlin; Zhang, Ziyun; Zhang, Wen

2017-10-01

In this research, we use the numerical simulation method to investigate the generation coefficients of the first three harmonics and the zeroth harmonic in the Ablative Rayleigh-Taylor Instability. It is shown that the interface shifts to the low temperature side during the ablation process. In consideration of the third-order perturbation theory, the first three harmonic amplitudes of the weakly nonlinear regime are calculated and then the harmonic generation coefficients are obtained by curve fitting. The simulation results show that the harmonic generation coefficients changed with time and wavelength. Using the higher-order perturbation theory, we find that more and more harmonics are generated in the later weakly nonlinear stage, which is caused by the negative feedback of the later higher harmonics. Furthermore, extending the third-order theory to the fifth-order theory, we find that the second and the third harmonics coefficients linearly depend on the wavelength, while the feedback coefficients are almost constant. Further analysis also shows that when the fifth-order theory is considered, the normalized effective amplitudes of second and third harmonics can reach about 25%-40%, which are only 15%-25% in the frame of the previous third-order theory. Therefore, the third order perturbation theory is needed to be modified by the higher-order theory when ηL reaches about 20% of the perturbation wavelength.

Stability properties of solitary waves for fractional KdV and BBM equations

NASA Astrophysics Data System (ADS)

Angulo Pava, Jaime

2018-03-01

This paper sheds new light on the stability properties of solitary wave solutions associated with Korteweg-de Vries-type models when the dispersion is very low. Using a compact, analytic approach and asymptotic perturbation theory, we establish sufficient conditions for the existence of exponentially growing solutions to the linearized problem and so a criterium of spectral instability of solitary waves is obtained for both models. Moreover, the nonlinear stability and spectral instability of the ground state solutions for both models is obtained for some specific regimen of parameters. Via a Lyapunov strategy and a variational analysis, we obtain the stability of the blow-up of solitary waves for the critical fractional KdV equation. The arguments presented in this investigation show promise for use in the study of the instability of traveling wave solutions of other nonlinear evolution equations.

Porosity localizing instability in a compacting porous layer in a pure shear flow and the evolution of porosity band wavelength

NASA Astrophysics Data System (ADS)

Butler, S. L.

2010-09-01

A porosity localizing instability occurs in compacting porous media that are subjected to shear if the viscosity of the solid matrix decreases with porosity ( Stevenson, 1989). This instability may have significant consequences for melt transport in regions of partial melt in the mantle and may significantly modify the effective viscosity of the asthenosphere ( Kohlstedt and Holtzman, 2009). Most analyses of this instability have been carried out assuming an imposed simple shear flow (e.g., Spiegelman, 2003; Katz et al., 2006; Butler, 2009). Pure shear can be realized in laboratory experiments and studying the instability in a pure shear flow allows us to test the generality of some of the results derived for simple shear and the flow pattern for pure shear more easily separates the effects of deformation from rotation. Pure shear flows may approximate flows near the tops of mantle plumes near earth's surface and in magma chambers. In this study, we present linear theory and nonlinear numerical model results for a porosity and strain-rate weakening compacting porous layer subjected to pure shear and we investigate the effects of buoyancy-induced oscillations. The linear theory and numerical model will be shown to be in excellent agreement. We will show that melt bands grow at the same angles to the direction of maximum compression as in simple shear and that buoyancy-induced oscillations do not significantly inhibit the porosity localizing instability. In a pure shear flow, bands parallel to the direction of maximum compression increase exponentially in wavelength with time. However, buoyancy-induced oscillations are shown to inhibit this increase in wavelength. In a simple shear flow, bands increase in wavelength when they are in the orientation for growth of the porosity localizing instability. Because the amplitude spectrum is always dominated by bands in this orientation, band wavelengths increase with time throughout simple shear simulations until the wavelength becomes similar to one compaction length. Once the wavelength becomes similar to one compaction length, the growth of the amplitude of the band slows and shorter wavelength bands that are increasing in amplitude at a greater rate take over. This may provide a mechanism to explain the experimental observation that band spacing is controlled by the compaction length ( Kohlstedt and Holtzman, 2009).

Curvature-Induced Instabilities of Shells

NASA Astrophysics Data System (ADS)

Pezzulla, Matteo; Stoop, Norbert; Steranka, Mark P.; Bade, Abdikhalaq J.; Holmes, Douglas P.

2018-01-01

Induced by proteins within the cell membrane or by differential growth, heating, or swelling, spontaneous curvatures can drastically affect the morphology of thin bodies and induce mechanical instabilities. Yet, the interaction of spontaneous curvature and geometric frustration in curved shells remains poorly understood. Via a combination of precision experiments on elastomeric spherical shells, simulations, and theory, we show how a spontaneous curvature induces a rotational symmetry-breaking buckling as well as a snapping instability reminiscent of the Venus fly trap closure mechanism. The instabilities, and their dependence on geometry, are rationalized by reducing the spontaneous curvature to an effective mechanical load. This formulation reveals a combined pressurelike term in the bulk and a torquelike term in the boundary, allowing scaling predictions for the instabilities that are in excellent agreement with experiments and simulations. Moreover, the effective pressure analogy suggests a curvature-induced subcritical buckling in closed shells. We determine the critical buckling curvature via a linear stability analysis that accounts for the combination of residual membrane and bending stresses. The prominent role of geometry in our findings suggests the applicability of the results over a wide range of scales.

Simulation, Theory, and Observations of the Spectrum of the Rayleigh-Taylor Instability due to Laser Imprint of Planar Targets

NASA Astrophysics Data System (ADS)

Keskinen, M. J.; Karasik, Max; Bates, J. W.; Schmitt, A. J.

2006-10-01

A limitation on the efficiency of high gain direct drive inertial confinement fusion is the extent of pellet disruption caused by the Rayleigh-Taylor (RT) instability. The RT instability can be seeded by pellet surface irregularities and/or laser imprint nonuniformities. It is important to characterize the evolution of the RT instability, e.g., the k-spectrum of areal mass. In this paper we study the time-dependent evolution of the spectrum of the Rayleigh-Taylor instability due to laser imprint in planar targets. This is achieved using the NRL FAST hydrodynamic simulation code together with analytical models. It is found that the optically smoothed laser imprint-driven RT spectrum develops into an inverse power law in k-space after several linear growth times. FAST simulation code results are compared with recent NRL Nike KrF laser experimental data. An analytical model, which is a function of Froude and Atwood numbers, is derived for the RT spectrum and favorably compared with both FAST simulation and Nike observations.

Theoretical and Experimental Methods in the Solution of Missile Nonlinear Roll Problems

DTIC Science & Technology

1978-03-01

OF ILLUSTRATIONS (Continued) 34 Typical Effect of Slot on Induced Rolling Moment .............. 35 35 Effect of Slot on Amplitude of Induced Rolling...Characteristics of Slotted Fill Vehicle .............. 40 41 Effects of Fin Configuration on Stability ..................... 41 42 Release Envelope...missiles depended strongly upon roll rate. The concept of Magnus instability had been developed earlier from the linear theory of missile dynamics, and

Aeroacoustics Computation for Nearly Fully Expanded Supersonic Jets Using the CE/SE Method

NASA Technical Reports Server (NTRS)

Loh, Ching Y.; Hultgren, Lennart S.; Wang, Xiao Y.; Chang, Sin-Chung; Jorgenson, Philip C. E.

2000-01-01

In this paper, the space-time conservation element solution element (CE/SE) method is tested in the classical axisymmetric jet instability problem, rendering good agreement with the linear theory. The CE/SE method is then applied to numerical simulations of several nearly fully expanded axisymmetric jet flows and their noise fields and qualitative agreement with available experimental and theoretical results is demonstrated.

Terrorist Networks, Money Laundering Schemes, and Nation Stability

DTIC Science & Technology

2010-06-01

Stabilization Initiative  $106,400,000.00 to recon/stab  Seven countries per fiscal year  American Academy of Actuaries insured losses (relatively...Indicators  Political Instability Task Force Report  Mathematical Model (Linear Program Optimization)  Develop a value system (utility theory) to...deeper ahead. 47 LIST OF REFERENCES American Academy of Actuaries (Finance Data). Retrieved September 20, 2009, from, http://www.actuary.org

Corrugation Instability of a Coronal Arcade

NASA Astrophysics Data System (ADS)

Klimushkin, D. Y.; Nakariakov, V. M.; Mager, P. N.; Cheremnykh, O. K.

2017-12-01

We analyse the behaviour of linear magnetohydrodynamic perturbations of a coronal arcade modelled by a half-cylinder with an azimuthal magnetic field and non-uniform radial profiles of the plasma pressure, temperature, and the field. Attention is paid to the perturbations with short longitudinal (in the direction along the arcade) wavelengths. The radial structure of the perturbations, either oscillatory or evanescent, is prescribed by the radial profiles of the equilibrium quantities. Conditions for the corrugation instability of the arcade are determined. It is established that the instability growth rate increases with decreases in the longitudinal wavelength and the radial wave number. In the unstable mode, the radial perturbations of the magnetic field are stronger than the longitudinal perturbations, creating an almost circularly corrugated rippling of the arcade in the longitudinal direction. For coronal conditions, the growth time of the instability is shorter than one minute, decreasing with an increase in the temperature. Implications of the developed theory for the dynamics of coronal active regions are discussed.

Gyrokinetic theory of slab universal modes and the non-existence of the gradient drift coupling (GDC) instability

NASA Astrophysics Data System (ADS)

Rogers, Barrett N.; Zhu, Ben; Francisquez, Manaure

2018-05-01

A gyrokinetic linear stability analysis of a collisionless slab geometry in the local approximation is presented. We focus on k∥=0 universal (or entropy) modes driven by plasma gradients at small and large plasma β. These are small scale non-MHD instabilities with growth rates that typically peak near k⊥ρi˜1 and vanish in the long wavelength k⊥→0 limit. This work also discusses a mode known as the Gradient Drift Coupling (GDC) instability previously reported in the gyrokinetic literature, which has a finite growth rate γ=√{β/[2 (1 +β)] }Cs/|Lp| with Cs2=p0/ρ0 for k⊥→0 and is universally unstable for 1 /Lp≠0 . We show that the GDC instability is a spurious, unphysical artifact that erroneously arises due to the failure to respect the total equilibrium pressure balance p0+B02/(8 π)=constant , which renders the assumption B0'=0 inconsistent if p0'≠0 .

Wave models for turbulent free shear flows

NASA Technical Reports Server (NTRS)

Liou, W. W.; Morris, P. J.

1991-01-01

New predictive closure models for turbulent free shear flows are presented. They are based on an instability wave description of the dominant large scale structures in these flows using a quasi-linear theory. Three model were developed to study the structural dynamics of turbulent motions of different scales in free shear flows. The local characteristics of the large scale motions are described using linear theory. Their amplitude is determined from an energy integral analysis. The models were applied to the study of an incompressible free mixing layer. In all cases, predictions are made for the development of the mean flow field. In the last model, predictions of the time dependent motion of the large scale structure of the mixing region are made. The predictions show good agreement with experimental observations.

Ion velocity analysis of rotating structures in a magnetic linear plasma device

NASA Astrophysics Data System (ADS)

Claire, N.; Escarguel, A.; Rebont, C.; Doveil, F.

2018-06-01

The MISTRAL device is designed to produce a linear magnetized plasma column. It has been used a few years ago to study a nonlinear low frequency instability exhibiting an azimuthal number m = 2. By changing the experimental configuration of MISTRAL, this work shows experimental results on an m = 1 rotating instability with strongly different behavior. The spatio-temporal evolution of the ion velocity distribution function given by a laser-induced fluorescence diagnostic is measured to infer the radial and azimuthal velocities, ion fluxes, and electric fields. The naive image of a plasma exhibiting a global rotation is again invalidated in this m = 1 mode but in a different way. Contrary to the m = 2 mode, the rotation frequency of the instability is lower than the ion cyclotron frequency and ions exhibit a complex behavior with a radial outward flux inside the unstable arm and azimuthal ion fluxes always directed toward the unstable arm. The azimuthal ion velocity is close to zero inside the ionization region, whereas the radial ion velocity grows linearly with radius. The radial electric field is oriented inward inside the unstable arm and outward outside. An axial velocity perturbation is also present, indicating that contrary to the m = 2 mode, the m = 1 mode is not a flute mode. These results cannot be easily interpreted with existing theories.

Linear instability of supersonic plane wakes

NASA Technical Reports Server (NTRS)

Papageorgiou, D. T.

1989-01-01

In this paper we present a theoretical and numerical study of the growth of linear disturbances in the high-Reynolds-number and laminar compressible wake behind a flat plate which is aligned with a uniform stream. No ad hoc assumptions are made as to the nature of the undisturbed flow (in contrast to previous investigations) but instead the theory is developed rationally by use of proper wake-profiles which satisfy the steady equations of motion. The initial growth of near wake perturbation is governed by the compressible Rayleigh equation which is studied analytically for long- and short-waves. These solutions emphasize the asymptotic structures involved and provide a rational basis for a nonlinear development. The evolution of arbitrary wavelength perturbations is addressed numerically and spatial stability solutions are presented that account for the relative importance of the different physical mechanisms present, such as three-dimensionality, increasing Mach numbers enough (subsonic) Mach numbers, there exists a region of absolute instability very close to the trailing-edge with the majority of the wake being convectively unstable. At higher Mach numbers (but still not large-hypersonic) the absolute instability region seems to disappear and the maximum available growth-rates decrease considerably. Three-dimensional perturbations provide the highest spatial growth-rates.

Weak turbulence theory for beam-plasma interaction

NASA Astrophysics Data System (ADS)

Yoon, Peter H.

2018-01-01

The kinetic theory of weak plasma turbulence, of which Ronald C. Davidson was an important early pioneer [R. C. Davidson, Methods in Nonlinear Plasma Theory, (Academic Press, New York, 1972)], is a venerable and valid theory that may be applicable to a large number of problems in both laboratory and space plasmas. This paper applies the weak turbulence theory to the problem of gentle beam-plasma interaction and Langmuir turbulence. It is shown that the beam-plasma interaction undergoes various stages of physical processes starting from linear instability, to quasilinear saturation, to mode coupling that takes place after the quasilinear stage, followed by a state of quasi-static "turbulent equilibrium." The long term quasi-equilibrium stage is eventually perturbed by binary collisional effects in order to bring the plasma to a thermodynamic equilibrium with increased entropy.

Thermonuclear instabilities and plasma edge transport in tokamaks

NASA Astrophysics Data System (ADS)

Fulop, Tunde Maria

High-energy ions generated by fusion reactions in a burning fusion plasma may give rise to different types of wave instabilities. The present thesis investigates two types of such instabilities which recently have been observed in fusion experiments: the Toroidal Alfvén Eigenmode (TAE) instability and the magnetoacoustic cyclotron instability (MCI) which is predicted to give rise to ion cyclotron emission (ICE). The TAE instability may degrade the confinement of fusion-produced high energy alpha particles and adversely affect the possibilities of reaching ignition. The present work derives it generalized expression for the linear growth rate of the instability, by including the effects of finite orbit width and finite Larmor radius of energetic particles, as well as the effects of mode localization and the possible mode excitation by both passing and trapped energetic ions. ICE does not threaten the plasma performance, but it might be useful as a fast ion diagnostic. The ICE originates from the MCI involving fast magnetoacoustic waves driven unstable by toroidicity-affected cyclotron resonance with fast ions. In the present thesis a detailed numerical and analytical investigation of this instability is presented, that explains most of the experimental ICE features observed in JET and TFTR. Moreover, the radial and poloidal localization of the fast magnetoacoustic eigenmodes is investigated, including the effects of toroidicity, ellipticity, the presence of a subpopulation of high energy ions and various profiles of the bulk ion density. In a fusion reactor, the transport of the particles near the edge have a strong influence on the global confinement of the plasma. In the edge region, where neutral atoms and impurity ions are abundant and the temperature and density gradients are large, the assumptions of the standard neoclassical theory break down. In this thesis, we explore the effect of neutral particles on the ion flow shear in the edge region. Furthermore, the neoclassical transport theory in an impure, toroidally rotating plasma is extended to allow for steeper pressure and temperature gradients than are usually considered.

Fokker-Planck analysis of transverse collective instabilities in electron storage rings

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lindberg, Ryan R.

We analyze single bunch transverse instabilities due to wakefields using a Fokker-Planck model. We first expand on the work of T. Suzuki, Part. Accel. 12, 237 (1982) to derive the theoretical model including chromaticity, both dipolar and quadrupolar transverse wakefields, and the effects of damping and diffusion due to the synchrotron radiation. We reduce the problem to a linear matrix equation, whose eigenvalues and eigenvectors determine the collective stability of the beam. We then show that various predictions of the theory agree quite well with results from particle tracking simulations, including the threshold current for transverse instability and the profilemore » of the unstable mode. In particular, we find that predicting collective stability for high energy electron beams at moderate to large values of chromaticity requires the full Fokker-Planck analysis to properly account for the effects of damping and diffusion due to synchrotron radiation.« less

Patterns induced by super cross-diffusion in a predator-prey system with Michaelis-Menten type harvesting.

PubMed

Liu, Biao; Wu, Ranchao; Chen, Liping

2018-04-01

Turing instability and pattern formation in a super cross-diffusion predator-prey system with Michaelis-Menten type predator harvesting are investigated. Stability of equilibrium points is first explored with or without super cross-diffusion. It is found that cross-diffusion could induce instability of equilibria. To further derive the conditions of Turing instability, the linear stability analysis is carried out. From theoretical analysis, note that cross-diffusion is the key mechanism for the formation of spatial patterns. By taking cross-diffusion rate as bifurcation parameter, we derive amplitude equations near the Turing bifurcation point for the excited modes by means of weakly nonlinear theory. Dynamical analysis of the amplitude equations interprets the structural transitions and stability of various forms of Turing patterns. Furthermore, the theoretical results are illustrated via numerical simulations. Copyright © 2018. Published by Elsevier Inc.

Composite rogue waves and modulation instability for the three-coupled Hirota system in an optical fiber

NASA Astrophysics Data System (ADS)

Chai, Han-Peng; Tian, Bo; Chai, Jun; Du, Zhong

2017-10-01

We investigate the three-coupled Hirota system, which is applied to model the long distance communication and ultrafast signal routing systems governing the propagation of light pulses. With the aid of the Darboux dressing transformation, composite rogue wave solutions are derived. Spatial-temporal structures, including the four-petaled structure for the three-coupled Hirota system, are exhibited. We find that the four-petaled rogue waves occur in two of the three components, whereas the eye-shaped rogue wave occurs in the other one. The composite rogue waves can split up into two or three single rogue waves. The corresponding conditions for the occurrence of such phenomena are discussed and presented. We find that the relative position of every single rogue wave is influenced by the ratios of certain parameters. Besides, the linear instability analysis is performed, and our results agree with those from the baseband modulation instability theory.

High-Frequency Planetary Waves in the Polar Middle Atmosphere as seen in a data Assimilation System

NASA Technical Reports Server (NTRS)

Coy, L.; Stajner, I.; DaSilva, A. M.; Joiner, J.; Rood, R. B.; Pawson, S.; Lin, S. J.

2003-01-01

This study examines the winter southern hemisphere vortex of 1998 using four times daily output from a data assimilation system to focus on the polar 2-day, wave number 2 component of the 4-day wave. The data assimilation system products are from a test version of the finite volume data assimilation system (fvDAS) being developed at Goddard Space Flight Center (GSFC) and include an ozone assimilation system. Results show that the polar 2-day wave dominates during July 1998 at 70 degrees. The period of the quasi 2-day wave is somewhat shorter than 2 days (about 1.7 days) during July 1998 with an average perturbation temperature amplitude for the month of over 2.5 K. The 2-day wave propagates more slowly than the zonal mean zonal wind, consistent with Rossby wave theory, and has EP flux divergence regions associated with regions of negative horizontal potential vorticity gradients, as expected from linear instability theory. Results for the assimilation-produced ozone mixing ratio show that the 2-day wave represents a major source of ozone variation in this region. The ozone wave in the assimilation system is in good agreement with the wave seen in the POAM (Polar Ozone and Aerosol Measurement) ozone observations for the same time period. Some differences with linear instability theory are noted as well as spectral peaks in the ozone field, not seen in the temperature field, that may be a consequence of advection.

Saturation and energy-conversion efficiency of auroral kilometric radiation

NASA Technical Reports Server (NTRS)

Wu, C. S.; Tsai, S. T.; Xu, M. J.; Shen, J. W.

1981-01-01

A quasi-linear theory is used to study the saturation level of the auroral kilometric radiation. The investigation is based on the assumption that the emission is due to a cyclotron maser instability as suggested by Wu and Lee and Lee et al. The thermodynamic bound on the radiation energy is also estimated separately. The energy-conversion efficiency of the radiation process is discussed. The results are consistent with observations.

Numerical simulation of swept-wing flows

NASA Technical Reports Server (NTRS)

Reed, Helen L.

1991-01-01

Efforts of the last six months to computationally model the transition process characteristics of flow over swept wings are described. Specifically, the crossflow instability and crossflow/Tollmien-Schlichting wave interactions are analyzed through the numerical solution of the full 3D Navier-Stokes equations including unsteadiness, curvature, and sweep. This approach is chosen because of the complexity of the problem and because it appears that linear stability theory is insufficient to explain the discrepancies between different experiments and between theory and experiment. The leading edge region of a swept wing is considered in a 3D spatial simulation with random disturbances as the initial conditions.

Parametric decay of plasma waves near the upper-hybrid resonance

DOE PAGES

Dodin, I. Y.; Arefiev, A. V.

2017-03-28

An intense X wave propagating perpendicularly to dc magnetic field is unstable with respect to a parametric decay into an electron Bernstein wave and a lower-hybrid wave. A modified theory of this effect is proposed that extends to the high-intensity regime, where the instability rate γ ceases to be a linear function of the incident-wave amplitude. An explicit formula for γ is derived and expressed in terms of cold-plasma parameters. Here, theory predictions are in reasonable agreement with the results of the particle-in-cell simulations presented in a separate publication.

Computational Study of Laminar Flow Control on a Subsonic Swept Wing Using Discrete Roughness Elements

NASA Technical Reports Server (NTRS)

Li, Fei; Choudhari, Meelan M.; Chang, Chau-Lyan; Streett, Craig L.; Carpenter, Mark H.

2011-01-01

A combination of parabolized stability equations and secondary instability theory has been applied to a low-speed swept airfoil model with a chord Reynolds number of 7.15 million, with the goals of (i) evaluating this methodology in the context of transition prediction for a known configuration for which roughness based crossflow transition control has been demonstrated under flight conditions and (ii) of analyzing the mechanism of transition delay via the introduction of discrete roughness elements (DRE). Roughness based transition control involves controlled seeding of suitable, subdominant crossflow modes, so as to weaken the growth of naturally occurring, linearly more unstable crossflow modes. Therefore, a synthesis of receptivity, linear and nonlinear growth of stationary crossflow disturbances, and the ensuing development of high frequency secondary instabilities is desirable to understand the experimentally observed transition behavior. With further validation, such higher fidelity prediction methodology could be utilized to assess the potential for crossflow transition control at even higher Reynolds numbers, where experimental data is currently unavailable.

Roughness Based Crossflow Transition Control: A Computational Assessment

NASA Technical Reports Server (NTRS)

Li, Fei; Choudhari, Meelan M.; Chang, Chau-Lyan; Streett, Craig L.; Carpenter, Mark H.

2009-01-01

A combination of parabolized stability equations and secondary instability theory has been applied to a low-speed swept airfoil model with a chord Reynolds number of 7.15 million, with the goals of (i) evaluating this methodology in the context of transition prediction for a known configuration for which roughness based crossflow transition control has been demonstrated under flight conditions and (ii) of analyzing the mechanism of transition delay via the introduction of discrete roughness elements (DRE). Roughness based transition control involves controlled seeding of suitable, subdominant crossflow modes, so as to weaken the growth of naturally occurring, linearly more unstable crossflow modes. Therefore, a synthesis of receptivity, linear and nonlinear growth of stationary crossflow disturbances, and the ensuing development of high frequency secondary instabilities is desirable to understand the experimentally observed transition behavior. With further validation, such higher fidelity prediction methodology could be utilized to assess the potential for crossflow transition control at even higher Reynolds numbers, where experimental data is currently unavailable.

Influence of two-stream relativistic electron beam parameters on the space-charge wave with broad frequency spectrum formation

NASA Astrophysics Data System (ADS)

Alexander, LYSENKO; Iurii, VOLK

2018-03-01

We developed a cubic non-linear theory describing the dynamics of the multiharmonic space-charge wave (SCW), with harmonics frequencies smaller than the two-stream instability critical frequency, with different relativistic electron beam (REB) parameters. The self-consistent differential equation system for multiharmonic SCW harmonic amplitudes was elaborated in a cubic non-linear approximation. This system considers plural three-wave parametric resonant interactions between wave harmonics and the two-stream instability effect. Different REB parameters such as the input angle with respect to focusing magnetic field, the average relativistic factor value, difference of partial relativistic factors, and plasma frequency of partial beams were investigated regarding their influence on the frequency spectrum width and multiharmonic SCW saturation levels. We suggested ways in which the multiharmonic SCW frequency spectrum widths could be increased in order to use them in multiharmonic two-stream superheterodyne free-electron lasers, with the main purpose of forming a powerful multiharmonic electromagnetic wave.

Excitation of Ion Cyclotron Waves by Ion and Electron Beams in Compensated-current System

NASA Astrophysics Data System (ADS)

Xiang, L.; Wu, D. J.; Chen, L.

2018-04-01

Ion cyclotron waves (ICWs) can play important roles in the energization of plasma particles. Charged particle beams are ubiquitous in space, and astrophysical plasmas and can effectively lead to the generation of ICWs. Based on linear kinetic theory, we consider the excitation of ICWs by ion and electron beams in a compensated-current system. We also investigate the competition between reactive and kinetic instabilities. The results show that ion and electron beams both are capable of generating ICWs. For ICWs driven by ion beams, there is a critical beam velocity, v bi c , and critical wavenumber, k z c , for a fixed beam density; the reactive instability dominates the growth of ICWs when the ion-beam velocity {v}{bi}> {v}{bi}c and the wavenumber {k}z< {k}zc, and the maximal growth rate is reached at {k}z≃ 2{k}zc/3 for a given {v}{bi}> {v}{bi}c. For the slow ion beams with {v}{bi}< {v}{bi}c, the kinetic instability can provide important growth rates of ICWs. On the other hand, ICWs driven by electron beams are excited only by the reactive instability, but require a critical velocity, {v}{be}c\\gg {v}{{A}} (the Alfvén velocity). In addition, the comparison between the approximate analytical results based on the kinetic theory and the exact numerical calculation based on the fluid model demonstrates that the reactive instabilities can well agree quantitatively with the numerical results by the fluid model. Finally, some possible applications of the present results to ICWs observed in the solar wind are briefly discussed.

Steady states and linear stability analysis of precipitation pattern formation at geothermal hot springs.

PubMed

Chan, Pak Yuen; Goldenfeld, Nigel

2007-10-01

A dynamical theory of geophysical precipitation pattern formation is presented and applied to irreversible calcium carbonate (travertine) deposition. Specific systems studied here are the terraces and domes observed at geothermal hot springs, such as those at Yellowstone National Park, and speleothems, particularly stalactites and stalagmites. The theory couples the precipitation front dynamics with shallow water flow, including corrections for turbulent drag and curvature effects. In the absence of capillarity and with a laminar flow profile, the theory predicts a one-parameter family of steady state solutions to the moving boundary problem describing the precipitation front. These shapes match the measured shapes near the vent at the top of observed travertine domes well. Closer to the base of the dome, the solutions deviate from observations and circular symmetry is broken by a fluting pattern, which we show is associated with capillary forces causing thin film break-up. We relate our model to that recently proposed for stalactite growth, and calculate the linear stability spectrum of both travertine domes and stalactites. Lastly, we apply the theory to the problem of precipitation pattern formation arising from turbulent flow down an inclined plane and identify a linear instability that underlies scale-invariant travertine terrace formation at geothermal hot springs.

Steady states and linear stability analysis of precipitation pattern formation at geothermal hot springs

NASA Astrophysics Data System (ADS)

Chan, Pak Yuen; Goldenfeld, Nigel

2007-10-01

A dynamical theory of geophysical precipitation pattern formation is presented and applied to irreversible calcium carbonate (travertine) deposition. Specific systems studied here are the terraces and domes observed at geothermal hot springs, such as those at Yellowstone National Park, and speleothems, particularly stalactites and stalagmites. The theory couples the precipitation front dynamics with shallow water flow, including corrections for turbulent drag and curvature effects. In the absence of capillarity and with a laminar flow profile, the theory predicts a one-parameter family of steady state solutions to the moving boundary problem describing the precipitation front. These shapes match the measured shapes near the vent at the top of observed travertine domes well. Closer to the base of the dome, the solutions deviate from observations and circular symmetry is broken by a fluting pattern, which we show is associated with capillary forces causing thin film break-up. We relate our model to that recently proposed for stalactite growth, and calculate the linear stability spectrum of both travertine domes and stalactites. Lastly, we apply the theory to the problem of precipitation pattern formation arising from turbulent flow down an inclined plane and identify a linear instability that underlies scale-invariant travertine terrace formation at geothermal hot springs.

Ab initio calculations of ideal strength and lattice instability in W-Ta and W-Re alloys

NASA Astrophysics Data System (ADS)

Yang, Chaoming; Qi, Liang

2018-01-01

An important theoretical criterion to evaluate the ductility of metals with a body-centered cubic (bcc) lattice is the mechanical failure mode of their perfect crystals under tension along <;100 >; directions. When the tensile stress reaches the ideal tensile strength, the pure W crystal fails by a cleavage fracture along the {100 } plane so that it is intrinsically brittle. To discover the strategy to improve its ductility, we performed density functional theory and density functional perturbation theory calculations to study the ideal tensile strength and the lattice instability under <100 > tension for both W-Ta and W-Re alloys. Anisotropic linear elastic fracture mechanics (LEFM) theory and Rice's criterion were also applied to analyze the mechanical instability at the crack tip under <100 > tension based on the competition between cleavage propagation and dislocation emission. The results show that the intrinsic ductility can be achieved in both W-Ta and W-Re, however, by different mechanisms. Even though W-Ta alloys with low Ta concentrations are still intrinsically brittle, the intrinsic ductility of W-Ta alloys with high Ta concentrations is promoted by elastic shear instability before the cleavage failure. The intrinsic ductility of W-Re alloys is produced by unstable transverse phonon waves before the cleavage failure, and the corresponding phonon mode is related to the generation of 1/2 <111 > {2 ¯11 } dislocation in bcc crystals. The ideal tensile calculations, phonon analyses, and anisotropic LEFM examinations are mutually consistent in the evaluation of intrinsic ductility. These results bring us physical insights on the ductility-brittle mechanisms of W alloys under extreme stress conditions.

Phase space evolution in linear instabilities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pantellini, F.G.E.; Burgess, D.; Schwartz, S.J.

1994-12-01

A simple and powerful way to investigate the linear evolution of particle distribution functions in kinetic instabilities in a homogeneous collisionless plasma is presented. The method can be applied to any kind of instability, provided the characteristics (growth rate, frequency, wave vector, and polarization) of the mode are known and can also be used to estimate the amplitude of the waves at the end of the linear phase of growth. Two didactic examples are used to illustrate the versatility of the technique: the Alfven Ion Cyclotron (AIC) instability, which is electromagnetic, and the Electron Ion Cyclotron (EIC) instability, which ismore » electrostatic.« less

Self-modulational formation of pulsar microstructures

NASA Technical Reports Server (NTRS)

Kennel, C. F.; Chian, A. C.-L.

1987-01-01

A nonlinear plasma theory for self modulation of pulsar radio pulses is discussed. A nonlinear Schroedinger equation is derived for strong electromagnetic waves propagating in an electron positron plasma. The nonlinearities arising from wave intensity induced particle mass variation may excite the modulational instability of circularly and linearly polarized pulsar radiation. The resulting wave envelopes can take the form of periodic wave trains or solitons. These nonlinear stationary waveforms may account for the formation of pulsar microstructures.

Plasma diffusion at the magnetopause - The case of lower hybrid drift waves

NASA Technical Reports Server (NTRS)

Treumann, R. A.; Labelle, J.; Pottelette, R.

1991-01-01

The diffusion expected from the quasi-linear theory of the lower hybrid drift instability at the earth's magnetopause is recalculated. The resulting diffusion coefficient is marginally large enough to explain the thickness of the boundary layer under quiet conditions, based on observational upper limits for the wave intensities. Thus, one possible model for the boundary layer could involve equilibrium between the diffusion arising from lower hybrid waves and various loss processes.

Secondary Instability of Second Modes in Hypersonic Boundary Layers

NASA Technical Reports Server (NTRS)

Li, Fei; Choudhari, Meelan M.; Chang, Chau-Lyan; White, Jeffery A.

2012-01-01

Second mode disturbances dominate the primary instability stage of transition in a number of hypersonic flow configurations. The highest amplification rates of second mode disturbances are usually associated with 2D (or axisymmetric) perturbations and, therefore, a likely scenario for the onset of the three-dimensionality required for laminar-turbulent transition corresponds to the parametric amplification of 3D secondary instabilities in the presence of 2D, finite amplitude second mode disturbances. The secondary instability of second mode disturbances is studied for selected canonical flow configurations. The basic state for the secondary instability analysis is obtained by tracking the linear and nonlinear evolution of 2D, second mode disturbances using nonlinear parabolized stability equations. Unlike in previous studies, the selection of primary disturbances used for the secondary instability analysis was based on their potential relevance to transition in a low disturbance environment and the effects of nonlinearity on the evolution of primary disturbances was accounted for. Strongly nonlinear effects related to the self-interaction of second mode disturbances lead to an upstream shift in the upper branch neutral location. Secondary instability computations confirm the previously known dominance of subharmonic modes at relatively small primary amplitudes. However, for the Purdue Mach 6 compression cone configuration, it was shown that a strong fundamental secondary instability can exist for a range of initial amplitudes of the most amplified second mode disturbance, indicating that the exclusive focus on subharmonic modes in the previous applications of secondary instability theory to second mode primary instability may not have been fully justified.

Kelvin-Helmholtz instability for flow in porous media under the influence of oblique magnetic fields: A viscous potential flow analysis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Moatimid, Galal M.; Obied Allah, M. H.; Hassan, Mohamed A.

2013-10-15

In this paper, the Kelvin-Helmholtz instability of viscous incompressible magnetic fluid fully saturated porous media is achieved through the viscous potential theory. The flow is considered to be through semi-permeable boundaries above and below the fluids through which the fluid may either be blown in or sucked out, in a direction normal to the main streaming direction of the fluid flow. An oblique magnetic field, mass, heat transfer, and surface tension are present across the interface. Through the linear stability analysis, a general dispersion relation is derived and the natural curves are plotted. Therefore, the linear stability condition is discussedmore » in some depth. In view of the multiple time scale technique, the Ginzburg–Landau equation, which describes the behavior of the system in the nonlinear approach, is obtained. The effects of the orientation of the magnetic fields on the stability configuration in linear, as well as nonlinear approaches, are discussed. It is found that the Darcy's coefficient for the porous layers plays a stabilizing role. The injection of the fluids at both boundaries has a stabilizing effect, in contrast with the suction at both boundaries.« less

Influence of electrical double-layer dispersion forces and size dependency on pull-in instability of clamped microplate immersed in ionic liquid electrolytes

NASA Astrophysics Data System (ADS)

Karimipour, I.; Beni, Yaghoub Tadi; Taheri, N.

2017-10-01

Plate-type clamped microplate is of the most common constructive elements for developing in-liquid-operating devices. While the electromechanical behavior of clamped microplate in non-liquid environments has exclusively been addressed in the literature, no theoretical studies have yet been conducted on precise modeling of the clamped microplate in electrolyte liquid. Herein, the electromechanical response and instability of the clamped microplate immersed in ionic electrolyte media are investigated. The electrochemical force field is determined using double layer theory and linearized Poisson-Boltzmann equation. The presence of dispersion forces, i.e., Casimir and van der Waals attractions, are included in the theoretical model considering the correction due to the presence of liquid media between the interacting surfaces (three-layer model). To this end, a kind of microplate has been designed, i.e., a square microplate with all edges clamped supported. The strain gradient elasticity is employed to model the size-dependent structural behavior of the clamped microplate. To solve the nonlinear constitutive equation of the system, Extended Kantorovich Method, is employed and the pull-in parameter of the microplate are extracted. Impacts of the dispersion forces and size effect on the instability characteristics are discussed as well as the effect of ion concentration and potential ratio. It is found that the significant difference between the pull-in instability parameters in the modified strain gradient theory and the classical theory for thin microplates is merely due to the consideration of size effect parameter in the modified strain gradient theory. To confirm the validity of formulations, the numerical values of the results are compared. The results predicted via the aforementioned approach are in excellent agreement with those in the literature. Some new examples are solved to demonstrate the applicability of the procedure.

Collisionless Isotropization of the Solar-Wind Protons by Compressive Fluctuations and Plasma Instabilities

NASA Astrophysics Data System (ADS)

Verscharen, D.; Chandran, B. D. G.; Klein, K. G.; Quataert, E.

2016-12-01

Compressive fluctuations are a minor yet significant component of astrophysical plasma turbulence. In the solar wind, long-wavelength compressive slow-mode fluctuations lead to changes in β∥p ≡ 8πnpkBT∥p/B2 and in Rp ≡ T⊥p/T∥p, where T⊥p and T∥p are the perpendicular and parallel temperatures of the protons, B is the magnetic field strength, and np is the proton density. If the amplitude of the compressive fluctuations is large enough, Rp crosses one or more instability thresholds for anisotropy-driven micro-instabilities. The enhanced field fluctuations from these micro-instabilities scatter the protons so as to reduce the anisotropy of the pressure tensor, driving the average value of Rp away from the marginal stability boundary until the fluctuating value of Rp stops crossing the boundary. We model this "fluctuating-anisotropy effect" using linear Vlasov-Maxwell theory to describe the large-scale compressive fluctuations. We show that this effect can explain why, in the nearly collisionless solar wind, the average value of Rp is close to unity.

Connecting Clump Sizes in Turbulent Disk Galaxies to Instability Theory

NASA Astrophysics Data System (ADS)

Fisher, David B.; Glazebrook, Karl; Abraham, Roberto G.; Damjanov, Ivana; White, Heidi A.; Obreschkow, Danail; Basset, Robert; Bekiaris, Georgios; Wisnioski, Emily; Green, Andy; Bolatto, Alberto D.

2017-04-01

In this letter we study the mean sizes of Hα clumps in turbulent disk galaxies relative to kinematics, gas fractions, and Toomre Q. We use ˜100 pc resolution HST images, IFU kinematics, and gas fractions of a sample of rare, nearby turbulent disks with properties closely matched to z˜ 1.5{--}2 main-sequence galaxies (the DYNAMO sample). We find linear correlations of normalized mean clump sizes with both the gas fraction and the velocity dispersion-to-rotation velocity ratio of the host galaxy. We show that these correlations are consistent with predictions derived from a model of instabilities in a self-gravitating disk (the so-called “violent disk instability model”). We also observe, using a two-fluid model for Q, a correlation between the size of clumps and self-gravity-driven unstable regions. These results are most consistent with the hypothesis that massive star-forming clumps in turbulent disks are the result of instabilities in self-gravitating gas-rich disks, and therefore provide a direct connection between resolved clump sizes and this in situ mechanism.

Wrinkle-to-fold transition in soft layers under equi-biaxial strain: A weakly nonlinear analysis

NASA Astrophysics Data System (ADS)

Ciarletta, P.

2014-12-01

Soft materials can experience a mechanical instability when subjected to a finite compression, developing wrinkles which may eventually evolve into folds or creases. The possibility to control the wrinkling network morphology has recently found several applications in many developing fields, such as scaffolds for biomaterials, stretchable electronics and surface micro-fabrication. Albeit much is known of the pattern initiation at the linear stability order, the nonlinear effects driving the pattern selection in soft materials are still unknown. This work aims at investigating the nature of the elastic bifurcation undertaken by a growing soft layer subjected to a equi-biaxial strain. Considering a skin effect at the free surface, the instability thresholds are found to be controlled by a characteristic length, defined by the ratio between capillary energy and bulk elasticity. For the first time, a weakly nonlinear analysis of the wrinkling instability is performed here using the multiple-scale perturbation method applied to the incremental theory in finite elasticity. The Ginzburg-Landau equations are derived for different superposing linear modes. This study proves that a subcritical pitchfork bifurcation drives the observed wrinkle-to-fold transition in swelling gels experiments, favoring the emergence of hexagonal creased patterns, albeit quasi-hexagonal patterns might later emerge because of an expected symmetry break. Moreover, if the surface energy is somewhat comparable to the bulk elastic energy, it has the same stabilizing effect as for fluid instabilities, driving the formation of stable wrinkles, as observed in elastic bi-layered materials.

Lattice Boltzmann methods for global linear instability analysis

NASA Astrophysics Data System (ADS)

Pérez, José Miguel; Aguilar, Alfonso; Theofilis, Vassilis

2017-12-01

Modal global linear instability analysis is performed using, for the first time ever, the lattice Boltzmann method (LBM) to analyze incompressible flows with two and three inhomogeneous spatial directions. Four linearization models have been implemented in order to recover the linearized Navier-Stokes equations in the incompressible limit. Two of those models employ the single relaxation time and have been proposed previously in the literature as linearization of the collision operator of the lattice Boltzmann equation. Two additional models are derived herein for the first time by linearizing the local equilibrium probability distribution function. Instability analysis results are obtained in three benchmark problems, two in closed geometries and one in open flow, namely the square and cubic lid-driven cavity flow and flow in the wake of the circular cylinder. Comparisons with results delivered by classic spectral element methods verify the accuracy of the proposed new methodologies and point potential limitations particular to the LBM approach. The known issue of appearance of numerical instabilities when the SRT model is used in direct numerical simulations employing the LBM is shown to be reflected in a spurious global eigenmode when the SRT model is used in the instability analysis. Although this mode is absent in the multiple relaxation times model, other spurious instabilities can also arise and are documented herein. Areas of potential improvements in order to make the proposed methodology competitive with established approaches for global instability analysis are discussed.

Manipulation of three-dimensional Richtmyer-Meshkov instability by initial interfacial principal curvatures

NASA Astrophysics Data System (ADS)

Guan, Ben; Zhai, Zhigang; Si, Ting; Lu, Xiyun; Luo, Xisheng

2017-03-01

The characteristics of three-dimensional (3D) Richtmyer-Meshkov instability (RMI) in the early stages are studied numerically. By designing 3D interfaces that initially possess various identical and opposite principal curvature combinations, the growth rate of perturbations can be effectively manipulated. The weighted essentially nonoscillatory scheme and the level set method combined with the real ghost fluid method are used to simulate the flow. The results indicate that the interface development and the shock propagation in 3D cases are much more complicated than those in 2D case, and the evolution of 3D interfaces is heavily dependent on the initial interfacial principal curvatures. The 3D structure of wave patterns induces high pressure zones in the flow field, and the pressure oscillations change the local instabilities of interfaces. In the linear stages, the perturbation growth rate follows regularity as the interfacial principal curvatures vary, which is further predicted by the stability theory of 2D and 3D interfaces. It is also found that hysteresis effects exist at the onset of the linear stages in the 3D case for the same initial perturbations as the 2D case, resulting in different evolutions of 3D RMI in the nonlinear stages.

Time evolution of linearized gauge field fluctuations on a real-time lattice

NASA Astrophysics Data System (ADS)

Kurkela, A.; Lappi, T.; Peuron, J.

2016-12-01

Classical real-time lattice simulations play an important role in understanding non-equilibrium phenomena in gauge theories and are used in particular to model the prethermal evolution of heavy-ion collisions. Due to instabilities, small quantum fluctuations on top of the classical background may significantly affect the dynamics of the system. In this paper we argue for the need for a numerical calculation of a system of classical gauge fields and small linearized fluctuations in a way that keeps the separation between the two manifest. We derive and test an explicit algorithm to solve these equations on the lattice, maintaining gauge invariance and Gauss' law.

E × B electron drift instability in Hall thrusters: Particle-in-cell simulations vs. theory

NASA Astrophysics Data System (ADS)

Boeuf, J. P.; Garrigues, L.

2018-06-01

The E × B Electron Drift Instability (E × B EDI), also called Electron Cyclotron Drift Instability, has been observed in recent particle simulations of Hall thrusters and is a possible candidate to explain anomalous electron transport across the magnetic field in these devices. This instability is characterized by the development of an azimuthal wave with wavelength in the mm range and velocity on the order of the ion acoustic velocity, which enhances electron transport across the magnetic field. In this paper, we study the development and convection of the E × B EDI in the acceleration and near plume regions of a Hall thruster using a simplified 2D axial-azimuthal Particle-In-Cell simulation. The simulation is collisionless and the ionization profile is not-self-consistent but rather is given as an input parameter of the model. The aim is to study the development and properties of the instability for different values of the ionization rate (i.e., of the total ion production rate or current) and to compare the results with the theory. An important result is that the wavelength of the simulated azimuthal wave scales as the electron Debye length and that its frequency is on the order of the ion plasma frequency. This is consistent with the theory predicting destruction of electron cyclotron resonance of the E × B EDI in the non-linear regime resulting in the transition to an ion acoustic instability. The simulations also show that for plasma densities smaller than under nominal conditions of Hall thrusters the field fluctuations induced by the E × B EDI are no longer sufficient to significantly enhance electron transport across the magnetic field, and transit time instabilities develop in the axial direction. The conditions and results of the simulations are described in detail in this paper and they can serve as benchmarks for comparisons between different simulation codes. Such benchmarks would be very useful to study the role of numerical noise (numerical noise can also be responsible to the destruction of electron cyclotron resonance) or the influence of the period of the azimuthal domain, as well as to reach a better and consensual understanding of the physics.

Resistive wall instabilities and tearing mode dynamics in the EXTRAP T2R thin shell reversed-field pinch

NASA Astrophysics Data System (ADS)

Malmberg, J.-A.; Brunsell, P. R.

2002-01-01

Observations of resistive wall instabilities and tearing mode dynamics in the EXTRAP T2R thin shell (τw=6 ms) reversed field pinch are described. A nonresonant mode (m=1,n=-10) with the same handedness as the internal field grows nearly exponentially with an average growth time of about 2.6 ms (less than 1/2 of the shell time) consistent with linear stability theory. The externally nonresonant unstable modes (m=1,n>0), predicted by linear stability theory, are observed to have only low amplitudes (in the normal low-Θ operation mode of the device). The radial field of the dominant internally resonant tearing modes (m=1,n=-15 to n=-12) remain low due to spontaneous fast mode rotation, corresponding to angular phase velocities up to 280 krad/s. Phase aligned mode structures are observed to rotate toroidally with an average angular velocity of 40 krad/s, in the opposite direction of the plasma current. Toward the end of the discharge, the radial field of the internally resonant modes grows as the modes slow down and become wall-locked, in agreement with nonlinear computations. Fast rotation of the internally resonant modes has been observed only recently and is attributed to a change of the front-end system (vacuum vessel, shell, and TF coil) of the device.

Kinetic water-bag model of global collisional drift waves and ion temperature gradient instabilities in cylindrical geometry

NASA Astrophysics Data System (ADS)

Gravier, E.; Plaut, E.

2013-04-01

Collisional drift waves and ion temperature gradient (ITG) instabilities are studied using a linear water-bag kinetic model [P. Morel et al., Phys. Plasmas 14, 112109 (2007)]. An efficient spectral method, already validated in the case of drift waves instabilities [E. Gravier et al., Eur. Phys. J. D 67, 7 (2013)], allows a fast solving of the global linear problem in cylindrical geometry. The comparison between the linear ITG instability properties thus computed and the ones given by the COLUMBIA experiment [R. G. Greaves et al., Plasma Phys. Controlled Fusion 34, 1253 (1992)] shows a qualitative agreement. Moreover, the transition between collisional drift waves and ITG instabilities is studied theoretically as a function of the ion temperature profile.

Testing higher-order Lagrangian perturbation theory against numerical simulation. 1: Pancake models

NASA Technical Reports Server (NTRS)

Buchert, T.; Melott, A. L.; Weiss, A. G.

1993-01-01

We present results showing an improvement of the accuracy of perturbation theory as applied to cosmological structure formation for a useful range of quasi-linear scales. The Lagrangian theory of gravitational instability of an Einstein-de Sitter dust cosmogony investigated and solved up to the third order is compared with numerical simulations. In this paper we study the dynamics of pancake models as a first step. In previous work the accuracy of several analytical approximations for the modeling of large-scale structure in the mildly non-linear regime was analyzed in the same way, allowing for direct comparison of the accuracy of various approximations. In particular, the Zel'dovich approximation (hereafter ZA) as a subclass of the first-order Lagrangian perturbation solutions was found to provide an excellent approximation to the density field in the mildly non-linear regime (i.e. up to a linear r.m.s. density contrast of sigma is approximately 2). The performance of ZA in hierarchical clustering models can be greatly improved by truncating the initial power spectrum (smoothing the initial data). We here explore whether this approximation can be further improved with higher-order corrections in the displacement mapping from homogeneity. We study a single pancake model (truncated power-spectrum with power-spectrum with power-index n = -1) using cross-correlation statistics employed in previous work. We found that for all statistical methods used the higher-order corrections improve the results obtained for the first-order solution up to the stage when sigma (linear theory) is approximately 1. While this improvement can be seen for all spatial scales, later stages retain this feature only above a certain scale which is increasing with time. However, third-order is not much improvement over second-order at any stage. The total breakdown of the perturbation approach is observed at the stage, where sigma (linear theory) is approximately 2, which corresponds to the onset of hierarchical clustering. This success is found at a considerable higher non-linearity than is usual for perturbation theory. Whether a truncation of the initial power-spectrum in hierarchical models retains this improvement will be analyzed in a forthcoming work.

The effect of gravity modulation on thermosolutal convection in an infinite layer of fluid

NASA Astrophysics Data System (ADS)

Saunders, B. V.; Murray, B. T.; McFadden, G. B.; Coriell, S. R.; Wheeler, A. A.

1992-06-01

The effect of time-periodic vertical gravity modulation on the onset of thermosolutal convection in an infinite horizontal layer with stress-free boundaries is investigated using Floquet theory for the linear stability analysis. Situations for which the fluid layer is stably stratified in either the fingering or diffusive regimes of double-diffusive convection are considered. Results are presented both with and without steady background acceleration. Modulation may stabilize an unstable base solution or destabilize a stable base solution. In addition to synchronous and subharmonic response to the modulation frequency, instability in the double diffusive system can occur via a complex conjugate mode. In the diffusive regime, where oscillatory onset occurs in the unmodulated system, regions of resonant instability occur and exhibit strong coupling with the unmodulated oscillatory frequency. The response to modulation of the fundamental instability of the unmodulated system is described both analytically and numerically; in the double-diffusive system this mode persists under subcritical conditions as a high-frequency lobe.

The effect of gravity modulation on thermosolutal convection in an infinite layer of fluid

NASA Technical Reports Server (NTRS)

Saunders, B. V.; Murray, B. T.; Mcfadden, G. B.; Coriell, S. R.; Wheeler, A. A.

1992-01-01

The effect of time-periodic vertical gravity modulation on the onset of thermosolutal convection in an infinite horizontal layer with stress-free boundaries is investigated using Floquet theory for the linear stability analysis. Situations for which the fluid layer is stably stratified in either the fingering or diffusive regimes of double-diffusive convection are considered. Results are presented both with and without steady background acceleration. Modulation may stabilize an unstable base solution or destabilize a stable base solution. In addition to synchronous and subharmonic response to the modulation frequency, instability in the double diffusive system can occur via a complex conjugate mode. In the diffusive regime, where oscillatory onset occurs in the unmodulated system, regions of resonant instability occur and exhibit strong coupling with the unmodulated oscillatory frequency. The response to modulation of the fundamental instability of the unmodulated system is described both analytically and numerically; in the double-diffusive system this mode persists under subcritical conditions as a high-frequency lobe.

Connections between centrifugal, stratorotational, and radiative instabilities in viscous Taylor-Couette flow

NASA Astrophysics Data System (ADS)

Leclercq, Colin; Nguyen, Florian; Kerswell, Rich R.

2016-10-01

The "Rayleigh line" μ =η2 , where μ =Ωo/Ωi and η =ri/ro are respectively the rotation and radius ratios between inner (subscript i ) and outer (subscript o ) cylinders, is regarded as marking the limit of centrifugal instability (CI) in unstratified inviscid Taylor-Couette flow, for both axisymmetric and nonaxisymmetric modes. Nonaxisymmetric stratorotational instability (SRI) is known to set in for anticyclonic rotation ratios beyond that line, i.e., η2<μ <1 for axially stably stratified Taylor-Couette flow, but the competition between CI and SRI in the range μ <η2 has not yet been addressed. In this paper, we establish continuous connections between the two instabilities at finite Reynolds number Re, as previously suggested by Le Bars and Le Gal [Phys. Rev. Lett. 99, 064502 (2007), 10.1103/PhysRevLett.99.064502], making them indistinguishable at onset. Both instabilities are also continuously connected to the radiative instability at finite Re. These results demonstrate the complex impact viscosity has on the linear stability properties of this flow. Several other qualitative differences with inviscid theory were found, among which are the instability of a nonaxisymmetric mode localized at the outer cylinder without stratification and the instability of a mode propagating against the inner cylinder rotation with stratification. The combination of viscosity and stratification can also lead to a "collision" between (axisymmetric) Taylor vortex branches, causing the axisymmetric oscillatory state already observed in past experiments. Perhaps more surprising is the instability of a centrifugal-like helical mode beyond the Rayleigh line, caused by the joint effects of stratification and viscosity. The threshold μ =η2 seems to remain, however, an impassable instability limit for axisymmetric modes, regardless of stratification, viscosity, and even disturbance amplitude.

Excitation of O+ Band EMIC Waves Through H+ Ring Velocity Distributions: Van Allen Probe Observations

NASA Astrophysics Data System (ADS)

Yu, Xiongdong; Yuan, Zhigang; Huang, Shiyong; Yao, Fei; Wang, Dedong; Funsten, Herbert O.; Wygant, John R.

2018-02-01

A typical case of electromagnetic ion cyclotron (EMIC) emissions with both He+ band and O+ band waves was observed by Van Allen Probe A on 14 July 2014. These emissions occurred in the morning sector on the equator inside the plasmasphere, in which region O+ band EMIC waves prefer to appear. Through property analysis of these emissions, it is found that the He+ band EMIC waves are linearly polarized and propagating quasi-parallelly along the background magnetic field, while the O+ band ones are of linear and left-hand polarization and propagating obliquely with respect to the background magnetic field. Using the in situ observations of plasma environment and particle data, excitation of these O+ band EMIC waves has been investigated with the linear growth theory. The calculated linear growth rate shows that these O+ band EMIC waves can be locally excited by ring current protons with ring velocity distributions. The comparison of the observed wave spectral intensity and the calculated growth rate suggests that the density of H+ rings providing the free energy for the instability has decreased after the wave grows. Therefore, this paper provides a direct observational evidence to the excitation mechanism of O+ band EMIC waves: ring current protons with ring distributions provide the free energy supporting the instability in the presence of rich O+ in the plasmasphere.

On an apparent discrepancy between pulsation and evolution masses for Cepheids.

NASA Technical Reports Server (NTRS)

Iben, I., Jr.; Tuggle, R. S.

1972-01-01

Results of new theoretical pulsation calculations in the linear nonadiabatic approximation are presented. Emphasis is placed on the location of blue edges (the borderline between stability and instability against pulsation) for pulsation in the fundamental mode. The results of evolutionary calculations for the helium-burning phase are introduced, and a theoretical period-luminosity relationship is obtained for Cepheids that lie on the blue edge of the instability strip. The theoretical results are then compared with current estimates of the intrinsic bulk properties of 13 Cepheids, and it is shown how theoretical and observational properties may be reconciled without assuming significant mass loss or the necessity of major adjustments in the theory. Finally, it is argued that the required revision in Cepheid luminosities lies within the observational uncertainties.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Emami, Razieh; Mukohyama, Shinji; Namba, Ryo

Many models of inflation driven by vector fields alone have been known to be plagued by pathological behaviors, namely ghost and/or gradient instabilities. In this work, we seek a new class of vector-driven inflationary models that evade all of the mentioned instabilities. We build our analysis on the Generalized Proca Theory with an extension to three vector fields to realize isotropic expansion. We obtain the conditions required for quasi de-Sitter solutions to be an attractor analogous to the standard slow-roll one and those for their stability at the level of linearized perturbations. Identifying the remedy to the existing unstable models,more » we provide a simple example and explicitly show its stability. This significantly broadens our knowledge on vector inflationary scenarios, reviving potential phenomenological interests for this class of models.« less

Effect of gravity modulation on thermosolutal convection in an infinite layer of fluid

NASA Astrophysics Data System (ADS)

Saunders, B. V.; Murray, B. T.; McFadden, G. B.; Coriell, S. R.; Wheeler, A. A.

1991-10-01

The effect of time-periodic vertical gravity modulation on the onset of thermosolutal convection in an infinite horizontal layer with stress free boundaries is studied using Floquet theory for the linear stability analysis. Situations are considered for which the fluid layer is stably stratified in either the fingering or diffusive regimes of double diffusive convection. Results are presented both with and without steady background acceleration. Modulation may stabilize an unstable base solution or destabilize a stable base solution. In addition to synchronous and subharmonic response to the modulation frequency, instability in the double diffusive system can occur via a complex conjugate mode. In the diffusive regime, where oscillatory onset occurs in the unmodulated system, regions of resonant instability occur and exhibit strong coupling with the unmodulated oscillatory frequency.

Stable solutions of inflation driven by vector fields

NASA Astrophysics Data System (ADS)

Emami, Razieh; Mukohyama, Shinji; Namba, Ryo; Zhang, Ying-li

2017-03-01

Many models of inflation driven by vector fields alone have been known to be plagued by pathological behaviors, namely ghost and/or gradient instabilities. In this work, we seek a new class of vector-driven inflationary models that evade all of the mentioned instabilities. We build our analysis on the Generalized Proca Theory with an extension to three vector fields to realize isotropic expansion. We obtain the conditions required for quasi de-Sitter solutions to be an attractor analogous to the standard slow-roll one and those for their stability at the level of linearized perturbations. Identifying the remedy to the existing unstable models, we provide a simple example and explicitly show its stability. This significantly broadens our knowledge on vector inflationary scenarios, reviving potential phenomenological interests for this class of models.

Observations of proton spectra (1.0 less than or equal to proton energy less than or equal to 300 keV) and pitch angle distributions at the plasmapause

NASA Technical Reports Server (NTRS)

Williams, D. J.; Fritz, T. A.; Konradi, A.

1972-01-01

Detailed proton spectral and pitch angle distribution observations were obtained from two proton detectors and a fluxgate magnetometer flown on Small Scientific Satellite A (Explorer 45). The data of interest are from orbit 99 in-bound occurring on 17 December 1971, some 8 hours prior to the sudden commencement of a magnetic storm. The data are consistent with the initiation of ion cyclotron instability when certain requirements are met. These criteria are met initially at the altitude at which the sudden intensity decrease occurs. However, after the initiation of the instability, the linear theory is unable to explain the further evolution of intensities, pitch angle distributions, and energy spectra of the ring current particles.

A hybrid Rayleigh-Taylor-current-driven coupled instability in a magnetohydrodynamically collimated cylindrical plasma with lateral gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhai, Xiang, E-mail: xzhai@caltech.edu; Bellan, Paul M., E-mail: pbellan@caltech.edu

We present an MHD theory of Rayleigh-Taylor instability on the surface of a magnetically confined cylindrical plasma flux rope in a lateral external gravity field. The Rayleigh-Taylor instability is found to couple to the classic current-driven instability, resulting in a new type of hybrid instability that cannot be described by either of the two instabilities alone. The lateral gravity breaks the axisymmetry of the system and couples all azimuthal modes together. The coupled instability, produced by combination of helical magnetic field, curvature of the cylindrical geometry, and lateral gravity, is fundamentally different from the classic magnetic Rayleigh-Taylor instability occurring atmore » a two-dimensional planar interface. The theory successfully explains the lateral Rayleigh-Taylor instability observed in the Caltech plasma jet experiment [Moser and Bellan, Nature 482, 379 (2012)]. Potential applications of the theory include magnetic controlled fusion, solar emerging flux, solar prominences, coronal mass ejections, and other space and astrophysical plasma processes.« less

Linear and weakly nonlinear aspects of free shear layer instability, roll-up, subharmonic interaction and wall influence

NASA Technical Reports Server (NTRS)

Cain, A. B.; Thompson, M. W.

1986-01-01

The growth of the momentum thickness and the modal disturbance energies are examined to study the nature and onset of nonlinearity in a temporally growing free shear layer. A shooting technique is used to find solutions to the linearized eigenvalue problem, and pseudospectral weakly nonlinear simulations of this flow are obtained for comparison. The roll-up of a fundamental disturbance follows linear theory predictions even with a 20 percent disturbance amplitude. A weak nonlinear interaction of the disturbance creates a finite-amplitude mean shear stress which dominates the growth of the layer momentum thickness, and the disturbance growth rate changes until the fundamental disturbance dominates. The fundamental then becomes an energy source for the harmonic, resulting in an increase in the growth rate of the subharmonic over the linear prediction even when the fundamental has no energy to give. Also considered are phase relations and the wall influence.

Kinetic water-bag model of global collisional drift waves and ion temperature gradient instabilities in cylindrical geometry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gravier, E.; Plaut, E.

2013-04-15

Collisional drift waves and ion temperature gradient (ITG) instabilities are studied using a linear water-bag kinetic model [P. Morel et al., Phys. Plasmas 14, 112109 (2007)]. An efficient spectral method, already validated in the case of drift waves instabilities [E. Gravier et al., Eur. Phys. J. D 67, 7 (2013)], allows a fast solving of the global linear problem in cylindrical geometry. The comparison between the linear ITG instability properties thus computed and the ones given by the COLUMBIA experiment [R. G. Greaves et al., Plasma Phys. Controlled Fusion 34, 1253 (1992)] shows a qualitative agreement. Moreover, the transition betweenmore » collisional drift waves and ITG instabilities is studied theoretically as a function of the ion temperature profile.« less

Nonsingular solutions and instabilities in Einstein-scalar-Gauss-Bonnet cosmology

NASA Astrophysics Data System (ADS)

Sberna, Laura; Pani, Paolo

2017-12-01

It is generically believed that higher-order curvature corrections to the Einstein-Hilbert action might cure the curvature singularities that plague general relativity. Here we consider Einstein-scalar-Gauss-Bonnet gravity, the only four-dimensional, ghost-free theory with quadratic curvature terms. For any choice of the coupling function and of the scalar potential, we show that the theory does not allow for bouncing solutions in the flat and open Friedmann universe. For the case of a closed universe, using a reverse-engineering method, we explicitly provide a bouncing solution which is nevertheless linearly unstable in the scalar gravitational sector. Moreover, we show that the expanding, singularity-free, early-time cosmologies allowed in the theory are unstable. These results rely only on analyticity and finiteness of cosmological variables at early times.

Cellular Spacing Selection During the Directional Solidification of Binary Alloys. A Numerical Approach

NASA Technical Reports Server (NTRS)

Catalina, Adrian V.; Sen, S.; Rose, M. Franklin (Technical Monitor)

2001-01-01

The evolution of cellular solid/liquid interfaces from an initially unstable planar front was studied by means of a two-dimensional computer simulation. The developed numerical model makes use of an interface tracking procedure and has the capability to describe the dynamics of the interface morphology based on local changes of the thermodynamic conditions. The fundamental physics of this formulation was validated against experimental microgravity results and the predictions of the analytical linear stability theory. The performed simulations revealed that in certain conditions, based on a competitive growth mechanism, an interface could become unstable to random perturbations of infinitesimal amplitude even at wavelengths smaller than the neutral wavelength, lambda(sub c), predicted by the linear stability theory. Furthermore, two main stages of spacing selection have been identified. In the first stage, at low perturbations amplitude, the selection mechanism is driven by the maximum growth rate of instabilities while in the second stage the selection is influenced by nonlinear phenomena caused by the interactions between the neighboring cells. Comparison of these predictions with other existing theories of pattern formation and experimental results will be discussed.

Computer Simulation Studies of the Tearing Mode Instability in a Field-Reversed Ion Layer.

DTIC Science & Technology

1980-09-15

CLASSIFICATION OF THIS PAGE (when Date Entered) 20. (Abstract continued) .those of the linear theory. In addition, it has been demonstrated that when...However, all the results obtained so far are very encouraging. Using the energy prin- ciple Sudan and Rosenbluth5 have shown with a hybrid model that a...found that finite length layers are stable to tearing modes as a consequence of axial kinetic pressure. Using a hybrid model , in which the ion layer is

Flow instabilities of magnetic flux tubes. IV. Flux storage in the solar overshoot region

NASA Astrophysics Data System (ADS)

Işık, E.; Holzwarth, V.

2009-12-01

Context: Flow-induced instabilities of magnetic flux tubes are relevant to the storage of magnetic flux in the interiors of stars with outer convection zones. The stability of magnetic fields in stellar interiors is of importance to the generation and transport of solar and stellar magnetic fields. Aims: We consider the effects of material flows on the dynamics of toroidal magnetic flux tubes located close to the base of the solar convection zone, initially within the overshoot region. The problem is to find the physical conditions in which magnetic flux can be stored for periods comparable to the dynamo amplification time, which is of the order of a few years. Methods: We carry out nonlinear numerical simulations to investigate the stability and dynamics of thin flux tubes subject to perpendicular and longitudinal flows. We compare the simulations with the results of simplified analytical approximations. Results: The longitudinal flow instability induced by the aerodynamic drag force is nonlinear in the sense that the growth rate depends on the perturbation amplitude. This result is consistent with the predictions of linear theory. Numerical simulations without friction show that nonlinear Parker instability can be triggered below the linear threshold of the field strength, when the difference in superadiabaticity along the tube is sufficiently large. A localised downflow acting on a toroidal tube in the overshoot region leads to instability depending on the parameters describing the flow, as well as the magnetic field strength. We determined ranges of the flow parameters for which a linearly Parker-stable magnetic flux tube is stored in the middle of the overshoot region for a period comparable to the dynamo amplification time. Conclusions: The longitudinal flow instability driven by frictional interaction of a flux tube with its surroundings is relevant to determining the storage time of magnetic flux in the solar overshoot region. The residence time for magnetic flux tubes with 2 × 1021 Mx in the convective overshoot layer can be comparable to the dynamo amplification time, provided that the average speed and the duration of an external downflow do not exceed about 50 m s -1 and 100 days, respectively, and that the lateral extension of the flow is smaller than about 10°. Appendix C and movies are only available in electronic form at http://www.aanda.org

Hybrid simulation of fishbone instabilities in the EAST tokamak

DOE PAGES

Shen, Wei; Wang, Feng; Fu, G. Y.; ...

2017-08-11

Hybrid simulations with the global kinetic-magnetohydrodynamic (MHD) code M3D-K have been carried out to investigate the linear stability and nonlinear dynamics of beam-driven fishbone in the experimental advanced superconducting tokamak (EAST) experiment. Linear simulations show that a low frequency fishbone instability is excited at experimental value of beam ion pressure. The mode is mainly driven by low energy beam ions via precessional resonance. Our results are consistent with the experimental measurement with respect to mode frequency and mode structure. When the beam ion pressure is increased to exceed a critical value, the low frequency mode transits to a beta-induced Alfvenmore » eigenmode (BAE) with much higher frequency. This BAE is driven by higher energy beam ions. Nonlinear simulations show that the frequency of the low frequency fishbone chirps up and down with corresponding hole-clump structures in phase space, consistent with the Berk-Breizman theory. In addition to the low frequency mode, the high frequency BAE is excited during the nonlinear evolution. Furthermore, for the transient case of beam pressure fraction where the low and high frequency modes are simultaneously excited in the linear phase, only one dominant mode appears in the nonlinear phase with frequency jumps up and down during nonlinear evolution.« less

Single-Mode Deceleration Stage Rayleigh-Taylor Instability Growth in Cylindrical Implosions

NASA Astrophysics Data System (ADS)

Sauppe, J. P.; Palaniyappan, S.; Bradley, P. A.; Batha, S. H.; Loomis, E. N.; Kline, J. L.; Srinivasan, B.; Bose, A.; Malka, E.; Shvarts, D.

2017-10-01

We present design calculations demonstrating the feasibility of measuring single-mode deceleration stage Rayleigh-Taylor instability (RTI) growth at a factor of four convergence. RTI growth rates are modified as a result of convergence [Bell LA-1321, 1951], and cylindrical targets are considered here, as they allow direct diagnostic access along the interface. The 2D computations, performed with the radiation-hydrodynamics code xRAGE [Gittings et al., CSD 2008] utilizing a new laser ray-tracing package, predict growth factors of 6 to 10 for mode 10 and 4 to 6 for mode 4, both of high interest in evaluating inertial confinement fusion capsule degradation mechanisms [Bose et al., this conference]. These results compare favorably to a linear theory [Epstein, PoP 2004] and to a buoyancy-drag model [Srebro et al., LPB 2003], which accounts for the linear and non-linear stages. Synthetic radiographs, produced by combining 2D computations of axial and transverse cross-sections, indicate this growth will be observable, and these will be compared to experimental data obtained at the OMEGA laser facility. Work performed by Los Alamos National Laboratory under contract DE-AC52-06NA25396 for the National Nuclear Security Administration of the U.S. Department of Energy. (LA-UR-17-25608).

Ghost instabilities of cosmological models with vector fields nonminimally coupled to the curvature

DOE Office of Scientific and Technical Information (OSTI.GOV)

Himmetoglu, Burak; Peloso, Marco; Contaldi, Carlo R.

2009-12-15

We prove that many cosmological models characterized by vectors nonminimally coupled to the curvature (such as the Turner-Widrow mechanism for the production of magnetic fields during inflation, and models of vector inflation or vector curvaton) contain ghosts. The ghosts are associated with the longitudinal vector polarization present in these models and are found from studying the sign of the eigenvalues of the kinetic matrix for the physical perturbations. Ghosts introduce two main problems: (1) they make the theories ill defined at the quantum level in the high energy/subhorizon regime (and create serious problems for finding a well-behaved UV completion), andmore » (2) they create an instability already at the linearized level. This happens because the eigenvalue corresponding to the ghost crosses zero during the cosmological evolution. At this point the linearized equations for the perturbations become singular (we show that this happens for all the models mentioned above). We explicitly solve the equations in the simplest cases of a vector without a vacuum expectation value in a Friedmann-Robertson-Walker geometry, and of a vector with a vacuum expectation value plus a cosmological constant, and we show that indeed the solutions of the linearized equations diverge when these equations become singular.« less

Precession Driven Instabilities and Dynamos in the Early Moon

NASA Astrophysics Data System (ADS)

Cebron, D.; Laguerre, R.; Noir, J.; Vidal, J.; Schaeffer, N.

2017-12-01

The Early Moon magnetic fields are probably due to a strong temporary dynamo, which may be due to lunar precession [1]. However, precession driven dynamos remain badly known, with only few studied cases [2,3,4]. Given the uncertainties of the early Moon precession, wider ranges of parameters need to be explored in order to assess if such lunar dynamos are possible. Using the efficient dynamo code XSHELLS, we have thus performed many simulations of precessing spherical shells, varying the parameters in a systematic way. This allows us to characterize the various excited instabilities, and to propose scaling laws. We also obtain that precession driven dynamos seem scarce and weak in our simulations, which makes difficult and uncertain the extrapolation of these dynamos to the Moon. However, our dynamo simulations, as every other in the literature, neglect the topographic torque effect on instabilities in order to use fast spectral codes [5]. By contrast, the topographic torque is dominant for the lunar core. Before exploring this effect numerically, which is a real challenge, we choose to study it theoretically. To do so, we have developed a novel global linear stability analysis of mechanically-driven flows in triaxial ellipsoids, with leading order viscous effects. Internal dissipation is obtained for the first time by extending the Greenspan's theory (1968) of geostrophic and inertial modes. By contrast with pioneering theories [6], we propose a new linear viscous model valid in arbitrary ellipsoid and for any precessing forcing. Then we perform the linear stability analysis by considering ellipsoidal perturbations of unprecedented spatial complexity with a self-consistent model of viscous damping. We show that forced precession-driven basic flows are bistable in triaxial ellipsoids. Then, we present the first stability analysis of precessing-flows in triaxial ellipsoids. [1] Dwyer et al. (2011), Nature, 479, 212-214.[2] Tilgner (2005), Phy. Fluids, 17, 034104.[3] Tilgner (2007), Geo. Astro. Fluid Dyn., 101 (1), 1-9.[4] Lin et al. (2016), Phys. Fluids, 28, 066601.[5] Tian et al., EPSL, in revision.[6] Busse (1968), J. Fluid. Mech, 33 (04), 739-751.

Universal elastic-hardening-driven mechanical instability in α-quartz and quartz homeotypes under pressure

PubMed Central

Dong, Juncai; Zhu, Hailiang; Chen, Dongliang

2015-01-01

As a fundamental property of pressure-induced amorphization (PIA) in ice and ice-like materials (notably α-quartz), the occurrence of mechanical instability can be related to violation of Born criteria for elasticity. The most outstanding elastic feature of α-quartz before PIA has been experimentally reported to be the linear softening of shear modulus C44, which was proposed to trigger the transition through Born criteria B3. However, by using density-functional theory, we surprisingly found that both C44 and C66 in α-quartz exhibit strong nonlinearity under compression and the Born criteria B3 vanishes dominated by stiffening of C14, instead of by decreasing of C44. Further studies of archetypal quartz homeotypes (GeO2 and AlPO4) repeatedly reproduced the same elastic-hardening-driven mechanical instability, suggesting a universal feature of this family of crystals and challenging the long-standing idea that negative pressure derivatives of individual elastic moduli can be interpreted as the precursor effect to an intrinsic structural instability preceding PIA. The implications of this elastic anomaly in relation to the dispersive softening of the lowest acoustic branch and the possible transformation mechanism were also discussed. PMID:26099720

Universal elastic-hardening-driven mechanical instability in α-quartz and quartz homeotypes under pressure.

PubMed

Dong, Juncai; Zhu, Hailiang; Chen, Dongliang

2015-06-23

As a fundamental property of pressure-induced amorphization (PIA) in ice and ice-like materials (notably α-quartz), the occurrence of mechanical instability can be related to violation of Born criteria for elasticity. The most outstanding elastic feature of α-quartz before PIA has been experimentally reported to be the linear softening of shear modulus C44, which was proposed to trigger the transition through Born criteria B3. However, by using density-functional theory, we surprisingly found that both C44 and C66 in α-quartz exhibit strong nonlinearity under compression and the Born criteria B3 vanishes dominated by stiffening of C14, instead of by decreasing of C44. Further studies of archetypal quartz homeotypes (GeO2 and AlPO4) repeatedly reproduced the same elastic-hardening-driven mechanical instability, suggesting a universal feature of this family of crystals and challenging the long-standing idea that negative pressure derivatives of individual elastic moduli can be interpreted as the precursor effect to an intrinsic structural instability preceding PIA. The implications of this elastic anomaly in relation to the dispersive softening of the lowest acoustic branch and the possible transformation mechanism were also discussed.

Radar observations of density gradients, electric fields, and plasma irregularities near polar cap patches in the context of the gradient-drift instability

NASA Astrophysics Data System (ADS)

Lamarche, Leslie J.; Makarevich, Roman A.

2017-03-01

We present observations of plasma density gradients, electric fields, and small-scale plasma irregularities near a polar cap patch made by the Super Dual Auroral Radar Network radar at Rankin Inlet (RKN) and the northern face of Resolute Bay Incoherent Scatter Radar (RISR-N). RKN echo power and occurrence are analyzed in the context of gradient-drift instability (GDI) theory, with a particular focus on the previously uninvestigated 2-D dependencies on wave propagation, electric field, and gradient vectors, with the latter two quantities evaluated directly from RISR-N measurements. It is shown that higher gradient and electric field components along the wave vector generally lead to the higher observed echo occurrence, which is consistent with the expected higher GDI growth rate, but the relationship with echo power is far less straightforward. The RKN echo power increases monotonically as the predicted linear growth rate approaches zero from negative values but does not continue this trend into positive growth rate values, in contrast with GDI predictions. The observed greater consistency of echo occurrence with GDI predictions suggests that GDI operating in the linear regime can control basic plasma structuring, but measured echo strength may be affected by other processes and factors, such as multistep or nonlinear processes or a shear-driven instability.

Interface Instabilities in the Interstellar Medium

NASA Technical Reports Server (NTRS)

Hunter, J. H., Jr.; Siopis, C.; Whitaker, R. W.; Lovelace, R. V. E.

1995-01-01

In the present communication, we reexamine two limiting cases of star-forming mechanisms involving self-gravity, thermodynamics, and velocity fields, that we believe must be ubiquitous in the ISM -- the generally oblique collision of supersonic gas streams or turbulent eddies. The general case of oblique collisions has not yet been examined. However, two limiting cases have been studied in detail: (1) The head-on collision of two identical gas streams that form dense, cool accretion shocks that become unstable and may form Jeans mass clouds, which subsequently undergo collapse. (2) Linearly unstable tangential velocity discontinuities, which result in Kelvin-Helmholtz (K-H) instabilities and related phenomena. The compressible K-H instabilities exhibit rich and unexpected behaviors. Moreover a new thermal-dynamic (T-D) mode was discovered that arises from the coupling of the perturbed thermal behavior and the unperturbed flow. The T-D mode has the curious characteristic that it may be strongly unstable to interface modes when the global modes in either medium are absolutely thermally stable. In the present communication additional models of case 1 are described and discussed, and self-gravity is added in the linear theory of tangential discontinuities, case 2. We prove that self-gravity fundamentally changes the behavior of interfacial modes -- density discontinuities (or steps) are inherently unstable on roughly the free-fall timescale of the denser medium to perturbations of all wavelengths.

Nonlinear evolution dynamics of holographic superconductor model with scalar self-interaction

NASA Astrophysics Data System (ADS)

Li, Ran; Zi, Tieguang; Zhang, Hongbao

2018-04-01

We investigate the holographic superconductor model that is described by the Einstein-Maxwell theory with the self-interaction term λ |Ψ |4 of complex scalar field in asymptotic anti-de Sitter (AdS) spacetime. Below critical temperature Tc, the planar Reissner-Nordström-AdS black hole is unstable due to the near-horizon scalar condensation instability. We study the full nonlinear development of this instability by numerically solving the gravitational dynamics in the asymptotic AdS spacetime, and observe a dynamical process from the perturbed Reissner-Nordström-AdS black hole to a hairy black hole when the initial black hole temperature T

Shape of Strained Solid He-4 at Low Temperatures

NASA Technical Reports Server (NTRS)

Kojima, Harry

2004-01-01

(1) Interferometer apparatus for measuring surface profile (2) For small strains, the expected linear decrease in height is not seen. (3) For large strains, undulation and irreversible deformations begin to set in, but we cannot yet make clear connection with stress-driven instability theory. Torii and Balibar have observed appearances of deformations beyond threshold stress on He-4 solid surface. The difference of our results from theory real? We are not ready to claim in affirmative. To be able to answer: 1) improve crystal growth techniques; (orientation, annealing, better pressure control) 2) improve homogeneity of stress; (better alignment with vertical, better understanding of interaction between solid He-4 and walls) 4) improve optics.

Galaxy clustering and the origin of large-scale flows

NASA Technical Reports Server (NTRS)

Juszkiewicz, R.; Yahil, A.

1989-01-01

Peebles's 'cosmic virial theorem' is extended from its original range of validity at small separations, where hydrostatic equilibrium holds, to large separations, in which linear gravitational stability theory applies. The rms pairwise velocity difference at separation r is shown to depend on the spatial galaxy correlation function xi(x) only for x less than r. Gravitational instability theory can therefore be tested by comparing the two up to the maximum separation for which both can reliably be determined, and there is no dependence on the poorly known large-scale density and velocity fields. With the expected improvement in the data over the next few years, however, this method should yield a reliable determination of omega.

de Sitter limit analysis for dark energy and modified gravity models

NASA Astrophysics Data System (ADS)

De Felice, Antonio; Frusciante, Noemi; Papadomanolakis, Georgios

2017-07-01

The effective field theory of dark energy and modified gravity is supposed to well describe, at low energies, the behavior of the gravity modifications due to one extra scalar degree of freedom. The usual curvature perturbation is very useful when studying the conditions for the avoidance of ghost instabilities as well as the positivity of the squared speeds of propagation for both the scalar and tensor modes, or the Stückelberg field performs perfectly when investigating the evolution of linear perturbations. We show that the viable parameter space identified by requiring no-ghost instabilities and positive squared speeds of propagation does not change by performing a field redefinition, while the requirement of the avoidance of tachyonic instability might instead be different. Therefore, we find it interesting to associate to the general modified gravity theory described in the effective field theory framework, a perturbation field which will inherit all of the properties of the theory. In the present paper we address the following questions: (1) how can we define such a field? and (2) what is the mass of such a field as the background approaches a final de Sitter state? We define a gauge-invariant quantity which identifies the density of the dark energy perturbation field valid for any background. We derive the mass associated to the gauge-invariant dark energy field on a de Sitter background, which we retain to be still a good approximation also at very low redshift (z ≃0 ). On this background we also investigate the value of the speed of propagation and we find that there exist classes of theories which admit a nonvanishing speed of propagation, even in the Horndeski model, for which a zero speed of sound has previously been found in the literature. We finally apply our results to specific well-known models.

Mode selection of magneto-Rayleigh-Taylor instability from the point of view of Landau phase transition theory

NASA Astrophysics Data System (ADS)

Dan, Jia Kun; Huang, Xian Bin; Ren, Xiao Dong; Wei, Bing

2017-08-01

A theoretical model referring to mode selection of Z-pinch-driven magneto-Rayleigh-Taylor (MRT) instability, which explains the generation of fundamental instability mode and evolution of fundamental wavelength in experiments, is proposed on the basis of the Landau theory of phase transition. The basic idea of this phase transition model lies in that the appearance of MRT instability pattern can be considered as a consequence of the spontaneous generation of interfacial structure like the spontaneous magnetization in a ferromagnetic system. It is demonstrated that the amplitude of instability is responsible for the order parameter in the Landau theory of phase transition and the fundamental wavelength appears to play a role analogous to inverse temperature in thermodynamics. Further analysis indicates that the MRT instability is characterized by first order phase transition and the fundamental wavelength is proportional to the square root of energy entering into the system from the driving source. The theory predicts that the fundamental wavelength grows rapidly and saturates reaching a limiting wavelength of the order of the liner's final outer radius. The results given by this theory show qualitative agreement with the available experimental data of MRT instability of liner implosions conducted on the Sandia Z machine as well as Primary Test Stand facility at the Institute of Fluid Physics.

Beyond generalized Proca theories

NASA Astrophysics Data System (ADS)

Heisenberg, Lavinia; Kase, Ryotaro; Tsujikawa, Shinji

2016-09-01

We consider higher-order derivative interactions beyond second-order generalized Proca theories that propagate only the three desired polarizations of a massive vector field besides the two tensor polarizations from gravity. These new interactions follow the similar construction criteria to those arising in the extension of scalar-tensor Horndeski theories to Gleyzes-Langlois-Piazza-Vernizzi (GLPV) theories. On the isotropic cosmological background, we show the existence of a constraint with a vanishing Hamiltonian that removes the would-be Ostrogradski ghost. We study the behavior of linear perturbations on top of the isotropic cosmological background in the presence of a matter perfect fluid and find the same number of propagating degrees of freedom as in generalized Proca theories (two tensor polarizations, two transverse vector modes, and two scalar modes). Moreover, we obtain the conditions for the avoidance of ghosts and Laplacian instabilities of tensor, vector, and scalar perturbations. We observe key differences in the scalar sound speed, which is mixed with the matter sound speed outside the domain of generalized Proca theories.

Linear Instability of a Uni-Directional Transversely Sheared Mean Flow

NASA Technical Reports Server (NTRS)

Wundrow, David W.

1996-01-01

The effect of spanwise-periodic mean-flow distortions (i.e. streamwise-vortex structures) on the evolution of small-amplitude, single-frequency instability waves in an otherwise two-dimensional shear flow is investigated. The streamwise-vortex structures are taken to be just weak enough so that the spatially growing instability waves behave (locally) like linear perturbations about a uni-directional transversely sheared mean flow. Numerical solutions are computed and discussed for both the mean flow and the instability waves. The influence of the streamwise-vortex wavelength on the properties of the most rapidly growing instability wave is also discussed.

Parametric dependence of density limits in the Tokamak Experiment for Technology Oriented Research (TEXTOR): Comparison of thermal instability theory with experiment

NASA Astrophysics Data System (ADS)

Kelly, F. A.; Stacey, W. M.; Rapp, J.

2001-11-01

The observed dependence of the TEXTOR [Tokamak Experiment for Technology Oriented Research: E. Hintz, P. Bogen, H. A. Claassen et al., Contributions to High Temperature Plasma Physics, edited by K. H. Spatschek and J. Uhlenbusch (Akademie Verlag, Berlin, 1994), p. 373] density limit on global parameters (I, B, P, etc.) and wall conditioning is compared with the predicted density limit parametric scaling of thermal instability theory. It is necessary first to relate the edge parameters of the thermal instability theory to n¯ and the other global parameters. The observed parametric dependence of the density limit in TEXTOR is generally consistent with the predicted density limit scaling of thermal instability theory. The observed wall conditioning dependence of the density limit can be reconciled with the theory in terms of the radiative emissivity temperature dependence of different impurities in the plasma edge. The thermal instability theory also provides an explanation of why symmetric detachment precedes radiative collapse for most low power shots, while a multifaceted asymmetric radiation from the edge MARFE precedes detachment for most high power shots.

Thermo-capillary effect on the linear temporal and spatial instability of viscous liquid jets falling under gravity

NASA Astrophysics Data System (ADS)

Alsharif, Abdullah M.; Althubaiti, Shadiah A.

2018-03-01

The thermal modulation of Newtonian liquid jets at the orifice causes a variation in surface tension, which propagates downstream inducing Marangoni instability. Therefore, the linear temporal and spatial instability should be investigated to predict the same size of producing small spherical pellets. In this paper, we consider a viscous liquid jet emerging from a nozzle subject to thermo-capillary effects falling under gravity. Moreover, we use the asymptotic approach to reduce the governing equation into one-dimensional (1-D). The steady state solutions have been found using a modified Newton's method, and then the linear instability analysis has been investigated of the resulting set of equations.

A general theory of linear cosmological perturbations: stability conditions, the quasistatic limit and dynamics

NASA Astrophysics Data System (ADS)

Lagos, Macarena; Bellini, Emilio; Noller, Johannes; Ferreira, Pedro G.; Baker, Tessa

2018-03-01

We analyse cosmological perturbations around a homogeneous and isotropic background for scalar-tensor, vector-tensor and bimetric theories of gravity. Building on previous results, we propose a unified view of the effective parameters of all these theories. Based on this structure, we explore the viable space of parameters for each family of models by imposing the absence of ghosts and gradient instabilities. We then focus on the quasistatic regime and confirm that all these theories can be approximated by the phenomenological two-parameter model described by an effective Newton's constant and the gravitational slip. Within the quasistatic regime we pinpoint signatures which can distinguish between the broad classes of models (scalar-tensor, vector-tensor or bimetric). Finally, we present the equations of motion for our unified approach in such a way that they can be implemented in Einstein-Boltzmann solvers.

When linear stability does not exclude nonlinear instability

DOE PAGES

Kevrekidis, P. G.; Pelinovsky, D. E.; Saxena, A.

2015-05-29

We describe a mechanism that results in the nonlinear instability of stationary states even in the case where the stationary states are linearly stable. In this study, this instability is due to the nonlinearity-induced coupling of the linearization’s internal modes of negative energy with the continuous spectrum. In a broad class of nonlinear Schrödinger equations considered, the presence of such internal modes guarantees the nonlinear instability of the stationary states in the evolution dynamics. To corroborate this idea, we explore three prototypical case examples: (a) an antisymmetric soliton in a double-well potential, (b) a twisted localized mode in a one-dimensionalmore » lattice with cubic nonlinearity, and (c) a discrete vortex in a two-dimensional saturable lattice. In all cases, we observe a weak nonlinear instability, despite the linear stability of the respective states.« less

Energy dynamics in a simulation of LAPD turbulence

NASA Astrophysics Data System (ADS)

Friedman, Brett

2012-10-01

It is often assumed that linear instabilities maintain turbulence in plasmas and some fluids, but this is not always the case. It is well known that many fluids display subcritical turbulence at a Reynolds number well below the threashold of linear instability. Certain plasma models such as drift waves in a sheared slab also exhibit subcritical turbulence [1]. In other instances such as drift-ballooning turbulence in tokamak edge plasmas, linear instabilities exist in a system, but they become subdominant to more robust nonlinear mechanisms that sustain a turbulent state [2, 3]. In our simulation of LAPD turbulence, which was previously analyzed in [4], we diagnose the results using an energy dynamics analysis [5]. This allows us to track energy input into turbulent fluctuations and energy dissipation out of them. We also track conservative energy transfer between different energy types (e.g. from potential to kinetic energy) and between different Fourier waves of the system. The result is that a nonlinear instability drives and maintains the turbulence in the steady state saturated phase of the simulation. While a linear restistive drift wave instability resides in the system, the nonlinear drift wave instability dominates when the fluctuation amplitude becomes large enough. The nonlinear instability is identified by its energy growth rate spectrum, which varies significantly from the linear growth rate spectrum. The main differences are the presence of positive growth rates when k|| = 0 and negative growth rates for nonzero k||, which is opposite that of the linear growth rate spectrum.[4pt] [1] B. D. Scott, Phys. Rev. Lett., 65, 3289 (1990).[0pt] [2] A. Zeiler et al, Phys. Plasmas, 3, 2951 (1996).[0pt] [3] B. D. Scott, Phys. Plasmas, 12, 062314 (2005).[0pt] [4] P. Popovich et al, Phys. Plasmas, 17, 122312 (2010).[0pt] [5] [physics.plasm-ph].

Secular evolution of eccentricity in protoplanetary discs with gap-opening planets

NASA Astrophysics Data System (ADS)

Teyssandier, Jean; Ogilvie, Gordon I.

2017-06-01

We explore the evolution of the eccentricity of an accretion disc perturbed by an embedded planet whose mass is sufficient to open a large gap in the disc. Various methods for representing the orbit-averaged motion of an eccentric disc are discussed. We characterize the linear instability that leads to the growth of eccentricity by means of hydrodynamical simulations. We numerically recover the known result that eccentricity growth in the disc is possible when the planet-to-star mass ratio exceeds 3 × 10-3. For mass ratios larger than this threshold, the precession rates and growth rates derived from simulations, as well as the shape of the eccentric mode, compare well with the predictions of a linear theory of eccentric discs. We study mechanisms by which the eccentricity growth eventually saturates into a non-linear regime.

Variations on holography from modifications of gravity in anti-de sitter

NASA Astrophysics Data System (ADS)

Apolo Velez, Luis Alberto

In this thesis we study aspects of the AdS/CFT correspondence that result from modifications of gravity in the bulk and lead to novel features in the dual theories at the boundary. The variations on the holographic theme studied in this thesis are model-independent since we have not assumed a particular UV-completion of gravity. Our results can be applied to a wide class of models that include higher-spin theories and compactifications of string theory on AdS backgrounds. The modifications of the bulk physics studied in this thesis include massive gravitons, higher-derivative terms in the Einstein-Hilbert action, and new boundary conditions for gravity. We begin by showing that it is possible to construct duals with a massive graviton in the bulk by deforming the dual theory at the boundary. This procedure does not break the translation invariance of the dual theory and might be useful in the study of certain condensed matter systems. We then construct the most general class of parity-even tricritical gravities in three and four dimensions. These higher-derivative theories are not unitary and characterized by the logarithmic fall-off of their linearized perturbations. They are conjectured to be dual to rank-3 logarithmic conformal field theories. We will show that, at linear order in the equations of motion, it is possible to truncate the theory to a unitary subsector. We also show that tricritical gravities in three and four dimensions suffer from a linearization instability that forbids unitary truncations beyond linear order. Finally we consider the role of boundary conditions in the AdS3/CFT2 correspondence. We show that free boundary conditions that lead to enhanced asymptotic symmetry groups are dual to 2D theories of quantum gravity in either the conformal or lightcone gauges. In particular we match the generators of symmetries in the bulk and boundary theories and show that a proper identification of the generator of Virasoro transformations in the bulk leads to a vanishing total central charge. We also show that this identification is consistent with the constraint equations of 2D gravity.

Instability of black strings in the third-order Lovelock theory

NASA Astrophysics Data System (ADS)

Giacomini, Alex; Henríquez-Báez, Carla; Lagos, Marcela; Oliva, Julio; Vera, Aldo

2016-05-01

We show that homogeneous black strings of third-order Lovelock theory are unstable under s-wave perturbations. This analysis is done in dimension D =9 , which is the lowest dimension that allows the existence of homogeneous black strings in a theory that contains only the third-order Lovelock term in the Lagrangian. As is the case in general relativity, the instability is produced by long wavelength perturbations and it stands for the perturbative counterpart of a thermal instability. We also provide a comparative analysis of the instabilities of black strings at a fixed radius in general relativity, Gauss-Bonnet, and third-order Lovelock theories. We show that the minimum critical wavelength that triggers the instability grows with the power of the curvature defined in the Lagrangian. The maximum exponential growth during the time of the perturbation is the largest in general relativity and it decreases with the number of curvatures involved in the Lagrangian.

Delay-induced Turing-like waves for one-species reaction-diffusion model on a network

NASA Astrophysics Data System (ADS)

Petit, Julien; Carletti, Timoteo; Asllani, Malbor; Fanelli, Duccio

2015-09-01

A one-species time-delay reaction-diffusion system defined on a complex network is studied. Traveling waves are predicted to occur following a symmetry-breaking instability of a homogeneous stationary stable solution, subject to an external nonhomogeneous perturbation. These are generalized Turing-like waves that materialize in a single-species populations dynamics model, as the unexpected byproduct of the imposed delay in the diffusion part. Sufficient conditions for the onset of the instability are mathematically provided by performing a linear stability analysis adapted to time-delayed differential equations. The method here developed exploits the properties of the Lambert W-function. The prediction of the theory are confirmed by direct numerical simulation carried out for a modified version of the classical Fisher model, defined on a Watts-Strogatz network and with the inclusion of the delay.

Candidate Elastic Quantum Critical Point in LaCu 6 - x Au x

DOE Office of Scientific and Technical Information (OSTI.GOV)

Poudel, Lekh; May, Andrew F.; Koehler, Michael R.

2016-11-30

In this paper, the structural properties of LaCu 6-xAu x are studied using neutron diffraction, x-ray diffraction, and heat capacity measurements. The continuous orthorhombic-monoclinic structural phase transition in LaCu 6 is suppressed linearly with Au substitution until a complete suppression of the structural phase transition occurs at the critical composition x c=0.3. Heat capacity measurements at low temperatures indicate residual structural instability at x c. The instability is ferroelastic in nature, with density functional theory calculations showing negligible coupling to electronic states near the Fermi level. Finally, the data and calculations presented here are consistent with the zero temperature terminationmore » of a continuous structural phase transition suggesting that the LaCu 6-xAu x series hosts an elastic quantum critical point.« less

Barotropic instability with divergence - Theory and applications to Venus

NASA Technical Reports Server (NTRS)

Dobrovolskis, Anthony R.; Diner, David J.

1990-01-01

IR images of Venus reveal a curious double-lobed hot spot in the polar region. Elson (1982) has suggested that this dipole represents a barotropic instability associated with a high-latitude jet. Unfortunately, the classical theory of barotropic instability cannot predict temperature variations. This paper generalizes the theory to include horizontal divergence, vertical motions, and temperature variations, and applies it to the stratosphere of Venus. The fastest-growing barotropic instability in the nominal model matches the observed dipole in period and horizontal temperature pattern. The accompanying wind variations are comparable to the speed of the mean jet, indicating strong nonlinear effects. It is concluded that the Venus dipole may represent the self-limited stage of a barotropic instability with divergence.

Testing Munk's hypothesis for submesoscale eddy generation using observations in the North Atlantic

NASA Astrophysics Data System (ADS)

Buckingham, Christian E.; Khaleel, Zammath; Lazar, Ayah; Martin, Adrian P.; Allen, John T.; Naveira Garabato, Alberto C.; Thompson, Andrew F.; Vic, Clément

2017-08-01

A high-resolution satellite image that reveals a train of coherent, submesoscale (6 km) vortices along the edge of an ocean front is examined in concert with hydrographic measurements in an effort to understand formation mechanisms of the submesoscale eddies. The infrared satellite image consists of ocean surface temperatures at ˜390 m resolution over the midlatitude North Atlantic (48.69°N, 16.19°W). Concomitant altimetric observations coupled with regular spacing of the eddies suggest the eddies result from mesoscale stirring, filamentation, and subsequent frontal instability. While horizontal shear or barotropic instability (BTI) is one mechanism for generating such eddies (Munk's hypothesis), we conclude from linear theory coupled with the in situ data that mixed layer or submesoscale baroclinic instability (BCI) is a more plausible explanation for the observed submesoscale vortices. Here we assume that the frontal disturbance remains in its linear growth stage and is accurately described by linear dynamics. This result likely has greater applicability to the open ocean, i.e., regions where the gradient Rossby number is reduced relative to its value along coasts and within strong current systems. Given that such waters comprise an appreciable percentage of the ocean surface and that energy and buoyancy fluxes differ under BTI and BCI, this result has wider implications for open-ocean energy/buoyancy budgets and parameterizations within ocean general circulation models. In summary, this work provides rare observational evidence of submesoscale eddy generation by BCI in the open ocean.