Density-shear instability in electron magneto-hydrodynamics
Wood, T. S. Hollerbach, R.; Lyutikov, M.
2014-05-15
We discuss a novel instability in inertia-less electron magneto-hydrodynamics (EMHD), which arises from a combination of electron velocity shear and electron density gradients. The unstable modes have a lengthscale longer than the transverse density scale, and a growth-rate of the order of the inverse Hall timescale. We suggest that this density-shear instability may be of importance in magnetic reconnection regions on scales smaller than the ion skin depth, and in neutron star crusts. We demonstrate that the so-called Hall drift instability, previously argued to be relevant in neutron star crusts, is a resistive tearing instability rather than an instability of the Hall term itself. We argue that the density-shear instability is of greater significance in neutron stars than the tearing instability, because it generally has a faster growth-rate and is less sensitive to geometry and boundary conditions. We prove that, for uniform electron density, EMHD is “at least as stable” as regular, incompressible MHD, in the sense that any field configuration that is stable in MHD is also stable in EMHD. We present a connection between the density-shear instability in EMHD and the magneto-buoyancy instability in anelastic MHD.
Compressibility effect on magnetic-shear-localized ideal magnetohydrodynamic interchange instability
Gupta, Sangeeta; Callen, J.D.; Hegna, C.C.
2005-08-15
Eigenmode analysis of a magnetic-shear-localized ideal magnetohydrodynamic interchange instability in the presence of plasma compressibility indicates the marginal stability criterion (D{sub I}=1/4) is not affected by the compressibility effects. Above the marginal stability criterion, plasma compressibility causes a significant reduction in the growth rate of an ideal interchange instability.
Magnetohydrodynamic instability
NASA Technical Reports Server (NTRS)
Priest, E. R.; Cargill, P.; Forbes, T. G.; Hood, A. W.; Steinolfson, R. S.
1986-01-01
There have been major advances in the theory of magnetic reconnection and of magnetic instability, with important implications for the observations, as follows: (1) Fast and slow magnetic shock waves are produced by the magnetohydrodynamics of reconnection and are potential particle accelerators. (2) The impulsive bursty regime of reconnection gives a rapid release of magnetic energy in a series of bursts. (3) The radiative tearing mode creates cool filamentary structures in the reconnection process. (4) The stability analyses imply that an arcade can become unstable when either its height or twist of plasma pressure become too great.
Magnetohydrodynamic instabilities in rotating and precessing sheared flows: An asymptotic analysis
NASA Astrophysics Data System (ADS)
Salhi, A.; Lehner, T.; Cambon, C.
2010-07-01
Linear magnetohydrodynamic instabilities are studied analytically in the case of unbounded inviscid and electrically conducting flows that are submitted to both rotation and precession with shear in an external magnetic field. For given rotation and precession the possible configurations of the shear and of the magnetic field and their interplay are imposed by the “admissibility” condition (i.e., the base flow must be a solution of the magnetohydrodynamic Euler equations): we show that an “admissible” basic magnetic field must align with the basic absolute vorticity. For these flows with elliptical streamlines due to precession we undertake an analytical stability analysis for the corresponding Floquet system, by using an asymptotic expansion into the small parameter ɛ (ratio of precession to rotation frequencies) by a method first developed in the magnetoelliptical instabilities study by Lebovitz and Zweibel [Astrophys. J. 609, 301 (2004)]10.1086/420972. The present stability analysis is performed into a suitable frame that is obtained by a systematic change of variables guided by symmetry and the existence of invariants of motion. The obtained Floquet system depends on three parameters: ɛ , η (ratio of the cyclotron frequency to the rotation frequency) and χ=cosα , with α being a characteristic angle which, for circular streamlines, ɛ=0 , identifies with the angle between the wave vector and the axis of the solid body rotation. We look at the various (centrifugal or precessional) resonant couplings between the three present modes: hydrodynamical (inertial), magnetic (Alfvén), and mixed (magnetoinertial) modes by computing analytically to leading order in ɛ the instabilities by estimating their threshold, growth rate, and maximum growth rate and their bandwidths as functions of ɛ , η , and χ . We show that the subharmonic “magnetic” mode appears only for η>5/2 and at large η (≫1) the maximal growth rate of both the
NASA Technical Reports Server (NTRS)
Zhang, W.; Diamond, P. H.; Vishniac, E. T.
1994-01-01
Recently, the magnetic shearing instability (MSI) has been proposed as a dynamical mechanism for angular momentum transport in accretion disks (Balbus & Hawley 1991; Hawley & Balbus 1991). In this paper, the nonlinear dynamics of MSI modes in the presence of a vertical magnetic field B(sub 0) is discussed. In particular, the saturation levels of the fluctuating fields, the angular momentum flux, and the energy dissipation mechanism, are examined in detail. It is shown that MSI induces strong magnetohydrodynamic (MHD) turbulence in a range of wavenumbers 1/H is less than K is less than or equal to Omega/V(sub A)(sub 0)), where H is the thickness, Omega is the rotation frequency of the disk, and V(sub A)(sub 0) is the Alfven velocity. Despite the fact that the linear growth rate of MSI is maximal at small-scale (i.e., k is approximately Omega/V(sub A(sub 0)), angular momentum transport due to MSI turbulence is dominated by the magnetic Reynolds stress driven by large-scale modes (k is approximately 1/H). It is shown that the amplitude of low k(sub r) MSI eddies is limited primarily by subscale shear flow instability. Thus, dominant MSI cells are quasi-isotropic. In a stationary state, the effective Shakura-Sunyaev 'alpha' value is predicted to be of order V(sub A)(sub 0)0/C(sub s). In addition, the veritcal magnetic-field-induced MSI cells convert vertical magnetic field B(sub 0) into azimuthal magnetic field B(sub theta) in the disk. The generation of azimuthal magnetic field in turn introduces new physical processes, such as dynamo activity and azimuthal MSI turbulence. We conclude that it is not possible to decouple vertical MSI saturation from azimuthal MSI evolution. Low-frequency MSI cells are shown to co-exist with high-frequency radial buoyancy or internal waves. We show that modulational interaction between waves on these two frequency ranges is usually weak in the case when mean magnetic field is vertical. Thus, MSI and internal wave dynamics must be
Qiu, X. M.; Huang, L.; Jian, G. D.
2007-03-15
The Rayleigh-Taylor (RT) instability in Z pinches with sheared axial flow (SAF) is analyzed using finite Larmor radius (FLR) magnetohydrodynamic theory, in whose momentum equation the FLR effect (also referred to as the effect of gyroviscosity) is introduced through an anisotropic ion (FLR) stress tensor. A dispersion relation is derived for the linear RT instability. Both analytical and numerical solutions of the dispersion equation are given. The results indicate that the short-wavelength modes of the RT instability can be stabilized by a sufficient FLR, whereas the long-wavelength modes can be stabilized by a sufficient SAF. In the small-wavenumber region, for normalized wavenumber K<2.4, the hybrid RT/KH (Kelvin-Helmholtz) instability is shown to be the most difficult to stabilize. However the synergistic effect of the SAF and gyroviscosity can mitigate both the RT instability in the large-wavenumber region (K>2.4) and the hybrid RT/KH instability in the small-wavenumber region. In addition, this synergistic effect can compress the RT instability to a narrow wavenumber region. Even the thorough stabilization of the RT instability in the large-wavenumber region is possible with a sufficient SAF and a sufficient gyroviscosity.
Current-driven magnetohydrodynamic thermal instabilities in sheared fields. [of solar corona
NASA Technical Reports Server (NTRS)
Bodo, G.; Ferrari, A.; Massaglia, S.; Rosner, R.
1987-01-01
Approximate analytic solutions are sought for the dispersion relation for the MHD stability of magnetized medium in current-driven filamentation modes such as those observed in the solar atmosphere. The magnetic field is assumed to have a self-consistent sheared equilibrium structure. The analysis is carried out in the small wavenumber regime, where shear length is similar to the mode wavelength. Instability is found to depend on the ratio between the thermal and magnetic diffusivities, i.e., the Prandtl number, which identifies the unstable transverse wavenumbers. The instability conditions are expressed in an algebraic equation amenable to numerical solution. Results are provided from use of the model to determine the maximum growth rate and typical scale lengths of instabilities in a precoronal atmosphere and the lower transition region.
NASA Technical Reports Server (NTRS)
Wu, S. T.; Song, M. T.; Martens, P. C. H.; Dryer, M.
1991-01-01
A situation wherein a bipolar magnetic field embedded in a stratified solar atmosphere undergoes symmetrical shear motion at the footpoints is investigated via a 2D (nonplanar) MHD simulation. It was found that the vertical plasma flow velocities grow exponentially, leading to a new type of global MHD instability. The growth rate increases almost linearly until it reaches the same order of magnitude as the Alfven speed. Then a nonlinear MHD instability occurs beyond this point. It was found that the central loops are pinched by opposing Lorentz forces, and the outer closed loops stretch upward with the vertically-rising mass flow. The nonlinear dynamical shearing instability is illustrated by a numerical example that is given for three different values of the plasma beta that span several orders of magnitude.
Nakamura, T. K. M.; Hasegawa, H.; Shinohara, I.
2010-01-01
Ion-to-magnetohydrodynamic scale physics of the transverse velocity shear layer and associated Kelvin–Helmholtz instability (KHI) in a homogeneous, collisionless plasma are investigated by means of full particle simulations. The shear layer is broadened to reach a kinetic equilibrium when its initial thickness is close to the gyrodiameter of ions crossing the layer, namely, of ion-kinetic scale. The broadened thickness is larger in B⋅Ω<0 case than in B⋅Ω>0 case, where Ω is the vorticity at the layer. This is because the convective electric field, which points out of (into) the layer for B⋅Ω<0 (B⋅Ω>0), extends (reduces) the gyrodiameters. Since the kinetic equilibrium is established before the KHI onset, the KHI growth rate depends on the broadened thickness. In the saturation phase of the KHI, the ion vortex flow is strengthened (weakened) for B⋅Ω<0 (B⋅Ω>0), due to ion centrifugal drift along the rotational plasma flow. In ion inertial scale vortices, this drift effect is crucial in altering the ion vortex size. These results indicate that the KHI at Mercury-like ion-scale magnetospheric boundaries could show clear dawn-dusk asymmetries in both its linear and nonlinear growth. PMID:20838425
NASA Astrophysics Data System (ADS)
Miura, Akira
2003-02-01
A nonideal magnetohydrodynamic (MHD) Kelvin-Helmholtz (K-H) instability peculiar to a high-β plasma with a nonuniform pressure is studied for the magnetosheath field due north at the subsolar magnetopause, where the ideal MHD K-H instability driven by the shear in the E × B drift velocity is not operative. This instability is driven by the shear in the ion diamagnetic drift velocity, which is a nonideal MHD drift in a high-β plasma and is a macroscopic effect not visible at the guiding center level. The two-dimensional stability (k · B0 = 0) of a model subsolar magnetopause is investigated by solving the eigenmode equation for a polygonal ion diamagnetic drift velocity profile with the density ratio across the magnetopause as a parameter. Near the subsolar magnetopause the fastest growing wave or vortex propagates duskward with a phase velocity from 8 km/s to 14 km/s, and the normalized growth rate decreases with an increase in the ratio of the magnetosheath density to the magnetospheric density. The wavelength and period of the fastest growing mode increases with the density ratio. For realistic parameters near the subsolar magnetopause the wave period becomes 750 s to 2000 s and the wavelength becomes 11000 km to 16000 km. The present K-H instability ("diamagnetically driven K-H instability") may cause a plasma transport across the subsolar magnetopause, since the plasma motion is decoupled from that of the magnetic field owing to nonideal MHD. We discuss a possible dawn-dusk asymmetry (caused by the ion diamagnetic drift velocity at the magnetopause) of the K-H instability when the present instability is extended to the dayside magnetopause off the noon meridian, where the tailward E × B drift is no longer negligible. The vortex created by the present instability near the subsolar magnetopause has the same rotational sense as that created by the E × B shear driven K-H instability within the dusk flank boundary but has the opposite rotational sense to that
Sheared Electroconvective Instability
NASA Astrophysics Data System (ADS)
Kwak, Rhokyun; Pham, Van Sang; Lim, Kiang Meng; Han, Jongyoon
2012-11-01
Recently, ion concentration polarization (ICP) and related phenomena draw attention from physicists, due to its importance in understanding electrochemical systems. Researchers have been actively studying, but the complexity of this multiscale, multiphysics phenomenon has been limitation for gaining a detailed picture. Here, we consider electroconvective(EC) instability initiated by ICP under pressure-driven flow, a scenario often found in electrochemical desalinations. Combining scaling analysis, experiment, and numerical modeling, we reveal unique behaviors of sheared EC: unidirectional vortex structures, its size selection and vortex propagation. Selected by balancing the external pressure gradient and the electric body force, which generates Hagen-Poiseuille(HP) flow and vortical EC, the dimensionless EC thickness scales as (φ2 /UHP)1/3. The pressure-driven flow(or shear) suppresses unfavorably-directed vortices, and simultaneously pushes favorably-directed vortices with constant speed, which is linearly proportional to the total shear of HP flow. This is the first systematic characterization of sheared EC, which has significant implications on the optimization of electrodialysis and other electrochemical systems.
Nonideal magnetohydrodynamic instabilities and toroidal magnetic confinement
Furth, H.P.
1985-05-01
The marked divergence of experimentally observed plasma instability phenomena from the predictions of ideal magnetohydrodynamics led in the early 1960s to the formulations of finite-resistivity stability theory. Beginning in the 1970s, advanced plasma diagnostics have served to establish a detailed correspondence between the predictions of the finite-resistivity theory and experimental plasma behavior - particularly in the case of the resistive kink mode and the tokamak plasma. Nonlinear resistive-kink phenomena have been found to govern the transport of magnetic flux and plasma energy in the reversed-field pinch. The other predicted finite-resistivity instability modes have been more difficult to identify directly and their implications for toroidal magnetic confinement are still unresolved.
Transverse electron-scale instability in relativistic shear flows
NASA Astrophysics Data System (ADS)
Alves, E. P.; Grismayer, T.; Fonseca, R. A.; Silva, L. O.
2015-08-01
Electron-scale surface waves are shown to be unstable in the transverse plane of a sheared flow in an initially unmagnetized collisionless plasma, not captured by (magneto)hydrodynamics. It is found that these unstable modes have a higher growth rate than the closely related electron-scale Kelvin-Helmholtz instability in relativistic shears. Multidimensional particle-in-cell simulations verify the analytic results and further reveal the emergence of mushroomlike electron density structures in the nonlinear phase of the instability, similar to those observed in the Rayleigh Taylor instability despite the great disparity in scales and different underlying physics. This transverse electron-scale instability may play an important role in relativistic and supersonic sheared flow scenarios, which are stable at the (magneto)hydrodynamic level. Macroscopic (≫c /ωp e ) fields are shown to be generated by this microscopic shear instability, which are relevant for particle acceleration, radiation emission, and to seed magnetohydrodynamic processes at long time scales.
Transverse electron-scale instability in relativistic shear flows.
Alves, E P; Grismayer, T; Fonseca, R A; Silva, L O
2015-08-01
Electron-scale surface waves are shown to be unstable in the transverse plane of a sheared flow in an initially unmagnetized collisionless plasma, not captured by (magneto)hydrodynamics. It is found that these unstable modes have a higher growth rate than the closely related electron-scale Kelvin-Helmholtz instability in relativistic shears. Multidimensional particle-in-cell simulations verify the analytic results and further reveal the emergence of mushroomlike electron density structures in the nonlinear phase of the instability, similar to those observed in the Rayleigh Taylor instability despite the great disparity in scales and different underlying physics. This transverse electron-scale instability may play an important role in relativistic and supersonic sheared flow scenarios, which are stable at the (magneto)hydrodynamic level. Macroscopic (≫c/ωpe) fields are shown to be generated by this microscopic shear instability, which are relevant for particle acceleration, radiation emission, and to seed magnetohydrodynamic processes at long time scales. PMID:26382337
Shear instabilities in granular flows
NASA Astrophysics Data System (ADS)
Goldfarb, David J.; Glasser, Benjamin J.; Shinbrot, Troy
2002-01-01
Unstable waves have been long studied in fluid shear layers. These waves affect transport in the atmosphere and oceans, in addition to slipstream stability behind ships, aeroplanes and heat-transfer devices. Corresponding instabilities in granular flows have not been previously documented, despite the importance of these flows in geophysical and industrial systems. Here we report that breaking waves can form at the interface between two streams of identical grains flowing on an inclined plane downstream of a splitter plate. Changes in either the shear rate or the angle of incline cause such waves to appear abruptly. We analyse a granular flow model that agrees qualitatively with our experimental data; the model suggests that the waves result from competition between shear and extensional strains in the flowing granular bed. We propose a dimensionless shear number that governs the transition between steady and wavy flows.
Shear instabilities in granular flows.
Goldfarb, David J; Glasser, Benjamin J; Shinbrot, Troy
2002-01-17
Unstable waves have been long studied in fluid shear layers. These waves affect transport in the atmosphere and oceans, in addition to slipstream stability behind ships, aeroplanes and heat-transfer devices. Corresponding instabilities in granular flows have not been previously documented, despite the importance of these flows in geophysical and industrial systems. Here we report that breaking waves can form at the interface between two streams of identical grains flowing on an inclined plane downstream of a splitter plate. Changes in either the shear rate or the angle of incline cause such waves to appear abruptly. We analyse a granular flow model that agrees qualitatively with our experimental data; the model suggests that the waves result from competition between shear and extensional strains in the flowing granular bed. We propose a dimensionless shear number that governs the transition between steady and wavy flows. PMID:11797003
Magnetic control of magnetohydrodynamic instabilities in tokamaks
Strait, E. J.
2015-02-15
Externally applied, non-axisymmetric magnetic fields form the basis of several relatively simple and direct methods to control magnetohydrodynamic (MHD) instabilities in a tokamak, and most present and planned tokamaks now include a set of non-axisymmetric control coils for application of fields with low toroidal mode numbers. Non-axisymmetric applied fields are routinely used to compensate small asymmetries (δB/B∼10{sup −3} to 10{sup −4}) of the nominally axisymmetric field, which otherwise can lead to instabilities through braking of plasma rotation and through direct stimulus of tearing modes or kink modes. This compensation may be feedback-controlled, based on the magnetic response of the plasma to the external fields. Non-axisymmetric fields are used for direct magnetic stabilization of the resistive wall mode—a kink instability with a growth rate slow enough that feedback control is practical. Saturated magnetic islands are also manipulated directly with non-axisymmetric fields, in order to unlock them from the wall and spin them to aid stabilization, or position them for suppression by localized current drive. Several recent scientific advances form the foundation of these developments in the control of instabilities. Most fundamental is the understanding that stable kink modes play a crucial role in the coupling of non-axisymmetric fields to the plasma, determining which field configurations couple most strongly, how the coupling depends on plasma conditions, and whether external asymmetries are amplified by the plasma. A major advance for the physics of high-beta plasmas (β = plasma pressure/magnetic field pressure) has been the understanding that drift-kinetic resonances can stabilize the resistive wall mode at pressures well above the ideal-MHD stability limit, but also that such discharges can be very sensitive to external asymmetries. The common physics of stable kink modes has brought significant unification to the topics of static error
Magnetic control of magnetohydrodynamic instabilities in tokamaks
NASA Astrophysics Data System (ADS)
Strait, E. J.
2015-02-01
Externally applied, non-axisymmetric magnetic fields form the basis of several relatively simple and direct methods to control magnetohydrodynamic (MHD) instabilities in a tokamak, and most present and planned tokamaks now include a set of non-axisymmetric control coils for application of fields with low toroidal mode numbers. Non-axisymmetric applied fields are routinely used to compensate small asymmetries ( δB /B ˜10-3 to 10-4 ) of the nominally axisymmetric field, which otherwise can lead to instabilities through braking of plasma rotation and through direct stimulus of tearing modes or kink modes. This compensation may be feedback-controlled, based on the magnetic response of the plasma to the external fields. Non-axisymmetric fields are used for direct magnetic stabilization of the resistive wall mode—a kink instability with a growth rate slow enough that feedback control is practical. Saturated magnetic islands are also manipulated directly with non-axisymmetric fields, in order to unlock them from the wall and spin them to aid stabilization, or position them for suppression by localized current drive. Several recent scientific advances form the foundation of these developments in the control of instabilities. Most fundamental is the understanding that stable kink modes play a crucial role in the coupling of non-axisymmetric fields to the plasma, determining which field configurations couple most strongly, how the coupling depends on plasma conditions, and whether external asymmetries are amplified by the plasma. A major advance for the physics of high-beta plasmas ( β = plasma pressure/magnetic field pressure) has been the understanding that drift-kinetic resonances can stabilize the resistive wall mode at pressures well above the ideal-MHD stability limit, but also that such discharges can be very sensitive to external asymmetries. The common physics of stable kink modes has brought significant unification to the topics of static error fields at low
Shear Instabilities in Granular Flows
NASA Astrophysics Data System (ADS)
Shinbrot, Troy
2003-03-01
Unstable waves have long been studied in fluid shear layers. These waves affect transport in the atmosphere and oceans as well as slipstream stability behind ships, planes, and heat transfer devices. Corresponding instabilities in granular flows have not previously been documented, despite the importance of these flows in geophysical and industrial systems. We report here that breaking waves can form at the interface between two streams of identical grains downstream of a splitter plate. These waves appear abruptly in flow down an inclined plane as either shear rate or angle of incline is changed, and we analyze a granular flow model that qualitatively agrees with our experimental data. The waves appear from the model to be a manifestation of a competition between shear and extensional strains in the flowing granular bed, and we propose a dimensionless group to govern the transition between steady and wavy flows.
A destabilizing effect of rotation shear on magnetohydrodynamic ballooning modes
Connor, J. W.; Hastie, R. J.; Webster, A. J.
2007-04-15
The destabilization of ideal magnetohydrodynamic ballooning modes at finite rotation shear is demonstrated for the model s-{alpha} equilibrium by exploiting low magnetic shear, s, to simplify the two-dimensional stability problem to a one-dimensional eigenvalue problem. This simpler calculation captures the same features as exhibited by a full two-dimensional treatment, namely that stable values in the s-{alpha} stability diagram become unstable above a critical rotation shear. The first and second stability boundaries at low s are calculated as functions of rotation shear.
Ring current instabilities in the magnetohydrodynamic frequency range
NASA Technical Reports Server (NTRS)
Hasegawa, A.; Chen, L.
1992-01-01
This report summarizes recent theoretical developments in ring current plasma instabilities in the magnetohydrodynamic (MHD) frequency range but with the effect of finite Larmor radius, and discusses its relevance to satellite-based observations. Possible instabilities are the bounce resonant instabilities caused by a humped energy distribution, the drift mirror instability caused by an anisotropic pressure and the drift wave type instability caused by a combination of drift-bounce resonance and reduced Alfven frequency due to a high beta loading of the flux tube. Here, beta is proportional to plasma/magnetic pressures. Mechanisms leading to turbulence are also discussed.
NASA Astrophysics Data System (ADS)
Gestrin, S. G.; Gorbatenko, B. B.; Mezhonnova, A. S.
2016-05-01
It is shown that the resonance effect of a magnetohydrodynamic hypersonic shear flow on an elastic plate placed in it causes the development of wind instability. Plate bending oscillations propagating along the flow are stabilized in the hypersonic flow regime, whereas waves running at an angle to the flow remain unstable. Expression derived for the instability increment allows conclusions about the effect of the magnetic field on the interaction of waves with the flow to be drawn as well as about the feasibility of its suppression in an unstable flow regime.
Instability of subharmonic resonances in magnetogravity shear waves
NASA Astrophysics Data System (ADS)
Salhi, A.; Nasraoui, S.
2013-12-01
We study analytically the instability of the subharmonic resonances in magnetogravity waves excited by a (vertical) time-periodic shear for an inviscid and nondiffusive unbounded conducting fluid. Due to the fact that the magnetic potential induction is a Lagrangian invariant for magnetohydrodynamic Euler-Boussinesq equations, we show that plane-wave disturbances are governed by a four-dimensional Floquet system in which appears, among others, the parameter ɛ representing the ratio of the periodic shear amplitude to the vertical Brunt-Väisälä frequency N3. For sufficiently small ɛ and when the magnetic field is horizontal, we perform an asymptotic analysis of the Floquet system following the method of Lebovitz and Zweibel [Astrophys. J. 609, 301 (2004), 10.1086/420972]. We determine the width and the maximal growth rate of the instability bands associated with subharmonic resonances. We show that the instability of subharmonic resonance occurring in gravity shear waves has a maximal growth rate of the form Δm=(3√3 /16)ɛ. This instability persists in the presence of magnetic fields, but its growth rate decreases as the magnetic strength increases. We also find a second instability involving a mixing of hydrodynamic and magnetic modes that occurs for all magnetic field strengths. We also elucidate the similarity between the effect of a vertical magnetic field and the effect of a vertical Coriolis force on the gravity shear waves considering axisymmetric disturbances. For both cases, plane waves are governed by a Hill equation, and, when ɛ is sufficiently small, the subharmonic instability band is determined by a Mathieu equation. We find that, when the Coriolis parameter (or the magnetic strength) exceeds N3/2, the instability of the subharmonic resonance vanishes.
Instability of subharmonic resonances in magnetogravity shear waves.
Salhi, A; Nasraoui, S
2013-12-01
We study analytically the instability of the subharmonic resonances in magnetogravity waves excited by a (vertical) time-periodic shear for an inviscid and nondiffusive unbounded conducting fluid. Due to the fact that the magnetic potential induction is a Lagrangian invariant for magnetohydrodynamic Euler-Boussinesq equations, we show that plane-wave disturbances are governed by a four-dimensional Floquet system in which appears, among others, the parameter ɛ representing the ratio of the periodic shear amplitude to the vertical Brunt-Väisälä frequency N(3). For sufficiently small ɛ and when the magnetic field is horizontal, we perform an asymptotic analysis of the Floquet system following the method of Lebovitz and Zweibel [Astrophys. J. 609, 301 (2004)]. We determine the width and the maximal growth rate of the instability bands associated with subharmonic resonances. We show that the instability of subharmonic resonance occurring in gravity shear waves has a maximal growth rate of the form Δ(m)=(3√[3]/16)ɛ. This instability persists in the presence of magnetic fields, but its growth rate decreases as the magnetic strength increases. We also find a second instability involving a mixing of hydrodynamic and magnetic modes that occurs for all magnetic field strengths. We also elucidate the similarity between the effect of a vertical magnetic field and the effect of a vertical Coriolis force on the gravity shear waves considering axisymmetric disturbances. For both cases, plane waves are governed by a Hill equation, and, when ɛ is sufficiently small, the subharmonic instability band is determined by a Mathieu equation. We find that, when the Coriolis parameter (or the magnetic strength) exceeds N(3)/2, the instability of the subharmonic resonance vanishes. PMID:24483566
Electrostatic ion cyclotron velocity shear instability
NASA Technical Reports Server (NTRS)
Lemons, D. S.; Winske, D.; Gary, S. P.
1992-01-01
A local electrostatic dispersion equation is derived for a shear flow perpendicular to an ambient magnetic field, which includes all kinetic effects and involves only one important parameter. The dispersion equation is cast in the form of Gordeyev integrals and is solved numerically. Numerical solutions indicate that an ion cyclotron instability is excited. The instability occurs roughly at multiples of the ion cyclotron frequency (modified by the shear), with the growth rate or the individual harmonics overlapping in the wavenumber. At large values of the shear parameter, the instability is confined to long wavelengths, but at smaller shear, a second distinct branch at shorter wavelengths also appears. The properties of the instability obtained are compared with those obtained in the nonlocal limit by Ganguli et al. (1985, 1988).
Magnetohydrodynamic thermal instabilities in cool inhomogeneous atmospheres
NASA Technical Reports Server (NTRS)
Bodo, G.; Ferrari, A.; Massaglia, S.; Rosner, R.; Vaiana, G. S.
1985-01-01
The stability of magnetic loops to current-driven filamentation instabilities is investigated. The unperturbed atmosphere is assumed to be composed of an (upper) isothermal optically thin low-density portion and a (lower) higher-density portion which is in radiative equilibrium; in both cases, the atmosphere is in hydrostatic equilibrium, so that gravitational stratification is taken into account. In order to provide specific equilibrium conditions for evaluation of the dispersion relation, conditions appropriate for the surface of a solar-type star are adopted; i.e., a fairly low temperature (T = 5000 K) appropriate for a 'precoronal' state associated, for example, with magnetic flux emerging from photospheric levels under the action of magnetic buoyancy. A linear stability analysis is performed, and numerical results show that physically plausible current densities, which would be generated by typical loop-footpoint motions, are effective in driving MHD instabilities in such a plasma. The instability growth rates are strongly dependent on the assumed current density distribution and on the density scale height.
Morrison, P. J.; Tassi, E.; Tronko, N.
2013-04-15
Stability analyses for equilibria of the compressible reduced magnetohydrodynamics (CRMHD) model are carried out by means of the Energy-Casimir (EC) method. Stability results are compared with those obtained for ideal magnetohydrodynamics (MHD) from the classical {delta}W criterion. An identification of the terms in the second variation of the free energy functional for CRMHD with those of {delta}W is made: two destabilizing effects present for CRMHD turn out to correspond to the kink and interchange instabilities in usual MHD, while the stabilizing roles of field line bending and compressibility are also identified in the reduced model. Also, using the EC method, stability conditions in the presence of toroidal flow are obtained. A formal analogy between CRMHD and a reduced incompressible model for magnetized rotating disks, due to Julien and Knobloch [EAS Pub. Series, 21, 81 (2006)], is discovered. In light of this analogy, energy stability analysis shows that the condition for magnetorotational instability (MRI) for the latter model corresponds to the condition for interchange instability in CRMHD, with the Coriolis term and shear velocity playing the roles of the curvature term and pressure gradient, respectively. Using the EC method, stability conditions for the rotating disk model, for a large class of equilibria with possible non-uniform magnetic fields, are obtained. In particular, this shows it is possible for the MRI system to undergo, in addition to the MRI, another instability that is analogous to the kink instability. For vanishing magnetic field, the Rayleigh hydrodynamical stability condition is recovered.
Magnetohydrodynamic instability of a two fluid interface
NASA Astrophysics Data System (ADS)
Radwan, Ahmed E.
1992-02-01
The stability of a gas cylinder (density ϱ) immersed in a liquid (density ϱ') subjected to capillary, pressure gradient, inertia and electro-magnetic forces has been developed analytically and numerically. A general hydromagnetic eigenvalue relation describing the characteristics of that model is derived based on the linearized perturbation technique. In the absence of a magnetic field, the model is only unstable to axisymmetric disturbances whose wavelength is longer than the circumference of the gas cylinder and stable in all other disturbance states. The instability of the model rapidly decreases with increasing (ϱ'/ϱ) but can never be suppressed, however large the (ϱ'/ϱ) value is. The magnetic field has a strong stabilizing effect on all perturbation modes for all wavelengths. Its influence is to decrease the wavelength at which the capillary instability occurs. The latter could be completely suppressed above a certain value of the applied magnetic field strength, independent of (ϱ'/ϱ) values, then the stability arises. However, in a two-dimensional perturbation ( k = 0, k is the axial wavenumber) it is found that the capillary force remains unaffected by such a magnetic field. The present results coincide with our results [A.E. Radwan, J. Magn. Magn. Mater. 72 (1988) 219] if we neglect here the gas inertia force and with some Chandrasekhar's results [S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability (Dover, New York, 1981)] with appropriate choices.
Kinetic effects on the velocity-shear-driven instability
NASA Technical Reports Server (NTRS)
Wang, Z.; Pritchett, P. L.; Ashour-Abdalla, M.
1992-01-01
A comparison is made between the properties of the low-frequency long-wavelength velocity-shear-driven instability in kinetic theory and magnetohydrodynamics (MHD). The results show that the removal of adiabaticity along the magnetic field line in kinetic theory leads to modifications in the nature of the instability. Although the threshold for the instability in the two formalisms is the same, the kinetic growth rate and the unstable range in wave-number space can be larger or smaller than the MHD values depending on the ratio between the thermal speed, Alfven speed, and flow speed. When the thermal speed is much larger than the flow speed and the flow speed is larger than the Alfven speed, the kinetic formalism gives a larger maximum growth rate and broader unstable range in wave-number space. In this regime, the normalized wave number for instability can be larger than unity, while in MHD it is always less than unity. The normal mode profile in the kinetic case has a wider spatial extent across the shear layer.
SUPERSONIC SHEAR INSTABILITIES IN ASTROPHYSICAL BOUNDARY LAYERS
Belyaev, Mikhail A.; Rafikov, Roman R.
2012-06-20
Disk accretion onto weakly magnetized astrophysical objects often proceeds via a boundary layer (BL) that forms near the object's surface, in which the rotation speed of the accreted gas changes rapidly. Here, we study the initial stages of formation for such a BL around a white dwarf or a young star by examining the hydrodynamical shear instabilities that may initiate mixing and momentum transport between the two fluids of different densities moving supersonically with respect to each other. We find that an initially laminar BL is unstable to two different kinds of instabilities. One is an instability of a supersonic vortex sheet (implying a discontinuous initial profile of the angular speed of the gas) in the presence of gravity, which we find to have a growth rate of order (but less than) the orbital frequency. The other is a sonic instability of a finite width, supersonic shear layer, which is similar to the Papaloizou-Pringle instability. It has a growth rate proportional to the shear inside the transition layer, which is of order the orbital frequency times the ratio of stellar radius to the BL thickness. For a BL that is thin compared to the radius of the star, the shear rate is much larger than the orbital frequency. Thus, we conclude that sonic instabilities play a dominant role in the initial stages of nonmagnetic BL formation and give rise to very fast mixing between disk gas and stellar fluid in the supersonic regime.
Electromotive force due to magnetohydrodynamic fluctuations in sheared rotating turbulence
Squire, J.; Bhattacharjee, A.
2015-11-01
This article presents a calculation of the mean electromotive force arising from general small-scale magnetohydrodynamical turbulence, within the framework of the second-order correlation approximation. With the goal of improving understanding of the accretion disk dynamo, effects arising through small-scale magnetic fluctuations, velocity gradients, density and turbulence stratification, and rotation, are included. The primary result, which supplements numerical findings, is that an off-diagonal turbulent resistivity due to magnetic fluctuations can produce large-scale dynamo action-the magnetic analog of the "shear-current" effect. In addition, consideration of alpha effects in the stratified regions of disks gives the puzzling result that there is no strong prediction for a sign of alpha, since the effects due to kinetic and magnetic fluctuations, as well as those due to shear and rotation, are each of opposing signs and tend to cancel each other.
Electromotive force due to magnetohydrodynamic fluctuations in sheared rotating turbulence.
Squire, J; Bhattacharjee, A
2015-11-01
This article presents a calculation of the mean electromotive force arising from general small-scale magnetohydrodynamical turbulence, within the framework of the second-order correlation approximation. With the goal of improving understanding of the accretion disk dynamo, effects arising through small-scale magnetic fluctuations, velocity gradients, density and turbulence stratification, and rotation, are included. The primary result, which supplements numerical findings, is that an off-diagonal turbulent resistivity due to magnetic fluctuations can produce large-scale dynamo action-the magnetic analog of the "shear-current" effect. In addition, consideration of α effects in the stratified regions of disks gives the puzzling result that there is no strong prediction for a sign of α, since the effects due to kinetic and magnetic fluctuations, as well as those due to shear and rotation, are each of opposing signs and tend to cancel each other. PMID:26651796
Electromotive force due to magnetohydrodynamic fluctuations in sheared rotating turbulence
Squire, J.; Bhattacharjee, A.
2015-11-02
Here, this article presents a calculation of the mean electromotive force arising from general small-scale magnetohydrodynamical turbulence, within the framework of the second-order correlation approximation. With the goal of improving understanding of the accretion disk dynamo, effects arising through small-scale magnetic fluctuations, velocity gradients, density and turbulence stratification, and rotation, are included. The primary result, which supplements numerical findings, is that an off-diagonal turbulent resistivity due to magnetic fluctuations can produce large-scale dynamo action-the magnetic analog of the "shear-current" effect. In addition, consideration of alpha effects in the stratified regions of disks gives the puzzling result that there is no strong prediction for a sign of alpha, since the effects due to kinetic and magnetic fluctuations, as well as those due to shear and rotation, are each of opposing signs and tend to cancel each other.
Electromotive force due to magnetohydrodynamic fluctuations in sheared rotating turbulence
Squire, J.; Bhattacharjee, A.
2015-11-02
Here, this article presents a calculation of the mean electromotive force arising from general small-scale magnetohydrodynamical turbulence, within the framework of the second-order correlation approximation. With the goal of improving understanding of the accretion disk dynamo, effects arising through small-scale magnetic fluctuations, velocity gradients, density and turbulence stratification, and rotation, are included. The primary result, which supplements numerical findings, is that an off-diagonal turbulent resistivity due to magnetic fluctuations can produce large-scale dynamo action-the magnetic analog of the "shear-current" effect. In addition, consideration of alpha effects in the stratified regions of disks gives the puzzling result that there is nomore » strong prediction for a sign of alpha, since the effects due to kinetic and magnetic fluctuations, as well as those due to shear and rotation, are each of opposing signs and tend to cancel each other.« less
Nonlinear electron magnetohydrodynamics physics. IV. Whistler instabilities
Urrutia, J. M.; Stenzel, R. L.; Strohmaier, K. D.
2008-06-15
A very large low-frequency whistler mode is excited with magnetic loop antennas in a uniform laboratory plasma. The wave magnetic field exceeds the ambient field causing in one polarity a field reversal, and a magnetic topology resembling that of spheromaks in the other polarity. These propagating ''whistler spheromaks'' strongly accelerate the electrons and create non-Maxwellian distributions in their toroidal current ring. It is observed that the locally energized electrons in the current ring excite new electromagnetic instabilities and emit whistler modes with frequencies unrelated to the applied frequency. Emissions are also observed from electrons excited in X-type neutral lines around the antenna. The properties of the excited waves such as amplitudes, frequency spectra, field topologies, propagation, polarization, growth, and damping have been investigated. The waves remain linear (B{sub wave}<
Radiative instabilities in sheared magnetic field
NASA Technical Reports Server (NTRS)
Drake, J. F.; Sparks, L.; Van Hoven, G.
1988-01-01
The structure and growth rate of the radiative instability in a sheared magnetic field B have been calculated analytically using the Braginskii fluid equations. In a shear layer, temperature and density perturbations are linked by the propagation of sound waves parallel to the local magnetic field. As a consequence, density clumping or condensation plays an important role in driving the instability. Parallel thermal conduction localizes the mode to a narrow layer where K(parallel) is small and stabilizes short wavelengths k larger-than(c) where k(c) depends on the local radiation and conduction rates. Thermal coupling to ions also limits the width of the unstable spectrum. It is shown that a broad spectrum of modes is typically unstable in tokamak edge plasmas and it is argued that this instability is sufficiently robust to drive the large-amplitude density fluctuations often measured there.
Observations of the parametric decay instability of nonlinear magnetohydrodynamic waves
Spangler, S.R.; Leckband, J.A.; Cairns, I.H.
1997-03-01
One of the most important nonlinear processes for Alfven and fast magnetosonic waves is the decay instability, in which a forward propagating magnetohydrodynamic (MHD) wave is converted into a forward propagating ion acoustic wave and a backward propagating MHD wave. Despite an extensive theoretical literature and numerous computer simulations of the process, there is minimal experimental or observational evidence for its existence. In this paper we report an extensive search for evidence of the decay instability in the MHD wave field upstream of the Earth`s bow shock. Twenty intervals of spacecraft magnetometer and density data with durations between 21 and 168 min were examined. The observational signature of the decay instability sought was a quasi-monochromatic feature in the density power spectrum, attributable to the daughter ion acoustic wave, at a frequency higher than the main wave features in the magnetic power spectra. Such a feature was in fact observed for the interval in which the theoretically predicted instability growth rate was highest, as well as in a second interval for which the instability was permitted with a slower growth rate. However, the data set also contains three long intervals of data in which the {open_quotes}decay line{close_quotes} signature is not seen, although theoretically permitted. The decay line is also absent in four shorter intervals in which the plasma {beta} is less than unity, and the instability accordingly facilitated. Possible reasons for the absence of the instability in these intervals are discussed, such as a finite bandwidth for the parent wave field and plasma kinetic effects. {copyright} {ital 1997 American Institute of Physics.}
Observations of the parametric decay instability of nonlinear magnetohydrodynamic waves
NASA Astrophysics Data System (ADS)
Spangler, Steven R.; Leckband, James A.; Cairns, Iver H.
1997-03-01
One of the most important nonlinear processes for Alfvén and fast magnetosonic waves is the decay instability, in which a forward propagating magnetohydrodynamic (MHD) wave is converted into a forward propagating ion acoustic wave and a backward propagating MHD wave. Despite an extensive theoretical literature and numerous computer simulations of the process, there is minimal experimental or observational evidence for its existence. In this paper we report an extensive search for evidence of the decay instability in the MHD wave field upstream of the Earth's bow shock. Twenty intervals of spacecraft magnetometer and density data with durations between 21 and 168 min were examined. The observational signature of the decay instability sought was a quasi-monochromatic feature in the density power spectrum, attributable to the daughter ion acoustic wave, at a frequency higher than the main wave features in the magnetic power spectra. Such a feature was in fact observed for the interval in which the theoretically predicted instability growth rate was highest, as well as in a second interval for which the instability was permitted with a slower growth rate. However, the data set also contains three long intervals of data in which the "decay line'' signature is not seen, although theoretically permitted. The decay line is also absent in four shorter intervals in which the plasma β is less than unity, and the instability accordingly facilitated. Possible reasons for the absence of the instability in these intervals are discussed, such as a finite bandwidth for the parent wave field and plasma kinetic effects.
Overstability of acoustic waves in strongly magnetized anisotropic magnetohydrodynamic shear flows
Uchava, E. S.; Shergelashvili, B. M.; Tevzadze, A. G.; Poedts, S.
2014-08-15
We present a linear stability analysis of the perturbation modes in anisotropic magnetohydrodynamic (MHD) flows with velocity shear and strong magnetic field. Collisionless or weakly collisional plasma is described within the 16-momentum MHD fluid closure model that takes into account not only the effect of pressure anisotropy but also the effect of anisotropic heat fluxes. In this model, the low frequency acoustic wave is revealed into a standard acoustic mode and higher frequency fast thermo-acoustic and lower frequency slow thermo-acoustic waves. It is shown that thermo-acoustic waves become unstable and grow exponentially when the heat flux parameter exceeds some critical value. It seems that velocity shear makes thermo-acoustic waves overstable even at subcritical heat flux parameters. Thus, when the effect of heat fluxes is not profound acoustic waves will grow due to the velocity shear, while at supercritical heat fluxes the flow reveals compressible thermal instability. Anisotropic thermal instability should be also important in astrophysical environments, where it will limit the maximal value of magnetic field that a low density ionized anisotropic flow can sustain.
Residual turbulence from velocity shear stabilized interchange instabilities
Hung, C. P.; Hassam, A. B.
2013-01-15
The stabilizing effect of velocity shear on the macroscopic, broad bandwidth, ideal interchange instability is studied in linear and nonlinear regimes. A 2D dissipative magnetohydrodynamic (MHD) code is employed to simulate the system. For a given flow shear, V Prime , linear growth rates are shown to be suppressed to below the shear-free level at both the small and large wavelengths. With increasing V Prime , the unstable band in wavenumber-space shrinks so that the peak growth results for modes that correspond to relatively high wavenumbers, on the scale of the density gradient. In the nonlinear turbulent steady state, a similar turbulent spectrum obtains, and the convection cells are roughly circular. In addition, the density fluctuation level and the degree of flattening of the initial inverted density profile are found to decrease as V Prime increases; in fact, unstable modes are almost completely stabilized and the density profile reverts to laminar when V Prime is a few times the classic interchange growth rate. Moreover, the turbulent particle flux diminishes with increasing velocity shear such that all the flux is carried by the classical diffusive flux in the asymptotic limit. The simulations are compared with measurements of magnetic fluctuations from the Maryland Centrifugal Experiment, MCX, which investigated interchange modes in the presence of velocity shear. The experimental spectral data, taken in the plasma edge, are in general agreement with the numerical data obtained in higher viscosity simulations for which the level of viscosity is chosen consistent with MCX Reynolds numbers at the edge. In particular, the residual turbulence in both cases is dominated by elongated convection cells. Finally, concomitant Kelvin-Helmholtz instabilities in the system are also examined. Complete stability to interchanges is obtained only in the parameter space wherein the generalized Rayleigh inflexion theorem is satisfied.
Rotation-driven Shear Flow Instabilities
NASA Astrophysics Data System (ADS)
Chiueh, Tzihong
1996-10-01
A general treatment of stability is considered for an isentropic flow equilibrium against three-dimensional incompressible perturbations by taking into account the difference in the orientations of the system rotation and flow vorticity. It is shown that the aforementioned orientation difference can indeed generate a coupling that drives instabilities at the expense of the rotational energy. Two types of instability are identified, with one growing algebraically and the other growing exponentially; the parameter regimes for both instabilities are also located. The algebraically growing modes are destabilized more easily than the exponentially growing modes; for example, the former can be unstable when the angle between the rotation axis and the vorticity is beyond 70°.5, whereas the latter becomes unstable when this angle is greater than 90°. In addition, we find that even in the limit of small vorticity, the system may still be unstable algebraically at a considerable strength, in contrast to the case of exact zero vorticity, which is absolutely stable. This finding indicates the existence of structural instability for a rotating fluid. The present analysis is applied also to examination of the problem of shear mixing interior of an accreting white dwarf in the context of nova explosions. In order for the nuclear fuels to be blended deep inside the star and make the explosion, the high angular momentum accreted materials combined with the stellar materials should undergo shear flow instabilities. We find that the shear flow instabilities happen when the disk rotation axis is off by more than 900 from the star rotation axis. The instability has in general an exponential growth, on a timescale much shorter than that of the runaway nuclear burning.
Magnetohydrodynamic Waves and Instabilities in Homogeneous Gyrotropic Ultrarelativistic Plasma
NASA Astrophysics Data System (ADS)
Chou, M.; Hau, L.-N.
2004-08-01
In some astrophysical systems the ionized gas may be of such high temperature and so strongly magnetized that relativistic effects and pressure anisotropy must be considered in the magnetohydrodynamic (MHD) model. This paper gives an overview of the characteristics of linear MHD waves and instabilities in homogeneous ultrarelativistic plasmas with gyrotropic pressure. The energy closure is the double-polytropic laws with two polytropic exponents, γ∥ and γ⊥, and for the adiabatic and monatomic cases, the polytropic values (γ∥, γ⊥) are respectively (3, 2) and (2, 1.5) for nonrelativistic and ultrarelativistic plasmas. In this formulation, the general dispersion relations can conveniently be reduced to isotropic and/or nonrelativistic limits. Slow waves are found to exhibit some anomalies due to the pressure anisotropy in that they may possess a positive density-magnetic field correlation such as for fast waves and may possibly travel faster than intermediate waves. They may also develop a mirror instability, as well as a new type of compressible fire-hose instability that for a certain parameter regime may grow faster than the standard incompressible fire hose. Both the fire-hose and mirror instability criteria are found to have the same forms of β∥-β⊥>2 and γ∥β∥<β2⊥/(2+γ⊥β⊥), respectively, as for nonrelativistic plasma, although the growth rates may be significantly modified by the relativistic effect.
Turbulent Magnetohydrodynamic Reconnection Mediated by the Plasmoid Instability
NASA Astrophysics Data System (ADS)
Huang, Yi-Min; Bhattacharjee, A.
2016-02-01
It has been established that the Sweet-Parker current layer in high Lundquist number reconnection is unstable to the super-Alfvénic plasmoid instability. Past two-dimensional magnetohydrodynamic simulations have demonstrated that the plasmoid instability leads to a new regime where the Sweet-Parker current layer changes into a chain of plasmoids connected by secondary current sheets, and the averaged reconnection rate becomes nearly independent of the Lundquist number. In this work, a three-dimensional simulation with a guide field shows that the additional degree of freedom allows plasmoid instabilities to grow at oblique angles, which interact and lead to self-generated turbulent reconnection. The averaged reconnection rate in the self-generated turbulent state is of the order of a hundredth of the characteristic Alfvén speed, which is similar to the two-dimensional result but is an order of magnitude lower than the fastest reconnection rate reported in recent studies of externally driven three-dimensional turbulent reconnection. Kinematic and magnetic energy fluctuations both form elongated eddies along the direction of the local magnetic field, which is a signature of anisotropic magnetohydrodynamic turbulence. Both energy fluctuations satisfy power-law spectra in the inertial range, where the magnetic energy spectral index is in the range from -2.3 to -2.1, while the kinetic energy spectral index is slightly steeper, in the range from -2.5 to -2.3. The anisotropy of turbulence eddies is found to be nearly scale-independent, in contrast with the prediction of the Goldreich-Sridhar theory for anisotropic turbulence in a homogeneous plasma permeated by a uniform magnetic field.
Axisymmetric single shear element combustion instability experiment
NASA Technical Reports Server (NTRS)
Breisacher, Kevin J.
1993-01-01
The combustion stability characteristics of a combustor consisting of a single shear element and a cylindrical chamber utilizing LOX and gaseous hydrogen as propellants are presented. The combustor geometry and the resulting longitudinal mode instability are axisymmetric. Hydrogen injection temperature and pyrotechnic pulsing were used to determine stability boundaries. Mixture ratio, fuel annulus gap, and LOX post configuration were varied. Performance and stability data are presented for chamber pressures of 300 and 1000 psia.
Axisymmetric single shear element combustion instability experiment
NASA Technical Reports Server (NTRS)
Breisacher, Kevin J.
1993-01-01
The combustion stability characteristics of a combustor consisting of a single shear element and a cylindrical chamber utilizing LOX and gaseous hydrogen as propellants are presented. The combustor geometry and the resulting longitudinal mode instability are axisymmetric. Hydrogen injection temperature and pyrotechnic pulsing were used to determine stability boundaries. Mixture ratio, fuel annulus gap, and LOX post configuration were varied. Performance and stability data were obtained for chamber pressures of 300 and 1000 psia.
Axisymmetric single shear element combustion instability experiment
NASA Astrophysics Data System (ADS)
Breisacher, Kevin J.
1993-06-01
The combustion stability characteristics of a combustor consisting of a single shear element and a cylindrical chamber utilizing LOX and gaseous hydrogen as propellants are presented. The combustor geometry and the resulting longitudinal mode instability are axisymmetric. Hydrogen injection temperature and pyrotechnic pulsing were used to determine stability boundaries. Mixture ratio, fuel annulus gap, and LOX post configuration were varied. Performance and stability data are presented for chamber pressures of 300 and 1000 psia.
Global magnetohydrodynamic instabilities in the L-2M stellarator
Mikhailov, M. I.; Shchepetov, S. V.; Nührenberg, C.; Nührenberg, J.
2015-12-15
Analysis of global magnetohydrodynamic (MHD) instabilities in the L-2M stellarator (Prokhorov General Physics Institute, Russian Academy of Sciences) is presented. The properties of free-boundary equilibria states are outlined, the stability conditions for small-scale modes are briefly discussed, and the number of trapped particles is estimated. All the magnetic configurations under study are stable against ballooning modes. It is shown that global ideal internal MHD modes can be found reliably only in Mercier unstable plasmas. In plasma that is stable with respect to the Mercier criterion, global unstable modes that are localized in the vicinity of the free plasma boundary and are not associated with any rational magnetic surface inside the plasma (the so-called peeling modes) can be found. The radial structure of all perturbations under study is almost entirely determined by the poloidal coupling of harmonics. The results of calculations are compared with the available experimental data.
Magnetohydrodynamic Instabilities in a Simple Gasdynamic Mirror Propulsion System
NASA Technical Reports Server (NTRS)
Emrich, William J., Jr.; Hawk, Clark W.
2004-01-01
The gasdynamic mirror has been proposed as a concept which could form the basis of a highly efficient fusion rocket engine. Gasdynamic mirrors differ from most other mirror type plasma confinement schemes in that they have much larger aspect ratios and operate at somewhat higher plasma densities. To evaluate whether a gasdynamic mirror could indeed confine plasmas in a stable manner for long periods of time, a small scale experimental gasdynamic mirror was built and tested. The objective of this experiment was to determine ranges of mirror ratios and plasma densities over which gasdynamic mirror could maintain stable plasmas. Theoretical analyses indicated that plasma magnetohydrodynamic instabilities were likely to occur during subsonic to supersonic flow transitions in the mirror throat region of the gasdynamic mirror. The experimental evidence based upon data derived from the Langmuir probe measurements seems to confirm this analysis. The assumption that a gasdynamic mirror using a simple mirror geometry could be used as a propulsion system, therefore, appears questionable. Modifications to the simple mirror concept are presented which could mitigate these MHD instabilities.
Fast reconnection in relativistic plasmas: the magnetohydrodynamics tearing instability revisited
NASA Astrophysics Data System (ADS)
Del Zanna, L.; Papini, E.; Landi, S.; Bugli, M.; Bucciantini, N.
2016-08-01
Fast reconnection operating in magnetically dominated plasmas is often invoked in models for magnetar giant flares, for magnetic dissipation in pulsar winds, or to explain the gamma-ray flares observed in the Crab nebula, hence its investigation is of paramount importance in high-energy astrophysics. Here we study, by means of two dimensional numerical simulations, the linear phase and the subsequent nonlinear evolution of the tearing instability within the framework of relativistic resistive magnetohydrodynamics, as appropriate in situations where the Alfven velocity approaches the speed of light. It is found that the linear phase of the instability closely matches the analysis in classical MHD, where the growth rate scales with the Lundquist number S as S^-1/2, with the only exception of an enhanced inertial term due to the thermal and magnetic energy contributions. In addition, when thin current sheets of inverse aspect ratio scaling as S^-1/3 are considered, the so-called "ideal" tearing regime is retrieved, with modes growing independently on S and extremely fast, on only a few light crossing times of the sheet length. The overall growth of fluctuations is seen to solely depend on the value of the background Alfven velocity. In the fully nonlinear stage we observe an inverse cascade towards the fundamental mode, with Petschek-type supersonic jets propagating at the external Alfven speed from the X-point, and a fast reconnection rate at the predicted value R~(ln S)^-1.
Shear-induced instabilities in layered liquids
NASA Astrophysics Data System (ADS)
Auernhammer, Günter K.; Brand, Helmut R.; Pleiner, Harald
2002-12-01
Motivated by the experimentally observed shear-induced destabilization and reorientation of smectic-A-like systems, we consider an extended formulation of smectic-A hydrodynamics. We include both, the smectic layering (via the layer displacement u and the layer normal pcirc) and the director ncirc of the underlying nematic order in our macroscopic hydrodynamic description and allow both directions to differ in nonequilibrium situations. In an homeotropically aligned sample the nematic director does couple to an applied simple shear, whereas the smectic layering stays unchanged. This difference leads to a finite (but usually small) angle between ncirc and pcirc, which we find to be equivalent to an effective dilatation of the layers. This effective dilatation leads, above a certain threshold, to an undulation instability of the layers. We generalize our earlier approach [G. K. Auernhammer, H. R. Brand, and H. Pleiner, Rheol. Acta 39, 215 (2000)] and include the cross couplings with the velocity field and the order parameters for orientational and positional order and show how the order parameters interact with the undulation instability. We explore the influence of various material parameters on the instability. Comparing our results to recent experiments and molecular dynamic simulations, we find a good qualitative agreement.
Fast reconnection in relativistic plasmas: the magnetohydrodynamics tearing instability revisited
NASA Astrophysics Data System (ADS)
Del Zanna, L.; Papini, E.; Landi, S.; Bugli, M.; Bucciantini, N.
2016-08-01
Fast reconnection operating in magnetically dominated plasmas is often invoked in models for magnetar giant flares, for magnetic dissipation in pulsar winds, or to explain the gamma-ray flares observed in the Crab nebula; hence, its investigation is of paramount importance in high-energy astrophysics. Here we study, by means of two-dimensional numerical simulations, the linear phase and the subsequent non-linear evolution of the tearing instability within the framework of relativistic resistive magnetohydrodynamics (MHD), as appropriate in situations where the Alfvén velocity approaches the speed of light. It is found that the linear phase of the instability closely matches the analysis in classical MHD, where the growth rate scales with the Lundquist number S as S-1/2, with the only exception of an enhanced inertial term due to the thermal and magnetic energy contributions. In addition, when thin current sheets of inverse aspect ratio scaling as S-1/3 are considered, the so-called ideal tearing regime is retrieved, with modes growing independently of S and extremely fast, on only a few light crossing times of the sheet length. The overall growth of fluctuations is seen to solely depend on the value of the background Alfvén velocity. In the fully non-linear stage, we observe an inverse cascade towards the fundamental mode, with Petschek-type supersonic jets propagating at the external Alfvén speed from the X-point, and a fast reconnection rate at the predicted value {R}˜ (ln S)^{-1}.
NASA Astrophysics Data System (ADS)
Burke, B. J.; Kruger, S. E.; Hegna, C. C.; Zhu, P.; Snyder, P. B.; Sovinec, C. R.; Howell, E. C.
2010-03-01
A linear benchmark between the linear ideal MHD stability codes ELITE [H. R. Wilson et al., Phys. Plasmas 9, 1277 (2002)], GATO [L. Bernard et al., Comput. Phys. Commun. 24, 377 (1981)], and the extended nonlinear magnetohydrodynamic (MHD) code, NIMROD [C. R. Sovinec et al.., J. Comput. Phys. 195, 355 (2004)] is undertaken for edge-localized (MHD) instabilities. Two ballooning-unstable, shifted-circle tokamak equilibria are compared where the stability characteristics are varied by changing the equilibrium plasma profiles. The equilibria model an H-mode plasma with a pedestal pressure profile and parallel edge currents. For both equilibria, NIMROD accurately reproduces the transition to instability (the marginally unstable mode), as well as the ideal growth spectrum for a large range of toroidal modes (n =1-20). The results use the compressible MHD model and depend on a precise representation of "ideal-like" and "vacuumlike" or "halo" regions within the code. The halo region is modeled by the introduction of a Lundquist-value profile that transitions from a large to a small value at a flux surface location outside of the pedestal region. To model an ideal-like MHD response in the core and a vacuumlike response outside the transition, separate criteria on the plasma and halo Lundquist values are required. For the benchmarked equilibria the critical Lundquist values are 108 and 103 for the ideal-like and halo regions, respectively. Notably, this gives a ratio on the order of 105, which is much larger than experimentally measured values using Te values associated with the top of the pedestal and separatrix. Excellent agreement with ELITE and GATO calculations are made when sharp boundary transitions in the resistivity are used and a small amount of physical dissipation is added for conditions very near and below marginal ideal stability.
Weakening of magnetohydrodynamic interchange instabilities by Alfven waves
Benilov, E. S.; Hassam, A. B.
2008-02-15
Alfven waves, made to propagate along an ambient magnetic field and polarized transverse to a gravitational field g, with wave amplitude stratified along g, are shown to reduce the growth rate of interchange instability by increasing the effective inertia by a factor of 1+(B{sub y}{sup '}/B{sub z}k{sub z}){sup 2}, where B{sub z} is the ambient magnetic field, k{sub z} is the wavenumber, and B{sub y}{sup '} is the wave amplitude shear. Appropriately placed Alfven wave power could thus be used to enhance the stability of interchange and ballooning modes in tokamaks and other interchange-limited magnetically confined plasmas.
Plasmoid Instabilities Mediated Three-Dimensional Magnetohydrodynamic Turbulent Reconnection
Huang, Yi-min; Guo, Fan
2015-07-21
After some introductory remarks on fast reconnection in resistive MHD due to plasmoid instability, oblique tearing modes in 3D, and previous studies on 3D turbulent reconnection, the subject is presented under the following topics: 3D simulation setup, time evolution of the 3D simulation, comparison with Sweet-Parker and 2D plasmoid reconnection, and diagnostics of the turbulent state (decomposition of mean fields and fluctuations, power spectra of energy fluctuations, structure function and eddy anisotropy with respect to local magnetic field). Three primary conclusions were reached: (1) The results suggest that 3D plasmoid instabilities can lead to self-generated turbulent reconnection (evidence of energy cascade and development of inertial range, energy fluctuations preferentially align with the local magnetic field, which is one of the characteristics of MHD turbulence); (2) The turbulence is highly inhomogeneous, due to the presence of magnetic shear and outflow jets (conventional MHD turbulence theories or phenomenologies may not be applicable – e.g. scale-dependent anisotropy as predicted by Goldreich & Sridhar is not found); (3) 3D turbulent reconnection is different from 2D plasmoid-dominated reconnection in many aspects. However, in fully developed state, reconnection rates in 2D and 3D are comparable — this result needs to be further checked in higher S.
Shear dynamo, turbulence, and the magnetorotational instability
NASA Astrophysics Data System (ADS)
Squire, Jonathan
The formation, evolution, and detailed structure of accretion disks remain poorly understood, with wide implications across a variety of astrophysical disciplines. While the most pressing question --- what causes the high angular momentum fluxes that are necessary to explain observations? --- is nicely answered by the idea that the disk is turbulent, a more complete grasp of the fundamental processes is necessary to capture the wide variety of behaviors observed in the night sky. This thesis studies the turbulence in ionized accretion disks from a theoretical standpoint, in particular focusing on the generation of magnetic fields in these processes, known as dynamo. Such fields are expected to be enormously important, both by enabling the magnetorotational instability (which evolves into virulent turbulence), and through large-scale structure formation, which may transport angular momentum in different ways and be fundamental for the formation of jets. The central result of this thesis is the suggestion of a new large-scale dynamo mechanism in shear flows --- the "magnetic shear-current effect" --- which relies on a positive feedback from small-scale magnetic fields. As well as being a very promising candidate for driving field generation in the central regions of accretion disks, this effect is interesting because small-scale magnetic fields have historically been considered to have a negative effect on the large-scale dynamo, damping growth and leading to dire predictions for final saturation amplitudes. Given that small-scale fields are ubiquitous in plasma turbulence above moderate Reynolds numbers, the finding that they could instead have a positive effect in some situations is interesting from a theoretical and practical standpoint. The effect is studied using direct numerical simulation, analytic techniques, and novel statistical simulation methods. In addition to the dynamo, much attention is given to the linear physics of disks and its relevance to
NASA Astrophysics Data System (ADS)
Bettarini, Lapo; Landi, Simone; Velli, Marco; Londrillo, Pasquale
2009-06-01
The problem of three-dimensional combined magnetic and velocity shear driven instabilities of a compressible magnetized jet modeled as a plane neutral/current double vortex sheet in the framework of the resistive magnetohydrodynamics is addressed. The resulting dynamics given by the stream+current sheet interaction is analyzed and the effects of a variable geometry of the basic fields are considered. Depending on the basic asymptotic magnetic field configuration, a selection rule of the linear instability modes can be obtained. Hence, the system follows a two-stage path developing either through a fully three-dimensional dynamics with a rapid evolution of kink modes leading to a final turbulent state, or rather through a driving two-dimensional instability pattern that develops on parallel planes on which a reconnection+coalescence process takes place.
Bettarini, Lapo; Landi, Simone; Velli, Marco; Londrillo, Pasquale
2009-06-15
The problem of three-dimensional combined magnetic and velocity shear driven instabilities of a compressible magnetized jet modeled as a plane neutral/current double vortex sheet in the framework of the resistive magnetohydrodynamics is addressed. The resulting dynamics given by the stream+current sheet interaction is analyzed and the effects of a variable geometry of the basic fields are considered. Depending on the basic asymptotic magnetic field configuration, a selection rule of the linear instability modes can be obtained. Hence, the system follows a two-stage path developing either through a fully three-dimensional dynamics with a rapid evolution of kink modes leading to a final turbulent state, or rather through a driving two-dimensional instability pattern that develops on parallel planes on which a reconnection+coalescence process takes place.
Leprovost, Nicolas; Kim, Eun-Jin
2009-08-01
We investigate three-dimensional magnetohydrodynamics turbulence in the presence of velocity and magnetic shear (i.e., with both a large-scale shear flow and a nonuniform magnetic field). By assuming a turbulence driven by an external forcing with both helical and nonhelical spectra, we investigate the combined effect of these two shears on turbulence intensity and turbulent transport represented by turbulent diffusivities (turbulent viscosity, alpha and beta effect) in Reynolds-averaged equations. We show that turbulent transport (turbulent viscosity and diffusivity) is quenched by a strong flow shear and a strong magnetic field. For a weak flow shear, we further show that the magnetic shear increases the turbulence intensity while decreasing the turbulent transport. In the presence of a strong flow shear, the effect of the magnetic shear is found to oppose the effect of flow shear (which reduces turbulence due to shear stabilization) by enhancing turbulence and transport, thereby weakening the strong quenching by flow shear stabilization. In the case of a strong magnetic field (compared to flow shear), magnetic shear increases turbulence intensity and quenches turbulent transport. PMID:19792244
NASA Astrophysics Data System (ADS)
Pratt, J.; Busse, A.; Müller, W.-C.
2013-09-01
Intermittent large-scale high-shear flows are found to occur frequently and spontaneously in direct numerical simulations of statistically stationary turbulent Boussinesq magnetohydrodynamic (MHD) convection. The energetic steady state of the system is sustained by convective driving of the velocity field and small-scale dynamo action. The intermittent emergence of flow structures with strong velocity and magnetic shearing generates magnetic energy at an elevated rate on time scales that are longer than the characteristic time of the large-scale convective motion. The resilience of magnetic energy amplification suggests that intermittent shear bursts are a significant driver of dynamo action in turbulent magnetoconvection.
Whistler Instability in an Electron-Magnetohydrodynamic Spheromak
Stenzel, R. L.; Urrutia, J. M.; Strohmaier, K. D.
2007-12-31
A three-dimensional magnetic vortex, propagating in the whistler mode, has been produced in a laboratory plasma. Its magnetic energy is converted into electron kinetic energy. Non-Maxwellian electron distributions are formed which give rise to kinetic whistler instabilities. The propagating vortex radiates whistler modes along the ambient magnetic field. A new instability mechanism is proposed.
Biglari, H.; Chen, L.; White, R.B.
1987-02-01
It is shown that, in present-day large-size tokamaks, finite resistivity modifies qualitatively the stability properties of magnetohydrodynamic instabilities resonantly excited by the unfavorable processional drift of energetic-trapped particles, i.e., the so-called ''fishbone''-type instabilities. Specifically, it is found that (1) the n = 1 energetic-trapped particle-induced internal kink (''fishbone'') instability is strongly stabilized by resistive dissipation and (2) finite resistivity lowers considerably the threshold conditions for resonant excitations of high-n ballooning/interchange modes. The possibility of exciting fishbones by alpha particles in ignition experiments is also considered.
Nonaxisymmetric linear instability of cylindrical magnetohydrodynamic Taylor-Couette flow
NASA Astrophysics Data System (ADS)
Child, Adam; Kersalé, Evy; Hollerbach, Rainer
2015-09-01
We consider the nonaxisymmetric modes of instability present in Taylor-Couette flow under the application of helical magnetic fields, mainly for magnetic Prandtl numbers close to the inductionless limit, and conduct a full examination of marginal stability in the resulting parameter space. We allow for the azimuthal magnetic field to be generated by a combination of currents in the inner cylinder and fluid itself and introduce a parameter governing the relation between the strength of these currents. A set of governing eigenvalue equations for the nonaxisymmetric modes of instability are derived and solved by spectral collocation with Chebyshev polynomials over the relevant parameter space, with the resulting instabilities examined in detail. We find that by altering the azimuthal magnetic field profiles the azimuthal magnetorotational instability, nonaxisymmetric helical magnetorotational instability, and Tayler instability yield interesting dynamics, such as different preferred mode types and modes with azimuthal wave number m >1 . Finally, a comparison is given to the recent WKB analysis performed by Kirillov et al. [Kirillov, Stefani, and Fukumoto, J. Fluid Mech. 760, 591 (2014), 10.1017/jfm.2014.614] and its validity in the linear regime.
PARAMETRIC INSTABILITY OF WHISTLER WAVES IN THE ELECTRON MAGNETOHYDRODYNAMICS
Zhao, J. S.; Wu, D. J.; Lu, J. Y. E-mail: djwu@pmo.ac.c
2010-05-01
Using an electron magnetohydrodynamic model, we investigate the parametric decay among three whistler waves. A nonlinear equation to describe both linear and nonlinear properties of whistler waves is derived. Then we discuss the growth rate of the parametric decay of whistler waves in the long-wavelength region and show that the growth rate for two reverse decay waves is larger than that for two decay waves in the same direction. The nonlinear interaction among the long-wavelength and short-wavelength waves is also studied in this paper. This wave-wave interaction implies that long-wavelength waves can be decayed to short-wavelength waves and then dissipate their energy in the short-wavelength region. The possibility of applying our results to account for the generation of sunward propagating whistler waves is also discussed.
Shear instabilities in a fully compressible polytropic atmosphere
NASA Astrophysics Data System (ADS)
Witzke, V.; Silvers, L. J.; Favier, B.
2015-05-01
Shear flows have a significant impact on the dynamics in an assortment of different astrophysical objects, including accretion discs and stellar interiors. Investigating shear flow instabilities in a polytropic atmosphere provides a fundamental understanding of the motion in stellar interiors where turbulent motions, mixing processes, and magnetic field generation take place. Here, a linear stability analysis for a fully compressible fluid in a two-dimensional Cartesian geometry is carried out. Our study focuses on determining the critical Richardson number for different Mach numbers and the destabilising effects of high thermal diffusion. We find that there is a deviation in the predicted stability threshold for moderate Mach number flows, along with a significant effect on the growth rate of the linear instability for small Péclet numbers. We show that in addition to a Kelvin-Helmholtz instability, a Holmboe instability can appear, and we discuss the implication of this in stellar interiors.
Mizuno, Yosuke; Lyubarsky, Yuri; Nishikawa, Ken-Ichi; Hardee, Philip E.
2012-09-20
We have investigated the influence of jet rotation and differential motion on the linear and nonlinear development of the current-driven (CD) kink instability of force-free helical magnetic equilibria via three-dimensional relativistic magnetohydrodynamic simulations. In this study, we follow the temporal development within a periodic computational box. Displacement of the initial helical magnetic field leads to the growth of the CD kink instability. We find that, in accordance with the linear stability theory, the development of the instability depends on the lateral distribution of the poloidal magnetic field. If the poloidal field significantly decreases outward from the axis, then the initial small perturbations grow strongly, and if multiple wavelengths are excited, then nonlinear interaction eventually disrupts the initial cylindrical configuration. When the profile of the poloidal field is shallow, the instability develops slowly and eventually saturates. We briefly discuss implications of our findings for Poynting-dominated jets.
Edge magnetohydrodynamic instability studies in the Pegasus Toroidal Experiment
NASA Astrophysics Data System (ADS)
Bongard, Michael W.
Peeling modes, an instability mechanism underlying deleterious Edge Localized Mode (ELM) activity in fusion-grade plasmas, are observed at the plasma edge in the PEGASUS Toroidal Experiment under conditions of high edge current density (Jedge(˜ 0.1 MA/m2) and low magnetic field (B ˜0.1 T) present at near-unity aspect ratio. Their macroscopic properties are measured using external Mirnov coil arrays, Langmuir probes, and high-speed visible imaging. The modest edge parameters and short pulse lengths of PEGASUS discharges permit direct measurement of the internal magnetic field structure with an insertable array of Hall-effect sensors, providing the current profile and its dynamical evolution on ELM-relevant timescales. Peeling modes generate coherent, edge-localized electromagnetic activity with low toroidal mode numbers n ≤ 3 and high poloidal mode numbers, in agreement with theoretical expectations of a low- n external kink structure. Coherent MHD fluctuation amplitudes are found to be strongly dependent on the experimentally measured J edge/B peeling instability drive, consistent with theory. An equilibrium reconstruction obtained during peeling activity with its current profile constrained by internal Hall measurements is used to test the predictions of analytic peeling stability theory and the ideal MHD stability model. Both approaches are in agreement with experiment, with the latter finding instability to an external kink. Peeling modes nonlinearly generate ELM-like, field-aligned filamentary structures. They detach from the edge and transiently accelerate radially outward, followed by propagation with constant velocity. Time-resolved Jedge measurements demonstrate that the filaments are formed from an initial current-hole perturbation and carry net toroidal currents If ˜ 100--200 A, less than 0.2% of the plasma current. Their constant-velocity radial motions are in qualitative agreement with rates given by electromagnetic blob transport theory.
Linear magnetohydrodynamic Taylor-Couette instability for liquid sodium
NASA Astrophysics Data System (ADS)
Rüdiger, Günther; Schultz, Manfred; Shalybkov, Dima
2003-04-01
The linear stability of MHD Taylor-Couette flow of infinite vertical extension is considered for liquid sodium with its small magnetic Prandtl number Pm of order 10-5. The calculations are performed for a container with Rout=2Rin, with an axial uniform magnetic field and with boundary conditions for both vacuum and perfect conductions. For resting outer cylinder subcritical excitation in comparison to the hydrodynamical case occurs for large Pm but it disappears for small Pm. For rotating outer cylinder the Rayleigh line plays an exceptional role. The hydromagnetic instability exists with Reynolds numbers exactly scaling with Pm-1/2 so that the moderate values of order 104 (for Pm=10-5) result. For the smallest step beyond the Rayleigh line, however, the Reynolds numbers scale as 1/Pm leading to much higher values of order 106. Then it is the magnetic Reynolds number Rm that directs the excitation of the instability. It results as lower for insulating than for conducting walls. The magnetic Reynolds number has to exceed here values of order 10 leading to frequencies of about 20 Hz for the rotation of the inner cylinder if containers with (say) 10 cm radius are considered. With vacuum boundary conditions the excitation of nonaxisymmetric modes is always more difficult than the excitation of axisymmetric modes. For conducting walls, however, crossovers of the lines of marginal stability exist for both resting and rotating outer cylinders, and this might be essential for future dynamo experiments. In this case the instability also can onset as an overstability.
NASA Astrophysics Data System (ADS)
Coon, E.; Kelemen, P.; Hirth, G.; Spiegelman, M.
2005-12-01
Kelemen and Hirth (Fall 2004 AGU) presented a model for periodic, viscous shear heating instabilities along pre-existing, fine grained shear zones. This provides an attractive alternative to dehydration embrittlement for explaining intermediate-depth earthquakes, especially those in a narrow thermal window within the mantle section of subducting oceanic plates (Hacker et al JGR03). Ductile shear zones with widths of cm to m are common in shallow mantle massifs and peridotite along oceanic fracture zones. Pseudotachylites in a mantle shear zone show that shear heating temperatures exceeded the mantle solidus (Obata & Karato Tectonophys95). Olivine grain growth in shear zones is pinned by closely spaced pyroxenes; thus, once formed, these features do not `heal' on geological time scales in the absence of melt or fluid (Warren & Hirth EPSL05). Grain-size sensitive creep will be localized within these shear zones, in preference to host rocks with olivine grain size from 1 to 10 mm. Inspired by the work of Whitehead & Gans (GJRAS74), we proposed that such pre-existing shear zones might undergo repeated shear heating instabilities. This is not a new concept; what is new is that viscous deformation is limited to a narrow shear zone, because grain boundary sliding, sensitive to both stress and grain size, may accommodate creep even at high stress and high temperature. These new ideas yield a new result: simple models for a periodic shear heating instability. Last year, we presented a 1D numerical model using olivine flow laws, assuming that viscous deformation remains localized in shear zones, surrounded by host rocks undergoing elastic deformation. Stress evolves due to elastic strain and drives viscous deformation in a shear zone of specified width. Shear heating and thermal diffusion control T. A maximum of 1400 C (substantial melting of peridotite ) was imposed. Grain size evolves due to recrystallization and diffusion. For strain rates of E-13 to E-14 per sec and
Relativistic thermal electron scale instabilities in sheared flow plasma
NASA Astrophysics Data System (ADS)
Miller, Evan D.; Rogers, Barrett N.
2016-04-01
> The linear dispersion relation obeyed by finite-temperature, non-magnetized, relativistic two-fluid plasmas is presented, in the special case of a discontinuous bulk velocity profile and parallel wave vectors. It is found that such flows become universally unstable at the collisionless electron skin-depth scale. Further analyses are performed in the limits of either free-streaming ions or ultra-hot plasmas. In these limits, the system is highly unstable in the parameter regimes associated with either the electron scale Kelvin-Helmholtz instability (ESKHI) or the relativistic electron scale sheared flow instability (RESI) recently highlighted by Gruzinov. Coupling between these modes provides further instability throughout the remaining parameter space, provided both shear flow and temperature are finite. An explicit parameter space bound on the highly unstable region is found.
Relativistic thermal electron scale instabilities in sheared flow plasma
NASA Astrophysics Data System (ADS)
Miller, Evan D.; Rogers, Barrett N.
2016-02-01
> The linear dispersion relation obeyed by finite-temperature, non-magnetized, relativistic two-fluid plasmas is presented, in the special case of a discontinuous bulk velocity profile and parallel wave vectors. It is found that such flows become universally unstable at the collisionless electron skin-depth scale. Further analyses are performed in the limits of either free-streaming ions or ultra-hot plasmas. In these limits, the system is highly unstable in the parameter regimes associated with either the electron scale Kelvin-Helmholtz instability (ESKHI) or the relativistic electron scale sheared flow instability (RESI) recently highlighted by Gruzinov. Coupling between these modes provides further instability throughout the remaining parameter space, provided both shear flow and temperature are finite. An explicit parameter space bound on the highly unstable region is found.
Masada, Youhei; Takiwaki, Tomoya; Kotake, Kei
2015-01-01
Magnetorotational instability (MRI) in a convectively stable layer around the neutrinosphere is simulated by a three-dimensional model of a supernova core. To resolve MRI-unstable modes, a thin layer approximation considering only the radial global stratification is adopted. Our intriguing finding is that the convectively stable layer around the neutrinosphere becomes fully turbulent due to the MRI and its nonlinear penetration into the strongly stratified MRI-stable region. The intensity of the MRI-driven turbulence increases with magnetic flux threading the core, but is limited by the free energy stored in the differential rotation. The turbulent neutrinosphere is a natural consequence of rotating core-collapse and could exert a positive impact on the supernova mechanism.
NASA Astrophysics Data System (ADS)
Masada, Youhei; Takiwaki, Tomoya; Kotake, Kei
2015-01-01
Magnetorotational instability (MRI) in a convectively stable layer around the neutrinosphere is simulated by a three-dimensional model of a supernova core. To resolve MRI-unstable modes, a thin layer approximation considering only the radial global stratification is adopted. Our intriguing finding is that the convectively stable layer around the neutrinosphere becomes fully turbulent due to the MRI and its nonlinear penetration into the strongly stratified MRI-stable region. The intensity of the MRI-driven turbulence increases with magnetic flux threading the core, but is limited by the free energy stored in the differential rotation. The turbulent neutrinosphere is a natural consequence of rotating core-collapse and could exert a positive impact on the supernova mechanism.
Spong, D. A.; Shaing, K. C.; Carreras, B. A.; Charlton, L. A.; Callen, J. D.; Garcia, L.
1988-10-01
The linearized neoclassical magnetohydrodynamic equations, including perturbed neoclassical flows and currents, have been solved for parameter regimes where the neoclassical pressure-gradient-driven instability becomes important. This instability is driven by the fluctuating bootstrap current term in Ohm's law. It begins to dominate the conventional resistive ballooning mode in the banana-plateau collisionality regime ({mu}{sub e}/{nu}{sub e} approx {radical}{epsilon}/(1 + {nu}{sub *e}) > {epsilon}{sup 2}) and is characterized by a larger radial mode width and higher growth rate. The neoclassical instability persists in the absence of the usual magnetic field curvature drive and is not significantly affected by compressibility. Scalings with respect to {beta}, n (toroidal mode number), and {mu} (neoclassical viscosity) are examined using a large-aspect-ratio, three-dimensional initial-value code that solves linearized equations for the magnetic flux, fluid vorticity, density, and parallel ion flow velocity in axisymmetric toroidal geometry. 13 refs., 10 figs.
NASA Astrophysics Data System (ADS)
Mizuno, Yosuke; Lyubarsky, Yuri; Nishikawa, Ken-Ichi; Hardee, Philip E.
2009-07-01
We have investigated the development of current-driven (CD) kink instability through three-dimensional relativistic magnetohydrodynamic simulations. A static force-free equilibrium helical magnetic configuration is considered in order to study the influence of the initial configuration on the linear and nonlinear evolution of the instability. We found that the initial configuration is strongly distorted but not disrupted by the kink instability. The instability develops as predicted by linear theory. In the nonlinear regime, the kink amplitude continues to increase up to the terminal simulation time, albeit at different rates, for all but one simulation. The growth rate and nonlinear evolution of the CD kink instability depend moderately on the density profile and strongly on the magnetic pitch profile. The growth rate of the kink mode is reduced in the linear regime by an increase in the magnetic pitch with radius and reaches the nonlinear regime at a later time than the case with constant helical pitch. On the other hand, the growth rate of the kink mode is increased in the linear regime by a decrease in the magnetic pitch with radius and reaches the nonlinear regime sooner than the case with constant magnetic pitch. Kink amplitude growth in the nonlinear regime for decreasing magnetic pitch leads to a slender helically twisted column wrapped by magnetic field. On the other hand, kink amplitude growth in the nonlinear regime nearly ceases for increasing magnetic pitch.
Aiba, N.; Hirota, M.
2015-08-15
In a rotating toroidal plasma surrounded by a resistive wall, it is shown that linear magnetohydrodynamic (MHD) instabilities can be excited by interplay between the resistive wall mode (RWM) and stable ideal MHD modes, where the RWM can couple with not only a stable external kink mode but also various stable Alfvén eigenmodes that abound in a toroidal plasma. The RWM growth rate is shown to peak repeatedly as the rotation frequency reaches specific values for which the frequencies of the ideal MHD modes are Doppler-shifted to the small RWM frequency. Such destabilization can be observed even when the RWM in a static plasma is stable. A dispersion relation clarifies that the unstable mode changes from the RWM to the ideal MHD mode destabilized by wall resistivity when the rotation frequency passes through these specific values. The unstable mode is excited at these rotation frequencies even though plasma rotation also tends to stabilize the RWM from the combination of the continuum damping and the ion Landau damping.
Heat release effects on the instability of parallel shear layers
Hegde, U.
1994-01-01
The influence of time-dependent heat addition on the linear instablity of shear layers is of considerable interest in understanding the dynamic behavior of reacting flows and combustion-turbulence interactions. The approach is based upon the Bernoulli enthalpy aeroacoustics theory, which utilizes the specific enthalpy and specific entropy as the primary thermodynamic variables. In addition, velocity oscillations are split into Helmoholtz decomposition theorem.
Shear Instabilities as a Probe of Jupiter's Atmosphere
NASA Astrophysics Data System (ADS)
Bosak, Tanja; Ingersoll, Andrew P.
2002-08-01
Linear wave patterns in Jupiter's clouds with wavelengths strongly clustered around 300 km are commonly observed in the planet's equatorial atmosphere (F. M. Flasar and P. J. Gierasch, 1986, J. Atmos. Sci.43, 2683-2707). We propose that the preferred wavelength is related to the thickness of an unstable shear layer within the clouds (A. P. Ingersoll and D. W. Koerner 1989, Bull. Am. Astron. Soc.21, 943). We numerically analyze the linear stability of wavelike disturbances that have nonzero horizontal phase speeds in Jupiter's atmosphere and find that, if the static stability in the shear layer is very low (but still nonnegative), a deep vertical shear layer like the one measured by the Galileo probe (D. H. Atkinson et al. 1998, J. Geophys. Res.103, 22911-22928) can generate the instabilities. The fastest growing waves grow exponentially within an hour, and their wavelengths match the observations. Close to zero values of static stability that permit the growth of instabilities are within the range of values measured by the Galileo probe in a hot spot (A. Seiff et al. 1998, J. Geophys. Res.103, 22857-22889). Our model probes Jupiter's equatorial atmosphere below the cloud deck and suggests that thick regions of wind shear and low static stability exist outside hot spots.
Linear simulations of the cylindrical Richtmyer-Meshkov instability in magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Bakhsh, A.; Gao, S.; Samtaney, R.; Wheatley, V.
2016-03-01
Numerical simulations and analysis indicate that the Richtmyer-Meshkov instability (RMI) is suppressed in ideal magnetohydrodynamics (MHD) in Cartesian slab geometry. Motivated by the presence of hydrodynamic instabilities in inertial confinement fusion and suppression by means of a magnetic field, we investigate the RMI via linear MHD simulations in cylindrical geometry. The physical setup is that of a Chisnell-type converging shock interacting with a density interface with either axial or azimuthal (2D) perturbations. The linear stability is examined in the context of an initial value problem (with a time-varying base state) wherein the linearized ideal MHD equations are solved with an upwind numerical method. Linear simulations in the absence of a magnetic field indicate that RMI growth rate during the early time period is similar to that observed in Cartesian geometry. However, this RMI phase is short-lived and followed by a Rayleigh-Taylor instability phase with an accompanied exponential increase in the perturbation amplitude. We examine several strengths of the magnetic field (characterized by β = /2 p Br 2 ) and observe a significant suppression of the instability for β ≤ 4. The suppression of the instability is attributed to the transport of vorticity away from the interface by Alfvén fronts.
Magnetar activity via the density-shear instability in Hall-MHD
NASA Astrophysics Data System (ADS)
Gourgouliatos, Konstantinos N.; Kondić, Todor; Lyutikov, Maxim; Hollerbach, Rainer
2015-10-01
We investigate the density-shear instability in Hall-magnetohydrodynamics (Hall-MHD) via numerical simulation of the full non-linear problem in the context of magnetar activity. We confirm the development of the instability of a plane-parallel magnetic field with an appropriate intensity and electron density profile, in accordance with analytic theory. We find that the instability also appears for a monotonically decreasing electron number density and magnetic field, a plane-parallel analogue of an azimuthal or meridional magnetic field in the crust of a magnetar. The growth rate of the instability depends on the Hall properties of the field (magnetic field intensity, electron number density and the corresponding scaleheights), while being insensitive to weak resistivity. Since the Hall effect is the driving process for the evolution of the crustal magnetic field of magnetars, we argue that this instability is critical for systems containing strong meridional or azimuthal fields. We find that this process mediates the formation of localized structures with much stronger magnetic field than the average, which can lead to magnetar activity and accelerate the dissipation of the field and consequently the production of Ohmic heating. Assuming a 5 × 1014 G magnetic field at the base of crust, we anticipate that magnetic field as strong as 1015 G will easily develop in regions of typical size of a few hundred metres, containing magnetic energy of 1043 erg, sufficient to power magnetar bursts. These active regions are more likely to appear in the magnetic equator where the tangential magnetic field is stronger.
NASA Astrophysics Data System (ADS)
Meister, C.-V.; Lee, B. R.; Hoffmann, D. H. H.
2014-08-01
The recent stage of the magnetohydrodynamic energy principle applied to laboratory and space plasmas is briefly reviewed. In detail, the energy principle is presented for an internally homogeneous pinch in a perfectly conducting wall. The plasma is separated from the wall by a vacuum. The principle is applied to ITER-type and lightning systems. Thereat, a system of mathematical equations of motion for fluid elements is derived using a cylindrical coordinate system. But the obtained equations may be also applied to plasmas with disturbances of non-cylindrical symmetry. From the equations of motion, an analytical relation for the radial displacements of the fluid elements is presented, which describes magnetohydrodynamic waves as e.g. sausage and kink ones. The numerical results here presented are, as a first step, only performed for plasma disturbances with cylindrical symmetry and outer azimuthal magnetic fields directed parallely to the conducting wall. Thus, the dispersion relations for sausage instabilities in ITER-type and lightning plasmas are solved. It is shown for which values of the inner and external magnetic fields of the systems instabilities occur. In case of lightnings, the radial displacements in the plasma are estimated.
Shear secondary instability in a precessing cylinder flow
NASA Astrophysics Data System (ADS)
Mouhali, Waleed; Lehner, Thierry; Ater Collaboration
2015-11-01
For a certain value of the forcing parameter, cyclones regime has been observed in our experiment involving water in a precessing cylinder. They result from an instability. We propose here to study the nature of this so-called instability. We consider first the mode coupling of two inertial waves with azimuthal wavenumber m =0 and m =1 (mode forced by the precession) in the inviscid regime (at high Re number limit) creates a differential rotation regime which has been observed in the same experiment at small enough Poincaré number ɛ (ratio of the precession to the rotation frequencies). Secondly, the radial profile of the corresponding axial mean flow vorticity shows an inflexion point leading to a localized inflectional secondary instability. We show that when ɛ is increased from low values the forced mode m =0 becomes the most instable in this induced differential rotation, which can be responsible for the observed eruptions of jets from the lateral walls of the cylinder leading to the cyclones formation within the volume from the development of an inviscid secondary shear instability.
Measurements of velocity shear and ion viscosity profile in a magnetohydrodynamic plasma jet
NASA Astrophysics Data System (ADS)
Dorf, L. A.; Intrator, T.; Sun, X.; Hendryx, J.; Wurden, G. A.; Furno, I.; Lapenta, G.
2010-10-01
Time-dependent, two-dimensional profiles of the axial flow velocity, density, electron temperature, and magnetic field components are measured at two axial locations in a screw pinch plasma column of the reconnection scaling experiment. The results show that the ion momentum flux for a given column radius is dissipated by the ion-ion Coulomb scattering viscosity due to a significant radial shear of the axial velocity. By comparing the terms of the magnetohydrodynamic momentum balance equation, radial profile of ion viscosity is determined. Chord-integrated ion temperature measurements performed at several radial locations using Doppler broadening spectroscopy show ion temperature of about 1 eV. Measured ion viscosity agrees within a factor of 2 with the classical Braginskii expectations.
Measurements of velocity shear and ion viscosity profile in a magnetohydrodynamic plasma jet
Dorf, L. A.; Intrator, T.; Sun, X.; Hendryx, J.; Wurden, G. A.; Furno, I; Lapenta, G.
2010-10-15
Time-dependent, two-dimensional profiles of the axial flow velocity, density, electron temperature, and magnetic field components are measured at two axial locations in a screw pinch plasma column of the reconnection scaling experiment. The results show that the ion momentum flux for a given column radius is dissipated by the ion-ion Coulomb scattering viscosity due to a significant radial shear of the axial velocity. By comparing the terms of the magnetohydrodynamic momentum balance equation, radial profile of ion viscosity is determined. Chord-integrated ion temperature measurements performed at several radial locations using Doppler broadening spectroscopy show ion temperature of about 1 eV. Measured ion viscosity agrees within a factor of 2 with the classical Braginskii expectations.
Viscous shear heating instabilities in a 1-D viscoelastic shear zone
NASA Astrophysics Data System (ADS)
Homburg, J. M.; Coon, E. T.; Spiegelman, M.; Kelemen, P. B.; Hirth, G.
2010-12-01
Viscous shear instabilities may provide a possible mechanism for some intermediate depth earthquakes where high confining pressure makes it difficult to achieve frictional failure. While many studies have explored the feedback between temperature-dependent strain rate and strain-rate dependent shear heating (e.g. Braeck and Podladchikov, 2007), most have used thermal anomalies to initiate a shear instability or have imposed a low viscosity region in their model domain (John et al., 2009). By contrast, Kelemen and Hirth (2007) relied on an initial grain size contrast between a predetermined fine-grained shear zone and coarse grained host rock to initiate an instability. This choice is supported by observations of numerous fine grained ductile shear zones in shallow mantle massifs as well as the possibility that annealed fine grained fault gouge, formed at oceanic transforms, subduction related thrusts and ‘outer rise’ faults, could be carried below the brittle/ductile transition by subduction. Improving upon the work of Kelemen and Hirth (2007), we have developed a 1-D numerical model that describes the behavior of a Maxwell viscoelastic body with the rheology of dry olivine being driven at a constant velocity at its boundary. We include diffusion and dislocation creep, dislocation accommodated grain boundary sliding, and low-temperature plasticity (Peierls mechanism). Initial results suggest that including low-temperature plasticity inhibits the ability of the system to undergo an instability, similar to the results of Kameyama et al. (1999). This is due to increased deformation in the background allowing more shear heating to take place, and thus softening the system prior to reaching the peak stress. However if the applied strain rate is high enough (e.g. greater than 0.5 x 10-11 s-1 for a domain size of 2 km, an 8 m wide shear zone, a background grain size of 1 mm, a shear zone grain size of 150 μm, and an initial temperature of 650°C) dramatic
On the vertical-shear instability in astrophysical discs
NASA Astrophysics Data System (ADS)
Barker, A. J.; Latter, H. N.
2015-06-01
We explore the linear stability of astrophysical discs exhibiting vertical shear, which arises when there is a radial variation in the temperature or entropy. Such discs are subject to a `vertical-shear instability', which recent non-linear simulations have shown to drive hydrodynamic activity in the MRI-stable regions of protoplanetary discs. We first revisit locally isothermal discs using the quasi-global reduced model derived by Nelson et al. This analysis is then extended to global axisymmetric perturbations in a cylindrical domain. We also derive and study a reduced model describing discs with power-law radial entropy profiles (`locally polytropic discs'), which are somewhat more realistic in that they possess physical (as opposed to numerical) surfaces. The fastest growing modes have very short wavelengths and are localized at the disc surfaces (if present), where the vertical shear is maximal. An additional class of modestly growing vertically global body modes is excited, corresponding to destabilized classical inertial waves (`r modes'). We discuss the properties of both types of modes, and stress that those that grow fastest occur on the shortest available length-scales (determined either by the numerical grid or the physical viscous length). This ill-posedness makes simulations of the instability difficult to interpret. We end with some brief speculation on the non-linear saturation and resulting angular momentum transport.
NASA Technical Reports Server (NTRS)
Mizuno, Yosuke; Lyubarsky, Yuri; ishikawa, Ken-Ichi; Hardee, Philip E.
2010-01-01
We have investigated the development of current-driven (CD) kink instability through three-dimensional relativistic MHD simulations. A static force-free equilibrium helical magnetic configuration is considered in order to study the influence of the initial configuration on the linear and nonlinear evolution of the instability. We found that the initial configuration is strongly distorted but not disrupted by the kink instability. The instability develops as predicted by linear theory. In the non-linear regime the kink amplitude continues to increase up to the terminal simulation time, albeit at different rates, for all but one simulation. The growth rate and nonlinear evolution of the CD kink instability depends moderately on the density profile and strongly on the magnetic pitch profile. The growth rate of the kink mode is reduced in the linear regime by an increase in the magnetic pitch with radius and the non-linear regime is reached at a later time than for constant helical pitch. On the other hand, the growth rate of the kink mode is increased in the linear regime by a decrease in the magnetic pitch with radius and reaches the non-linear regime sooner than the case with constant magnetic pitch. Kink amplitude growth in the non-linear regime for decreasing magnetic pitch leads to a slender helically twisted column wrapped by magnetic field. On the other hand, kink amplitude growth in the non-linear regime nearly ceases for increasing magnetic pitch.
Sheared graphene: Electronic properties shaped by a mechanical instability
NASA Astrophysics Data System (ADS)
Concha, Andres; Cheng, Shengfeng; Covaci, Lucian; Mahadevan, L.
2015-03-01
We explore the effects of shearing graphene ribbons on its geometry, and electronic properties. Inspired by macroscopic experiments, we show that spontaneous patterns appear when a wide ribbon is subject to shear. We compared this pattern and different regimes obtained via MD simulations with macroscopic experiments, and find good agreement between them. Beyond the low shear regime a second generation of wrinkles emerge when the system relaxes trying to keep the bond lengths as close to the relaxed length as possible. Remarkably, for all shear ratios the induced superlattice generates a momentum kick when electronic excitations enter the deformed region, an effective pseudo-magnetic superlattice, and a strong Fermi velocity renormalization. These effects modify electronic properties and suggest a simple route to engineer electronic waveguides and switches at the nanoscale. Our proposal is a concrete realization of a quantum device that takes full advantage of an elastic instability that spans from the nano to macro -scales. AC was partially supported by Conicyt Grant 79112004, and Fondecyt under Grant 11130075. LC acknowledges individual support from FWO-Vlaanderen.
NASA Astrophysics Data System (ADS)
Shukla, Chandrasekhar; Das, Amita; Patel, Kartik
2016-08-01
We carry out particle-in-cell simulations to study the instabilities associated with a 2-D sheared electron flow configuration against a neutralizing background of ions. Both weak and strong relativistic flow velocities are considered. In the weakly relativistic case, we observe the development of electromagnetic Kelvin-Helmholtz instability with similar characteristics as that predicted by the electron Magnetohydrodynamic (EMHD) model. On the contrary, in a strong relativistic case, the compressibility effects of electron fluid dominate and introduce upper hybrid electrostatic oscillations transverse to the flow which are very distinct from EMHD fluid behavior. In the nonlinear regime, both weak and strong relativistic cases lead to turbulence with broad power law spectrum.
Murakami, Tomoyuki; Okuno, Yoshihiro; Yamasaki, Hiroyuki
2005-05-09
We describe the suppression of ionization instability and the control of a magnetohydrodynamic electrical power-generating plasma by coupling with a radio-frequency (rf) electromagnetic field. The rf heating stabilizes the unstable plasma behavior and homogenizes the nonuniform plasma structure, whereby the power-generating performance is significantly improved.
NASA Astrophysics Data System (ADS)
Zheng, L. J.; Kotschenreuther, M. T.; Valanju, P.
2013-06-01
Low-n magnetohydrodynamic (MHD) modes in the quiescent high confinement mode (H-mode) pedestal are investigated in this paper. Here, n is the toroidal mode number. The low collisionality regime is considered, so that a safety-factor plateau arises in the pedestal region because of the strong bootstrap current. The JET-like (Joint European Torus) equilibria of quiescent H-mode discharges are generated numerically using the VMEC code. The stability of this type of equilibria is analysed using the AEGIS code, with subsonic rotation effects taken into account. The current investigation extends the previous studies of n = 1 modes to n = 2 and 3 modes. The numerical results show that the MHD instabilities in this type of equilibria have characteristic features of the infernal mode. We find that this type of mode tends to prevail when the safety-factor value in the shear-free region is slightly larger than an integer. In this case the frequencies (ωn) of modes with toroidal mode number n roughly follow the rule ωn ˜ -nΩp, where Ωp is the local rotation frequency where the infernal harmonic prevails. Since the infernal mode tends to develop near the pedestal top, where pressure driving is strong but magnetic shear stabilization is weak, this local rotation frequency tends to be close to the pedestal top value. These typical mode features bear close resemblance to the edge harmonic oscillations (or outer modes) at the quiescent H-mode discharges observed experimentally.
NASA Astrophysics Data System (ADS)
Delacroix, Jules; Davoust, Laurent
2014-03-01
As a first step towards two-phase magnetohydrodynamics (MHD), this paper addresses an original analytical coupling between surface rheology, e.g., a gradually oxidizing liquid metal surface, ruled by the Boussinesq number Bo, and a supporting annular MHD flow, ruled by the Hartmann number Ha, in the general layout of a classical annular deep-channel viscometer, as developed by Mannheimer and Schechter [J. Colloid Interface Sci. 32, 195-211 (1970)]. Using a matched asymptotic expansion based on the small parameter 1/Ha, we can express the surface velocity as a coupling variable in the jump momentum balance at the liquid surface. By solving the latter through the determination of the Green's function, the whole flow can be analytically calculated. A modified Boussinesq number, tilde{B_o}, is produced as a new non-dimensional parameter that provides the balance between surface viscous shearing and the Lorentz force. It is shown that the tilde{B_o} number drives the electrical activation of the Hartmann layers, heavily modifying the MHD flow topology and leading to the emergence of the Lorentz force, for which interaction with the flow is not classical. Finally, the evolution laws given in this study allow the determination of scaling laws for an original experimental protocol, which would make it possible to accurately determine the surface shear viscosity of a liquid metal with respect to the quality of the ambient atmosphere.
Sheared flow effects on ballooning instabilities in three-dimensional equilibria
Hegna, C.C.
2005-12-15
The stability of ideal magnetohydrodynamic ballooning modes in the presence of sheared flow is investigated for three-dimensional equilibria. Application of ballooning formalism reduces the problem to a partial differential equation in three dimensions that can be solved in the limit of small flow. Analytic calculations demonstrate the stabilizing effect of shear flow. The derived stability criterion generalizes prior work related to axisymmetric equilibrium with sheared toroidal flow.
NASA Astrophysics Data System (ADS)
Bakhsh, Abeer; Samtaney, Ravi
2015-11-01
Numerical simulations and analysis in Cartesian slab geometry for nonlinear ideal magnetohydrodynamics (MHD) indicate that the Richtmyer-Meshkov instability (RMI) is suppressed in the presence of a magnetic field. An analytical solution of incompressible 2-D MHD RMI of an impulsively accelerated interface was investigated by Wheatley et al. (Phys. Rev. Lett. 2005; J. Fluid Mech. 2005) who found that, for a finite magnetic field, although the initial growth rate of the interface is unaffected by the presence of magnetic field, the late-time amplitude of the interface asymptotes to a constant value. In the framework of incompressible MHD, we examine analytically the behavior of an impulsively accelerated interface separating conducting fluids of different densities in cylindrical geometry. We investigate the stability properties of such a system and study the influence of the magnetic field on the growth rate of the interface. In converging cylindrical geometry, the RMI is followed by a Rayleigh-Taylor (RT) phase. Our analysis does not account for the RT phase of the instability but is valid for the duration of the RMI phase. We compare results of the incompressible analysis with linear compressible MHD simulations. Supported by the KAUST Office of Competitive Research Funds under Award No. URF/1/2162-01.
Li, C. K.; Frenje, J. A.; Petrasso, R. D.; Seguin, F. H.; Amendt, P. A.; Landen, O. L.; Town, R. P. J.; Betti, R.; Knauer, J. P.; Meyerhofer, D. D.; Soures, J. M.
2009-07-15
Recent experiments using proton backlighting of laser-foil interactions provide unique opportunities for studying magnetized plasma instabilities in laser-produced high-energy-density plasmas. Time-gated proton radiograph images indicate that the outer structure of a magnetic field entrained in a hemispherical plasma bubble becomes distinctly asymmetric after the laser turns off. It is shown that this asymmetry is a consequence of pressure-driven, resistive magnetohydrodynamic (MHD) interchange instabilities. In contrast to the predictions made by ideal MHD theory, the increasing plasma resistivity after laser turn-off allows for greater low-mode destabilization (m>1) from reduced stabilization by field-line bending. For laser-generated plasmas presented herein, a mode-number cutoff for stabilization of perturbations with m>{approx}[8{pi}{beta}(1+D{sub m}k{sub perpendicular}{sup 2}{gamma}{sub max}{sup -1})]{sup 1/2} is found in the linear growth regime. The growth is measured and is found to be in reasonable agreement with model predictions.
On Linear Instability and Stability of the Rayleigh-Taylor Problem in Magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Jiang, Fei; Jiang, Song
2015-12-01
We investigate the stabilizing effects of the magnetic fields in the linearized magnetic Rayleigh-Taylor (RT) problem of a nonhomogeneous incompressible viscous magnetohydrodynamic fluid of zero resistivity in the presence of a uniform gravitational field in a three-dimensional bounded domain, in which the velocity of the fluid is non-slip on the boundary. By adapting a modified variational method and careful deriving a priori estimates, we establish a criterion for the instability/stability of the linearized problem around a magnetic RT equilibrium state. In the criterion, we find a new phenomenon that a sufficiently strong horizontal magnetic field has the same stabilizing effect as that of the vertical magnetic field on growth of the magnetic RT instability. In addition, we further study the corresponding compressible case, i.e., the Parker (or magnetic buoyancy) problem, for which the strength of a horizontal magnetic field decreases with height, and also show the stabilizing effect of a sufficiently large magnetic field.
The effect of compressibility on magnetohydrodynamic jets and Kelvin-Helmholtz instability
NASA Astrophysics Data System (ADS)
Praturi, Divya Sri; Girimaji, Sharath
2015-11-01
We investigate the effect of compressibility and magnetic field on the evolution of planar magnetohydrodynamic (MHD) jets. These jets are susceptible to Kelvin-Helmholtz (KH) instability when subjected to an in-plane transverse velocity perturbation. Various linear stability analyses have shown that compressibility and magnetic field along the jet have a stabilizing influence on the KH instability. We performed three-dimensional numerical simulations using magneto gas kinetic method (MGKM) to study the effect of the Mach number, Alfvén Mach number, and the orientation of the magnetic field with respect to the jet velocity direction on the flow-field evolution. In MGKM, the magnetic effects are added as source terms in the hydrodynamic gas kinetic scheme which also take into account the non-ideal MHD terms for finite plasma conductivity and the Hall effects. An in-depth analysis of linear and nonlinear physics is presented. The first author was supported by Texas A&M University Institute for Advanced Study HEEP fellowship.
Evidence for thermal anisotropy effects on shear modified ion acoustic instabilities
NASA Astrophysics Data System (ADS)
Scime, E. E.; Keesee, A. M.; Spangler, R. S.; Koepke, M. E.; Teodorescu, C.; Reynolds, E. W.
2002-10-01
Inclusion of thermal anisotropy effects is shown to be required to describe recently reported experimental measurements as shear-modified, ion acoustic instabilities. For the reported experimental conditions, isotropic theory yields no instability growth that depends on the magnitude of the shear in the parallel flow.
Heinemann, Tobias; Quataert, Eliot E-mail: eliot@berkeley.edu
2014-09-01
We derive the conductivity tensor for axisymmetric perturbations of a hot, collisionless, and charge-neutral plasma in the shearing sheet approximation. Our results generalize the well-known linear Vlasov theory for uniform plasmas to differentially rotating plasmas and can be used for wide range of kinetic stability calculations. We apply these results to the linear theory of the magneto-rotational instability (MRI) in collisionless plasmas. We show analytically and numerically how the general kinetic theory results derived here reduce in appropriate limits to previous results in the literature, including the low-frequency guiding center (or 'kinetic MHD') approximation, Hall magnetohydrodynamics (MHD), and the gyro-viscous approximation. We revisit the cold plasma model of the MRI and show that, contrary to previous results, an initially unmagnetized collisionless plasma is linearly stable to axisymmetric perturbations in the cold plasma approximation. In addition to their application to astrophysical plasmas, our results provide a useful framework for assessing the linear stability of differentially rotating plasmas in laboratory experiments.
Local magnetohydrodynamic instabilities and the wave-driven dynamo in accretion disks
NASA Technical Reports Server (NTRS)
Vishniac, Ethan T.; Diamond, Patrick
1992-01-01
We consider the consequences of magnetic buoyancy and the magnetic shearing instability (MSI) on the strength and organization of the magnetic field in a thin accretion disk. We discuss a model in which the wave-driven dynamo growth rate is balanced by the dissipative effects of the MSI. As in earlier work, the net helicity is due to small advective motions driven by nonlinear interactions between internal waves. Assuming a simple model of the internal wave spectrum generated from the primary m = 1 internal waves, we find that the magnetic energy density saturates at about (H/r) exp 4/3 times the local pressure (where H is the disk thickness and r is its radius). On very small scales the shearing instability will produce an isotropic fluctuating field. For a stationary disk this is equivalent to a dimensionless 'viscosity' of about (H/r) exp 4/3. The vertical and radial diffusion coefficients will be comparable to each other. Magnetic buoyancy will be largely suppressed by the turbulence due to the MSI. We present a rough estimate of its effects and find that it removes magnetic flux from the disk at a rate comparable to that caused by turbulent diffusion.
Bogdanovic, Tamara; Reynolds, Christopher S.; Balbus, Steven A.; Parrish, Ian J. E-mail: chris@astro.umd.ed E-mail: iparrish@astro.berkeley.ed
2009-10-10
We perform a suite of simulations of cooling cores in clusters of galaxies in order to investigate the effect of the recently discovered heat flux buoyancy instability (HBI) on the evolution of cores. Our models follow the three-dimensional magnetohydrodynamics of cooling cluster cores and capture the effects of anisotropic heat conduction along the lines of magnetic field, but do not account for the cosmological setting of clusters or the presence of active galactic nuclei (AGNs). Our model clusters can be divided into three groups according to their final thermodynamical state: catastrophically collapsing cores, isothermal cores, and an intermediate group whose final state is determined by the initial configuration of magnetic field. Modeled cores that are reminiscent of real cluster cores show evolution toward thermal collapse on a timescale which is prolonged by a factor of approx2-10 compared with the zero-conduction cases. The principal effect of the HBI is to re-orient field lines to be perpendicular to the temperature gradient. Once the field has been wrapped up onto spherical surfaces surrounding the core, the core is insulated from further conductive heating (with the effective thermal conduction suppressed to less than 10{sup -2} of the Spitzer value) and proceeds to collapse. We speculate that, in real clusters, the central AGN and possibly mergers play the role of 'stirrers', periodically disrupting the azimuthal field structure and allowing thermal conduction to sporadically heat the core.
Mikhailenko, V. S.; Chibisov, D. V.
2007-08-15
The effects of the shear flow along the magnetic field on the development of the ion cyclotron, ion sound, and drift instabilities in the radially inhomogeneous cylindrical plasma are studied on the ground of a kinetic approach. It is shown that flow shear not only modifies the frequencies and growth rates of known current driven electrostatic ion cyclotron, ion sound, and drift instabilities, but is the source of the development of specific shear-flow-driven ion cyclotron, ion sound, and drift instabilities. These instabilities are excited at the levels of current along the ambient magnetic field which is below the critical value for the development of the modified by flow shear current driven ion cyclotron, ion sound, and drift instabilities.
Flow instability and wall shear stress variation in intracranial aneurysms
Baek, H.; Jayaraman, M. V.; Richardson, P. D.; Karniadakis, G. E.
2010-01-01
We investigate the flow dynamics and oscillatory behaviour of wall shear stress (WSS) vectors in intracranial aneurysms using high resolution numerical simulations. We analyse three representative patient-specific internal carotid arteries laden with aneurysms of different characteristics: (i) a wide-necked saccular aneurysm, (ii) a narrower-necked saccular aneurysm, and (iii) a case with two adjacent saccular aneurysms. Our simulations show that the pulsatile flow in aneurysms can be subject to a hydrodynamic instability during the decelerating systolic phase resulting in a high-frequency oscillation in the range of 20–50 Hz, even when the blood flow rate in the parent vessel is as low as 150 and 250 ml min−1 for cases (iii) and (i), respectively. The flow returns to its original laminar pulsatile state near the end of diastole. When the aneurysmal flow becomes unstable, both the magnitude and the directions of WSS vectors fluctuate at the aforementioned high frequencies. In particular, the WSS vectors around the flow impingement region exhibit significant spatio-temporal changes in direction as well as in magnitude. PMID:20022896
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.
Modeling Shear Instabilities With Block Sliders: Brittle and Ductile
NASA Astrophysics Data System (ADS)
Riedel, M. R.
2003-12-01
Block slider-type models have been succesfully used for almost 35 years to describe the spatio-temporal development of shear instabilities in the brittle crust (Burridge & Knopoff, 1967; Olami et al., 1992). More recently, increasing attention is paid on the extension of the classical Burridge-Knopoff model (based on a pure Mohr-Coulomb rheology) with a viscous component, either to include depth-dependent properties into the model or aiming at a more accurate description of fore- and aftershock sequences of a main earthquake event (e.g. Hainzl et al., 1999). On the other hand, viscous feedback mechanisms of various types have become an increasingly attractive mechanism for the generation of intermediate-depth and deep-focus earthquakes in the ductile mantle lithosphere (e.g. Wiens & Snider, 2001). Heat generated during viscous deformation provides a positive feedback to creep and eventually faulting under high pressure (Karato et al., 2001, Bercovici & Karato, 2003). The present paper discusses the specific properties of block slider-type models that are extended with a viscous component and compare their behaviour with the pure brittle ("classical") case. Block slider-type models for ductile instabilities are numerically much less demanding than solutions based on the corresponding, thermal-mechanically coupled, continuum equations. They allow for the inclusion of possible non-equilibrium effects associated with mineral phase transformations in a subducting slab (kinetic overshoot, grainsize reduction, latent heat release) in a straightforward manner. They may therefore serve as an effective tool to study the coupling of viscous heating, temperature-dependent viscosity and brittle stress transfer that are thought to cause the specific spatial-temporal clustering of intermediate-depth and deep-focus eartquakes. References D. Bercovici and S. Karato "Theoretical Analysis of Shear Localization in the Lithosphere", in: Reviews in Mineralogy and Geochemistry 51, eds. S
Hydrodynamic instability and shear layer effects in turbulent premixed combustion
NASA Astrophysics Data System (ADS)
Schlimpert, S.; Feldhusen, A.; Grimmen, J. H.; Roidl, B.; Meinke, M.; Schröder, W.
2016-01-01
A turbulent premixed plane jet flame is analyzed by large-eddy simulations. The analysis shows that the flame front wrinkling is strongly influenced by the shear layer effect when the gas expansion effects are small leading to larger flame front amplitudes at the flame base than at high gas expansion ratios. However, the hydrodynamic instability effect induces a continuously increasing flame front amplitude which yields an enhanced flame pocket generation at the flame tip. Both phenomena influence the magnitude of the turbulent burning area and burning area rate response through the flame front deflections which are determined by the contribution coefficient. This coefficient represents the mutual interaction between the flame and the flow. At low gas expansion ratios, the total heat release rate spectra of the turbulent flame are wider in terms of dominant modes at Strouhal numbers which are linked to the mean flame height oscillations. Thus, at low gas expansion ratios, the vortex-flame interaction is less damped by the flame in the sense that vortices can perturb the flame front stronger. The total heat release rate trend of St-2.2 previously found for a round jet flame is also determined for the current slot jet at realistic gas expansion ratios indicating a general tendency to transfer energy from large to small flame structures. At high gas expansion ratios, an increasing Markstein length leads to an energy transfer between neighboring dominant modes in the low frequency range 1 < St < 10 and the burning area rate response becomes more important for the total heat release rate spectra of the turbulent slot flames which agrees with recent findings for a laminar premixed plane flame.
Cooling Requirements for the Vertical Shear Instability in Protoplanetary Disks
NASA Astrophysics Data System (ADS)
Lin, Min-Kai; Youdin, Andrew N.
2015-09-01
The vertical shear instability (VSI) offers a potential hydrodynamic mechanism for angular momentum transport in protoplanetary disks (PPDs). The VSI is driven by a weak vertical gradient in the disk’s orbital motion, but must overcome vertical buoyancy, a strongly stabilizing influence in cold disks, where heating is dominated by external irradiation. Rapid radiative cooling reduces the effective buoyancy and allows the VSI to operate. We quantify the cooling timescale tc needed for efficient VSI growth, through a linear analysis of the VSI with cooling in vertically global, radially local disk models. We find the VSI is most vigorous for rapid cooling with {t}{{c}}\\lt {{{Ω }}}{{K}}-1h| q| /(γ -1) in terms of the Keplerian orbital frequency, {{{Ω }}}{{K}}, the disk’s aspect-ratio, h\\ll 1, the radial power-law temperature gradient, q, and the adiabatic index, γ. For longer tc, the VSI is much less effective because growth slows and shifts to smaller length scales, which are more prone to viscous or turbulent decay. We apply our results to PPD models where tc is determined by the opacity of dust grains. We find that the VSI is most effective at intermediate radii, from ∼5 to ∼50 AU with a characteristic growth time of ∼30 local orbital periods. Growth is suppressed by long cooling times both in the opaque inner disk and the optically thin outer disk. Reducing the dust opacity by a factor of 10 increases cooling times enough to quench the VSI at all disk radii. Thus the formation of solid protoplanets, a sink for dust grains, can impede the VSI.
Instabilities in wormlike micelle systems. From shear-banding to elastic turbulence.
Fardin, M-A; Lerouge, S
2012-09-01
Shear-banding is ubiquitous in complex fluids. It is related to the organization of the flow into macroscopic bands bearing different viscosities and local shear rates and stacked along the velocity gradient direction. This flow-induced transition towards a heterogeneous flow state has been reported in a variety of systems, including wormlike micellar solutions, telechelic polymers, emulsions, clay suspensions, colloidal gels, star polymers, granular materials, or foams. In the past twenty years, shear-banding flows have been probed by various techniques, such as rheometry, velocimetry and flow birefringence. In wormlike micelle solutions, many of the data collected exhibit unexplained spatio-temporal fluctuations. Different candidates have been identified, the main ones being wall slip, interfacial instability between bands or bulk instability of one of the bands. In this review, we present experimental evidence for a purely elastic instability of the high shear rate band as the main origin for fluctuating shear-banding flows. PMID:23001785
Mizuno, Yosuke; Nishikawa, Ken-Ichi; Hardee, Philip E.
2011-06-10
We have investigated the influence of a velocity shear surface on the linear and nonlinear development of the current-driven (CD) kink instability of force-free helical magnetic equilibria in three dimensions. In this study, we follow the temporal development within a periodic computational box and concentrate on flows that are sub-Alfvenic on the cylindrical jet's axis. Displacement of the initial force-free helical magnetic field leads to the growth of CD kink instability. We find that helically distorted density structure propagates along the jet with speed and flow structure dependent on the radius of the velocity shear surface relative to the characteristic radius of the helically twisted force-free magnetic field. At small velocity shear surface radius, the plasma flows through the kink with minimal kink propagation speed. The kink propagation speed increases as the velocity shear radius increases and the kink becomes more embedded in the plasma flow. A decreasing magnetic pitch profile and faster flow enhance the influence of velocity shear. Simulations show continuous transverse growth in the nonlinear phase of the instability. The growth rate of the CD kink instability and the nonlinear behavior also depend on the velocity shear surface radius and flow speed, and the magnetic pitch radial profile. Larger velocity shear radius leads to slower linear growth, makes a later transition to the nonlinear stage, and with larger maximum amplitude than that occuring for a static plasma column. However, when the velocity shear radius is much greater than the characteristic radius of the helical magnetic field, linear and nonlinear development can be similar to the development of a static plasma column.
Azimuthal instability of the interface in a shear banded flow by direct visual observation.
Decruppe, J P; Bécu, L; Greffier, O; Fazel, N
2010-12-17
The stability of the shear banded flow of a Maxwellian fluid is studied from an experimental point of view using rheology and flow visualization with polarized light. We show that the one-layer homogeneous flow cannot sustain shear rates corresponding to the end of the stress plateau. The high shear rate branch is not found and the shear stress oscillates at the end of the plateau. An azimuthal instability appears: the shear induced band becomes unstable and the interface between the two bands undulates in time and space with a period τ, a wavelength λ and a wave vector k parallel to the direction of the tangential velocity. PMID:21231629
Casanellas, Laura; Alves, Manuel A; Poole, Robert J; Lerouge, Sandra; Lindner, Anke
2016-07-20
We determine both experimentally and numerically the onset of elastic flow instabilities in viscoelastic polymer solutions with different levels of shear thinning. Previous experiments realized in microfluidic serpentine channels using dilute polymeric solutions showed that the onset of elastic instabilities strongly depends on the channel curvature. The scaling dependence is well captured by the general instability scaling criterion proposed by Pakdel and McKinley [Phys. Rev. Lett., 1996, 76, 2459:1-4]. We determine here the influence of fluid shear thinning on the onset of such purely-elastic flow instabilities. By testing a set of polyethylene oxide solutions of high molecular weight at different polymer concentrations in microfluidic serpentine channels we observe that shear thinning has a stabilizing effect on the microfluidic flow. Three-dimensional numerical simulations performed using the White-Metzner model predict similar trends, which are not captured by a simple scaling analysis using the Pakdel-McKinley criterion. PMID:27265240
NASA Astrophysics Data System (ADS)
Kelemen, P. B.; Hirth, G.
2004-12-01
Localized ductile shear zones with widths of cm to m are observed in exposures of Earth's shallow mantle (e.g., Kelemen & Dick JGR 95; Vissers et al. Tectonophys 95) and dredged from oceanic fracture zones (e.g., Jaroslow et al. Tectonophys 96). These are mylonitic (grain size 10 to 100 microns) and record mineral cooling temperatures from 1100 to 600 C. Pseudotachylites in a mantle shear zone show that shear heating temperatures can exceed the mantle solidus (e.g., Obata & Karato Tectonophys 95). Simple shear, recrystallization, and grain boundary sliding all decrease the spacing between pyroxenes, so olivine grain growth at lower stress is inhibited; thus, once formed, these shear zones do not "heal" on geological time scales. Reasoning that grain-size sensitive creep will be localized within these shear zones, rather than host rocks (grain size 1 to 10 mm), and inspired by the work of Whitehead & Gans (GJRAS 74), we thought these might undergo repeated shear heating instabilities. In this view, as elastic stress increases, the shear zone weakens via shear heating; rapid deformation of the weak shear zone releases most stored elastic stress; lower stress and strain rate coupled with diffusion of heat into host rocks leads to cooling and strengthening, after which the cycle repeats. We constructed a simple numerical model incorporating olivine flow laws for dislocation creep, diffusion creep, grain boundary sliding, and low T plasticity. We assumed that viscous deformation remains localized in shear zones, surrounded by host rocks undergoing elastic deformation. We fixed the velocity along one side of an elastic half space, and calculated stress due to elastic strain. This stress drives viscous deformation in a shear zone of specified width. Shear heating and thermal diffusion control temperature evolution in the shear zone and host rocks. A maximum of 1400 C (where substantial melting of peridotite would occur) is imposed. Grain size evolves during dislocation
Excitation of shear layer instability in flow past a cylinder at low Reynolds number
NASA Astrophysics Data System (ADS)
Mittal, S.
2005-12-01
The instability of the separated shear layer for flow past a cylinder, in two dimensions, is investigated for low Reynolds numbers (Re 350). The line of symmetry, downstream of the cylinder, in the wake is forced to be a streamline. This hypothetical situation allows slip of velocity along the wake centreline but prevents any flow normal to it. With this arrangement the flow is completely stable for Re 250. It suppresses the primary instability of the wake that is responsible for the von Karman vortex shedding. Unlike the conventional splitter plate such an arrangement does not have a wake of its own. At Re = 300 and above the wake instability and the shear layer instability are observed. The fluctuations due to the instabilities are intermittent in nature. The shear layer frequency is smaller than the frequency of the von Karman vortex shedding for the regular flow past a cylinder. It is also found that flow past half a cylinder, with symmetry conditions at the wake centreline, at Re = 300 is stable. However, when a secondary cylinder with one-fifth the diameter of the half-cylinder is placed close to it, the vortex shedding from the smaller cylinder again leads to instability of the separated shear layer of the half-cylinder. This suggests that although the separated shear layer is stable, at such low Re, the shear layer instability can be excited by some other disturbances. It is found that even at such low Re, the normalized shear layer frequency follows the Re0.67 power law. All the computations have been carried out using a stabilized finite element formulation.
NASA Technical Reports Server (NTRS)
Vinas, A. F.; Madden, T. R.
1986-01-01
A unified linear electromagnetic analysis of both the Kelvin-Helmholtz (shear flow) instability and of the ballooning (interchange) instability is carried out on the basis of MHD theory. In the analysis, the concept of the Richardson instability of hydrodynamic flows is extended into the hydromagnetic context by unifying both the shear flow and the ballooning instability. As essential concept of the analysis is the role played by the magnetic buoyancy due to an effective gravity produced by the curvature of the field lines which provides the basic step by which both instabilities could be coupled. The results of the study are applied to the plasmapause to explain the excitation of hydromagnetic waves in that region, including the effect of the hot particles from the plasma sheet.
NASA Astrophysics Data System (ADS)
Kwak, Rhokyun; Pham, Van Sang; Han, Jongyoon
2014-11-01
Suppression of turbulence and transport by shear flow is a common process in plasma fluid dynamics, while it has been rarely observed in nonionized fluids. Here, we visualize this effect in microfluidic nonionized system with electroconvective instability (EC) initiated by ion concentration polarization on ion selective membrane. The membranes act as the source of both instability and flow shear (wall shear of Hagen-Poiseuille (HP) flow) simultaneously, fitting the requisite for this shear suppression effect; turbulence in the domain of flow shear. To the best of our knowledge, this is the first characterization of flow-shear-induced transport barrier in microfluidics, captured by scaling analysis, experiment, and numerical modeling. Selected by balancing flow shear and velocity fluctuation, which generated by HP flow and vortical EC, the threshold for shear suppression scales by EC thickness dec/ w < 0.618. Stable unidirectional EC occurs under the threshold, while chaotic EC occurs over the threshold by overcoming flow shear. It also has significant implications on the energy saving of electrochemical systems (e . g . electrodialysis) to prevent chaotic turbulences and corresponding energy dissipations. This work was supported by the Advanced Research Projects Agency-Energy Grant (DE-AR0000294).
Instability of Stratified Shear Flow: Intermittency and Length Scales
NASA Astrophysics Data System (ADS)
Ecke, Robert; Odier, Philippe
2015-11-01
The stability of stratified shear flows which occur in oceanic overflows, wind-driven thermoclines, and atmospheric inversion layers is governed by the Richardson Number Ri , a non-dimensional balance between stabilizing stratification and destabilizing shear. For a shear flow with velocity difference U, density difference Δρ and characteristic length H, one has Ri = g (Δρ / ρ) H /U2 . A more precise definition is the gradient Richardson Number Rig =N2 /S2 where the buoyancy frequency N =√{ (g / ρ) ∂ρ / ∂z } , the mean strain S = ∂U / ∂z with z parallel to gravity and with ensemble or time averages defining the gradients. We explore the stability and mixing properties of a wall-bounded shear flow for 0 . 1 < Rig < 1 using simultaneous measurements of density and velocity fields. The flow, confined from the top by a horizontal boundary, is a lighter alcohol-water mixture injected from a nozzle into quiescent heavier salt-water fluid. The injected flow is turbulent with Taylor Reynolds number about 75. We compare a set of length scales that characterize the mixing properties of our turbulent stratified shear flow including Thorpe Length LT, Ozmidov Length LO, and Ellison Length LE.
Finite-width currents, magnetic shear, and the current-driven ion-cyclotron instability
NASA Technical Reports Server (NTRS)
Bakshi, P.; Ganguli, G.; Palmadesso, P.
1983-01-01
Our earlier results that non-local effects due to even a small magnetic shear produce a significant reduction of the growth rate of the ion cyclotron instability driven by a uniform current are now generalized to finite width currents. Externally prescribed as well as self-consistent shears are considered. If the current width Lc exceeds the shear length Ls, the previous results are recovered. Shear becomes less effective with reduction of Lc, and for typical parameters, the growth rate attains its (shearless) local value for Lc/Ls approximately less than 10 to the minus 2. Non-local effects of the finite current width itself come into play if Lc is further reduced to a few ion Larmor radii and can quench the instability. Previously announced in STAR as N83-28996
NASA Astrophysics Data System (ADS)
Hamlin, Nathaniel D.; Newman, William I.
2013-04-01
We explore, via analytical and numerical methods, the Kelvin-Helmholtz (KH) instability in relativistic magnetized plasmas, with applications to astrophysical jets. We solve the single-fluid relativistic magnetohydrodynamic (RMHD) equations in conservative form using a scheme which is fourth order in space and time. To recover the primitive RMHD variables, we use a highly accurate, rapidly convergent algorithm which improves upon such schemes as the Newton-Raphson method. Although the exact RMHD equations are marginally stable, numerical discretization renders them unstable. We include numerical viscosity to restore numerical stability. In relativistic flows, diffusion can lead to a mathematical anomaly associated with frame transformations. However, in our KH studies, we remain in the rest frame of the system, and therefore do not encounter this anomaly. We use a two-dimensional slab geometry with periodic boundary conditions in both directions. The initial unperturbed velocity peaks along the central axis and vanishes asymptotically at the transverse boundaries. Remaining unperturbed quantities are uniform, with a flow-aligned unperturbed magnetic field. The early evolution in the nonlinear regime corresponds to the formation of counter-rotating vortices, connected by filaments, which persist in the absence of a magnetic field. A magnetic field inhibits the vortices through a series of stages, namely, field amplification, vortex disruption, turbulent breakdown, and an approach to a flow-aligned equilibrium configuration. Similar stages have been discussed in MHD literature. We examine how and to what extent these stages manifest in RMHD for a set of representative field strengths. To characterize field strength, we define a relativistic extension of the Alfvénic Mach number MA. We observe close complementarity between flow and magnetic field behavior. Weaker fields exhibit more vortex rotation, magnetic reconnection, jet broadening, and intermediate turbulence
Experimental and numerical study of the shear layer instability between two counter-rotating disks
NASA Astrophysics Data System (ADS)
Moisy, F.; Doaré, O.; Pasutto, T.; Daube, O.; Rabaud, M.
2004-05-01
The shear layer instability in the flow between two counter-rotating disks enclosed by a cylinder is investigated experimentally and numerically, for radius-to-height ratio Gamma {=} R/h between 2 and 21. For sufficiently large rotation ratio, the internal shear layer that separates two regions of opposite azimuthal velocities is prone to an azimuthal symmetry breaking, which is investigated experimentally by means of visualization and particle image velocimetry. The associated pattern is a combination of a sharp-cornered polygonal pattern, as observed by Lopez et al. (2002) for low aspect ratio, surrounded by a set of spiral arms, first described by Gauthier et al. (2002) for high aspect ratio. The spiral arms result from the interaction of the shear layer instability with the Ekman boundary layer over the faster rotating disk. Stability curves and critical modes are experimentally measured for the whole range of aspect ratios, and are found to compare well with numerical simulations of the three-dimensional time-dependent Navier Stokes equations over an extensive range of parameters. Measurements of a local Reynolds number based on the shear layer thickness confirm that a shear layer instability, with only weak curvature effect, is responsible for the observed patterns. This scenario is supported by the observed onset modes, which scale as the shear layer radius, and by the measured phase velocities.
Instability in Three-Dimensional Magnetohydrodynamic Flows of an Electrically Conducting Fluid
NASA Astrophysics Data System (ADS)
Zakir, Hussain; Liu, Chan; Zhang, Nianmei; Ni, Mingjiu
2013-12-01
The three-dimensional instability of an electrically conducting fluid between two parallel plates affected by an imposed transversal magnetic field is numerically investigated by a Chebyshev collocation method. The QZ method is utilized to obtain neutral curves of the linear instability. The details of instability are analyzed by solving the generalized Orr-Sommerfeld equation. The critical Reynolds number Rec, the stream-wise and span-wise critical wave numbers αc and βc are obtained for a wide range of Hartmann number Ha. The effects of Lorentz force and span-wise perturbation on three-dimensional instability are investigated. The results show that magnetic field would suppress the instability and critical Reynolds number tends to be larger than that for two-dimensional instability.
Inertial ranges and resistive instabilities in two-dimensional magnetohydrodynamic turbulence
NASA Astrophysics Data System (ADS)
Politano, H.; Pouquet, A.; Sulem, P. L.
1989-12-01
Direct numerical simulations of decaying two-dimensional magnetohydrodynamic flows at Reynolds numbers of several thousand are performed, using resolutions of 1024-squared collocation points. An inertial range extending to about one decade is observed, with spectral properties depending on the velocity-magnetic field correlation. At very small scales, resistive tearing destabilizes current sheets generated by the inertial dynamics and leads to the formation of small-scale magnetic islands, which may then grow and reach the size of inertial scales.
Generalized reduced magnetohydrodynamic equations
Kruger, S.E.
1999-02-01
A new derivation of reduced magnetohydrodynamic (MHD) equations is presented. A multiple-time-scale expansion is employed. It has the advantage of clearly separating the three time scales of the problem associated with (1) MHD equilibrium, (2) fluctuations whose wave vector is aligned perpendicular to the magnetic field, and (3) those aligned parallel to the magnetic field. The derivation is carried out without relying on a large aspect ratio assumption; therefore this model can be applied to any general configuration. By accounting for the MHD equilibrium and constraints to eliminate the fast perpendicular waves, equations are derived to evolve scalar potential quantities on a time scale associated with the parallel wave vector (shear-Alfven wave time scale), which is the time scale of interest for MHD instability studies. Careful attention is given in the derivation to satisfy energy conservation and to have manifestly divergence-free magnetic fields to all orders in the expansion parameter. Additionally, neoclassical closures and equilibrium shear flow effects are easily accounted for in this model. Equations for the inner resistive layer are derived which reproduce the linear ideal and resistive stability criterion of Glasser, Greene, and Johnson. The equations have been programmed into a spectral initial value code and run with shear flow that is consistent with the equilibrium input into the code. Linear results of tearing modes with shear flow are presented which differentiate the effects of shear flow gradients in the layer with the effects of the shear flow decoupling multiple harmonics.
Experimental Verification of the Shear-Modified Ion-Acoustic Instability
NASA Astrophysics Data System (ADS)
Teodorescu, C.; Reynolds, E. W.; Koepke, M. E.
2002-05-01
The predicted shear-induced shift of the wave phase velocity, the essence of the shear-modified ion-acoustic (SMIA) instability mechanism that reduces ion Landau damping for otherwise damped ion-acoustic waves [V. Gavrishchaka et al., 80, 728 (1998)], is verified with direct measurements in a strongly magnetized laboratory plasma. The SMIA growth rate is shown to increase with increasing shear, as predicted. SMIA wave propagation is shown to be possible at both small and large angles to the magnetic field, consistent with space observations of ion-acoustic-like waves.
Study of micro-instabilities in toroidal plasmas with negative magnetic shear
Dong, J.Q.; Zhang, Y.Z.; Mahajan, S.M.; Guzdar, P.N.
1996-03-01
The micro-instabilities driven by a parallel velocity shear, and a temperature gradient of ions are studied in toroidal plasmas with negative magnetic shear. Both the fluid and the gyro-kinetic formulations are investigated. It is found that for a broad range of parameters, the linear growth rates of the modes are lower, and the threshold temperature gradient {eta}{sub icr} is higher for plasmas with negative magnetic shear compared to plasmas with positive magnetic shear of equal magnitude. The reduction in the growth rate (with negative shear), although not insignificant, does not seem to be enough to account for the dramatic improvement in the confinement observed experimentally. Other possible physical mechanisms for the improved confinement are discussed.
NASA Astrophysics Data System (ADS)
Billeter, P.
2004-04-01
The basic findings of an experimental investigation of flow-induced vibrations of gate plates with multiple degrees of freedom are presented. The study focused on the fluid dynamic behaviour of the single shear layer separating from a thick rectangular plate. The principal aim of the study was to further the physical understanding of instability-induced excitation mechanisms (IIE) involving shear layer instabilities and vortex generation. It is shown that this type of gate vibration is caused by two dominant excitation mechanisms: cross-flow and streamwise impinging-leading-edge-vortex (ILEV) excitation and streamwise body-resonant leading-edge-vortex-shedding (BR-LEVS) excitation. The first mechanism is caused by the local interaction of the shear layer underneath the gate plate with the trailing edge of the gate lip. The second mechanism is produced by the instability of the shear layer in the tailwater of the gate, with the instability being necessarily triggered by the elastic motion of the flow separation at the leading edge of the gate. Former address. Laboratory of Hydraulics (VAW), Swiss Federal Institute of Technology (ETH), Zurich, Switzerland.
Long-wave shear instability of fluid interfaces
NASA Astrophysics Data System (ADS)
Cherniavski, Vladimir
2010-05-01
The earlier oceanographic works largely focused on the case of very large density differences between the two fluids sepa¬rated by an interface. The aim of this investigation is to extend the shear-flow analysis to more wide range of density ratios for the log profile of the "wind". Long wave asymptotic leads to the analytic determination of the stability characteristics of the flow. The present work is originally motivated by a laboratory experiment and can be useful for an astrophysical problem.
NASA Astrophysics Data System (ADS)
Vetcha, N.; Smolentsev, S.; Abdou, M.; Moreau, R.
2013-02-01
We consider magnetohydrodynamic (MHD) rectangular duct flows with volumetric heating. The flows are upward, subject to a strong transverse magnetic field perpendicular to the temperature gradient, such that the flow dynamics is quasi-two-dimensional. The internal volumetric heating imitates conditions of a blanket of a fusion power reactor, where a buoyancy-driven flow is imposed on the forced flow. Studies of this mixed-convection flow include analysis for the basic flow, linear stability analysis and Direct Numerical Simulation (DNS)-type computations. The parameter range covers the Hartmann number (Ha) up to 500, the Reynolds number (Re) from 1000 to 10 000, and the Grashof number (Gr) from 105 to 5 × 108. The linear stability analysis predicts two primary instability modes: (i) bulk instability associated with the inflection point in the velocity profile near the "hot" wall and (ii) side-wall boundary layer instability. A mixed instability mode is also possible. An equation for the critical Hartmann number has been obtained as a function of Re and Gr. Effects of Ha, Re, and Gr on turbulent flows are addressed via nonlinear computations that demonstrate two characteristic turbulence regimes. In the "weak" turbulence regime, the induced vortices are localized near the inflection point of the basic velocity profile, while the boundary layer at the wall parallel to the magnetic field is slightly disturbed. In the "strong" turbulence regime, the bulk vortices interact with the boundary layer causing its destabilization and formation of secondary vortices that may travel across the flow, even reaching the opposite wall. In this regime, the key phenomena are vortex-wall and various vortex-vortex interactions. Flow and magnetic field effects on heat transfer are also analyzed.
Nonlinear Instability of a Uni-directional Transversely Sheared Mean Flow
NASA Technical Reports Server (NTRS)
Wundrow, David W.; Goldstein, Marvin E.
1994-01-01
It is well known that the presence of a weak cross flow in an otherwise two-dimensional shear flow results in a spanwise variation in the mean streamwise velocity profile that can lead to an amplification of certain three-dimensional disturbances through a kind of resonant-interaction mechanism (Goldstein and Wundrow 1994). The spatial evolution of an initially linear, finite-growth-rate, instability wave in such a spanwise-varying shear flow is considered, The base flow, which is governed by the three-dimensional parabolized Navier-Stokes equations, is initiated by imposing a spanwise- periodic cross-flow velocity on an otherwise two-dimensional shear flow at some fixed streamwise location. The resulting mean-flow distortion initially grows with increasing streamwise distance, reaches a maximum and eventually decays through the action of viscosity. This decay, which coincides with the viscous spread of of the shear layer, means that the local growth rate of the instability wave will eventually decrease as the wave propagates downstream. Nonlinear effects can then become important within a thin spanwise-modulated critical layer once the local instability-wave amplitude and growth rate become sufficiently large and small, respectively. The amplitude equation that describes this stage of evolution is shown to be a generalization of the one obtained by Goldstein and Choi (1989) who considered the related problem of the interaction of two oblique modes in a two-dimensional shear layer.
Interchange and Flow Velocity Shear Instabilities in the Presence of Finite Larmor Radius Effects
NASA Astrophysics Data System (ADS)
Sotnikov, V.; Kim, T.; Mishin, E.; Genoni, T.; Rose, D.; Mehlhorn, T.
2014-09-01
Ionospheric irregularities cause scintillations of electromagnetic signals that can severely affect navigation and transionospheric communication, in particular during Equatorial Plasma Bubbles (EPBs) events. However, the existing ionospheric models do not describe density irregularities with typical scales of several ion Larmor radii that affect UHF and L bands. These irregularities can be produced in the process of nonlinear evolution of interchange or flow velocity shear instabilities. The model of nonlinear development of these instabilities based on two-fluid hydrodynamic description with inclusion of finite Larmor radius effects will be presented. The derived nonlinear equations will be numerically solved by using the code Flute, which was originally developed for High Energy Density applications and modified to describe interchange and flow velocity shear instabilities in the ionosphere. The high-resolution simulations will be driven by the ambient conditions corresponding to the AFRL C/NOFS satellite low-resolution data during EPBs.
Effects of a weakly 3-D equilibrium on ideal magnetohydrodynamic instabilities
Hegna, C. C.
2014-07-15
The effect of a small three-dimensional equilibrium distortion on an otherwise axisymmetric configuration is shown to be destabilizing to ideal magnetohydrodynamic modes. The calculations assume that the 3-D fields are weak and that shielding physics is present so that no islands appear in the resulting equilibrium. An eigenfunction that has coupled harmonics of different toroidal mode number is constructed using a perturbation approach. The theory is applied to the case of tokamak H-modes with shielded resonant magnetic perturbations (RMPs) present indicating RMPs can be destabilizing to intermediate-n peeling-ballooning modes.
Squire, J.; Bhattacharjee, A.
2014-12-10
We study magnetorotational instability (MRI) using nonmodal stability techniques. Despite the spectral instability of many forms of MRI, this proves to be a natural method of analysis that is well-suited to deal with the non-self-adjoint nature of the linear MRI equations. We find that the fastest growing linear MRI structures on both local and global domains can look very different from the eigenmodes, invariably resembling waves shearing with the background flow (shear waves). In addition, such structures can grow many times faster than the least stable eigenmode over long time periods, and be localized in a completely different region of space. These ideas lead—for both axisymmetric and non-axisymmetric modes—to a natural connection between the global MRI and the local shearing box approximation. By illustrating that the fastest growing global structure is well described by the ordinary differential equations (ODEs) governing a single shear wave, we find that the shearing box is a very sensible approximation for the linear MRI, contrary to many previous claims. Since the shear wave ODEs are most naturally understood using nonmodal analysis techniques, we conclude by analyzing local MRI growth over finite timescales using these methods. The strong growth over a wide range of wave-numbers suggests that nonmodal linear physics could be of fundamental importance in MRI turbulence.
Nonlinear shearing modes approach to the diocotron instability of a planar electron strip
Mikhailenko, V. V. Mikhailenko, V. S.; Jo, Younghyun; Lee, Hae June
2015-09-15
The nonlinear evolution of the diocotron instability of a planar electron strip is investigated analytically by means of the nonlinear shearing mode for the solution of the initial and boundary value problems. The method is based on the sheared spatial coordinates which account for the motion of electron flow in the electrostatic field of the unstable diocotron modes in addition to the unperturbed sheared motion of the electron flow on the transformed shear coordinates. The time evolutions are studied by the solution of the initial and boundary value problems. The obtained solutions for the perturbed electrostatic potential include two nonlinear effects—the effect of the distortion of the boundaries of the planar electron strip and the effect of the coupling of the sheared nonmodal diocotron modes. It was proved by a two-dimensional particle-in-cell simulation that the developed theory is valid as long as the distortion of the boundaries of the basic shear flow does not change the frequency and growth rate of the linear diocotron instability in the transformed coordinates.
J Squire, A Bhattacharjee
2014-07-01
We study the magnetorotational instability (MRI) (Balbus & Hawley 1998) using non-modal stability techniques.Despite the spectral instability of many forms of the MRI, this proves to be a natural method of analysis that is well-suited to deal with the non-self-adjoint nature of the linear MRI equations. We find that the fastest growing linear MRI structures on both local and global domains can look very diff erent to the eigenmodes, invariably resembling waves shearing with the background flow (shear waves). In addition, such structures can grow many times faster than the least stable eigenmode over long time periods, and be localized in a completely di fferent region of space. These ideas lead – for both axisymmetric and non-axisymmetric modes – to a natural connection between the global MRI and the local shearing box approximation. By illustrating that the fastest growing global structure is well described by the ordinary diff erential equations (ODEs) governing a single shear wave, we find that the shearing box is a very sensible approximation for the linear MRI, contrary to many previous claims. Since the shear wave ODEs are most naturally understood using non-modal analysis techniques, we conclude by analyzing local MRI growth over finite time-scales using these methods. The strong growth over a wide range of wave-numbers suggests that non-modal linear physics could be of fundamental importance in MRI turbulence (Squire & Bhattacharjee 2014).
Nonlocal theory of the parallel velocity shear instability
NASA Astrophysics Data System (ADS)
Migliuolo, S.; Coppi, B.; Sen, A. K.
1997-11-01
The stability of a plasma flowing, with a nonuniform velocity, in the direction parallel to the main component of the confining magnetic field is examined in the presence of density gradients^1. We treat the simple sheared slab geometry, where equilibrium quantities (n,v,B) vary in the x-direction and examine both the linear stability of eigenmodes, as well as their nonlinear saturation. The basic nonlinear process consists of coupling the linearly unstable mode with linearly damped radial harmonics^2. Consequences for the radial transport of momentum in magnetically confined plasmas will be discussed. Supported in part by the U.S. Department of Energy. ^1 S. Migliuolo, W. Daughton, B. Coppi, 1996 International Sherwood Fusion Theory Conference (Philadelphia, PA). ^2 A. Ponomarev and A. K. Sen, 1997 International Sherwood Fusion Theory Conference (Madison, WI).
Finn, J.M.; Lau, Y. )
1991-09-01
Results pertaining to two-dimensional ({partial derivative}/{partial derivative}{ital z}=0) magnetohydrodynamic equilibria in the presence of an {ital X}-type neutral line are presented. Naive analyses indicate that there may be tangential discontinuities in {bold B}, specifically discontinuities in {ital B}{sub {ital z}} across the separatrix connected to the {ital X} line. However, such analyses indicate an infinite {ital z} component of footpoint displacement (or safety factor {ital q} in the toroidal case) at the separatrix. The solutions presented here allow the specification of footpoint displacement (or safety factor {ital q}) that is finite as the separatrix is approached. These solutions are scale-invariant, or similarity, solutions. They are appropriate near the {ital X} line on length scales intermediate between the boundary layer width because of resistivity (or other nonideal effects) and the macroscopic length scale. Force balance across the separatrix implies identical radial dependence in all four quadrants and continuity of {ital B}{sup 2}{sub {ital z}} across the separatrix. The latter shows that there are two classes of solutions: those with {ital B}{sub {ital z}} continuous across the separatrix and those with {vert bar}{ital B}{sub {ital z}}{vert bar} continuous but with a sign change in {ital B}{sub {ital z}}. The former class has fractional power-law singularities at the separatrix. The latter class has, in addition, a sheet current along the separatrix in the {ital x}-{ital y} plane associated with the jump in {ital B}{sub {ital z}}. Detailed properties of these solutions are explored. In particular, sheetlike one-dimensional solutions are found to be limiting cases of the general solutions. Except for one special case, these sheet solutions cannot have finite footpoint displacement if they are force free, but can in the presence of pressure gradient.
Stick-slip instabilities in sheared granular flow: The role of friction and acoustic vibrations
NASA Astrophysics Data System (ADS)
Lieou, Charles K. C.; Elbanna, Ahmed E.; Langer, James S.; Carlson, Jean M.
We propose a theory of shear flow in dense granular materials. A key ingredient of the theory is an effective temperature that determines how the material responds to external driving forces such as shear stresses and vibrations. We show that, within our model, friction between grains produces stick-slip behavior at intermediate shear rates, even if the material is rate strengthening at larger rates. In addition, externally generated acoustic vibrations alter the stick-slip amplitude, or suppress stick-slip altogether, depending on the pressure and shear rate. We construct a phase diagram that indicates the parameter regimes for which stick-slip occurs in the presence and absence of acoustic vibrations of a fixed amplitude and frequency. These results connect the microscopic physics to macroscopic dynamics and thus produce useful information about a variety of granular phenomena, including rupture and slip along earthquake faults, the remote triggering of instabilities, and the control of friction in material processing.
The radiation of sound by the instability waves of a compressible plane turbulent shear layer
NASA Technical Reports Server (NTRS)
Tam, C. K. W.; Morris, P. J.
1980-01-01
The problem of acoustic radiation generated by instability waves of a compressible plane turbulent shear layer is solved. The solution provided is valid up to the acoustic far-field region. It represents a significant improvement over the solution obtained by classical hydrodynamic-stability theory which is essentially a local solution with the acoustic radiation suppressed. The basic instability-wave solution which is valid in the shear layer and the near-field region is constructed in terms of an asymptotic expansion using the method of multiple scales. This solution accounts for the effects of the slightly divergent mean flow. It is shown that the multiple-scales asymptotic expansion is not uniformly valid far from the shear layer. Continuation of this solution into the entire upper half-plane is described. The extended solution enables the near- and far-field pressure fluctuations associated with the instability wave to be determined. Numerical results show that the directivity pattern of acoustic radiation into the stationary medium peaks at 20 degrees to the axis of the shear layer in the downstream direction for supersonic flows. This agrees qualitatively with the observed noise-directivity patterns of supersonic jets.
Dynamical instability of shear-free collapsing star in extended teleparallel gravity
NASA Astrophysics Data System (ADS)
Jawad, Abdul; Rani, Shamaila
2015-11-01
We study the spherically symmetric collapsing star in terms of dynamical instability. We take the framework of extended teleparallel gravity with a non-diagonal tetrad, a power-law form of the model presenting torsion and a matter distribution as a non-dissipative anisotropic fluid. The vanishing shear scalar condition is adopted to gain insight in a collapsing star. We apply a first order linear perturbation scheme to the metric, the matter, and f( T) functions. The dynamical equations are formulated under this perturbation scheme to develop collapsing equation for finding dynamical instability limits in two regimes, such as the Newtonian and the post-Newtonian regime. We obtain a constraint-free solution of a perturbed time dependent part with the help of a vanishing shear scalar. The adiabatic index exhibits the instability ranges through the second dynamical equation which depend on physical quantities such as the density, the pressure components, the perturbed parts of the symmetry of the star, etc. We also develop some constraints on the positivity of these quantities and obtain instability ranges to satisfy the dynamical instability condition.
Wall slip, shear banding, and instability in the flow of a triblock copolymer micellar solution
NASA Astrophysics Data System (ADS)
Manneville, Sébastien; Colin, Annie; Waton, Gilles; Schosseler, François
2007-06-01
The shear flow of a triblock copolymer micellar solution (PEO-PPO-PEO Pluronic P84 in brine) is investigated using simultaneous rheological and velocity profile measurements in the concentric cylinder geometry. We focus on two different temperatures below and above the transition temperature Tc which was previously associated with the apparition of a stress plateau in the flow curve. (i) At T=37.0°C
Flow Instability of Soft Gels from Pluronic F108 Aqueous Solution Under Steady Shear
NASA Astrophysics Data System (ADS)
Park, Hanjin; Jung, Gyoo Yeol; Ryu, Chang Yeol
2012-02-01
Nonionic surfactants of Pluronic tri-block copolymers have received special interest during the past decades because of the temperature dependent self-assembly characteristics that would lead to the formation of hydrogels upon heating. Here, we investigate the gelation behavior of Pluronic F108, (PEO)132-(PPO)50-(PEO)132, aqueous solution with an aim to elucidate how the shear affects the thermo-reversible transitions between micellar liquids and hydrogels. Specifically, we have studied the rheological characteristics of soft gels as an intermediate state between liquid to hard gels. From steady shear experiments, we found that there exists a shear rate window, where the flow instability of soft gels is observed. On the contrary, non-Newtonian behaviors following power-law are still observed at the shear rates above and below the shear rate window showing the flow instability. Small angle x-ray scattering and dynamic light scattering experiments had been performed to reveal how the temperature dependent rheological behavior correlates with the structural changes in the micellar aqueous solutions of F108.
Ion acceleration and coherent structures generated by lower hybrid shear-driven instabilities
NASA Technical Reports Server (NTRS)
Romero, H.; Ganguli, G.; Lee, Y. C.
1992-01-01
It is shown that if k = omega(S)/omega(LH) greater than 1 (omega(S) and omega(LH) are the shear and lower hybrid frequencies), a sheared electron cross-field flow excites the electron-ion-hybrid mode, causing significant perpendicular ion acceleration. The electric potential develops coherent structures (vortexlike) longer than the electron Larmor radius, rho(e). For k less than 1, a smooth transition occurs where the wavelength becomes of the order of rho(e), the lower hybrid drift instability dominates, and the formation of vortexlike structures is no longer observed. The results are relevant to laboratory, laser-produced, and space plasmas.
Sundar, Sita; Das, Amita; Kaw, Predhiman
2012-05-15
In the interaction of intense lasers with matter/plasma, energetic electrons having relativistic energies get created. These energetic electrons can often have sheared flow profiles as they propagate through the plasma medium. In an earlier study [Phys. Plasmas 17, 022101 (2010)], it was shown that a relativistic sheared electron flow modifies the growth rate and threshold condition of the conventional Kelvin-Helmholtz instability. A perturbative analytic treatment for the case of weakly relativistic regime has been provided here. It provides good agreement with the numerical results obtained earlier.
Vortex Dynamics and Shear-Layer Instability in High-Intensity Cyclotrons.
Cerfon, Antoine J
2016-04-29
We show that the space-charge dynamics of high-intensity beams in the plane perpendicular to the magnetic field in cyclotrons is described by the two-dimensional Euler equations for an incompressible fluid. This analogy with fluid dynamics gives a unified and intuitive framework to explain the beam spiraling and beam breakup behavior observed in experiments and in simulations. Specifically, we demonstrate that beam breakup is the result of a classical instability occurring in fluids subject to a sheared flow. We give scaling laws for the instability and predict the nonlinear evolution of beams subject to it. Our work suggests that cyclotrons may be uniquely suited for the experimental study of shear layers and vortex distributions that are not achievable in Penning-Malmberg traps. PMID:27176525
Vortex Dynamics and Shear-Layer Instability in High-Intensity Cyclotrons
NASA Astrophysics Data System (ADS)
Cerfon, Antoine J.
2016-04-01
We show that the space-charge dynamics of high-intensity beams in the plane perpendicular to the magnetic field in cyclotrons is described by the two-dimensional Euler equations for an incompressible fluid. This analogy with fluid dynamics gives a unified and intuitive framework to explain the beam spiraling and beam breakup behavior observed in experiments and in simulations. Specifically, we demonstrate that beam breakup is the result of a classical instability occurring in fluids subject to a sheared flow. We give scaling laws for the instability and predict the nonlinear evolution of beams subject to it. Our work suggests that cyclotrons may be uniquely suited for the experimental study of shear layers and vortex distributions that are not achievable in Penning-Malmberg traps.
Shear flow instability in a partially-ionized plasma sheath around a fast-moving vehicle
Sotnikov, V. I.; Mudaliar, S.; Genoni, T. C.; Rose, D. V.; Oliver, B. V.; Mehlhorn, T. A.
2011-06-15
The stability of ion acoustic waves in a sheared-flow, partially-ionized compressible plasma sheath around a fast-moving vehicle in the upper atmosphere, is described and evaluated for different flow profiles. In a compressible plasma with shear flow, instability occurs for any velocity profile, not just for profiles with an inflection point. A second-order differential equation for the electrostatic potential of excited ion acoustic waves in the presence of electron and ion collisions with neutrals is derived and solved numerically using a shooting method with boundary conditions appropriate for a finite thickness sheath in contact with the vehicle. We consider three different velocity flow profiles and find that in all cases that neutral collisions can completely suppress the instability.
2D instabilities of surface gravity waves on a linear shear current
NASA Astrophysics Data System (ADS)
Francius, Marc; Kharif, Christian
2016-04-01
Periodic 2D surface water waves propagating steadily on a rotational current have been studied by many authors (see [1] and references therein). Although the recent important theoretical developments have confirmed that periodic waves can exist over flows with arbitrary vorticity, their stability and their nonlinear evolution have not been much studied extensively so far. In fact, even in the rather simple case of uniform vorticity (linear shear), few papers have been published on the effect of a vertical shear current on the side-band instability of a uniform wave train over finite depth. In most of these studies [2-5], asymptotic expansions and multiple scales method have been used to obtain envelope evolution equations, which allow eventually to formulate a condition of (linear) instability to long modulational perturbations. It is noted here that this instability is often referred in the literature as the Benjamin-Feir or modulational instability. In the present study, we consider the linear stability of finite amplitude two-dimensional, periodic water waves propagating steadily on the free surface of a fluid with constant vorticity and finite depth. First, the steadily propagating surface waves are computed with steepness up to very close to the highest, using a Fourier series expansions and a collocation method, which constitutes a simple extension of Fenton's method [6] to the cases with a linear shear current. Then, the linear stability of these permanent waves to infinitesimal 2D perturbations is developed from the fully nonlinear equations in the framework of normal modes analysis. This linear stability analysis is an extension of [7] to the case of waves in the presence of a linear shear current and permits the determination of the dominant instability as a function of depth and vorticity for a given steepness. The numerical results are used to assess the accuracy of the vor-NLS equation derived in [5] for the characteristics of modulational
Hamlin, Nathaniel D; Newman, William I
2013-04-01
We explore, via analytical and numerical methods, the Kelvin-Helmholtz (KH) instability in relativistic magnetized plasmas, with applications to astrophysical jets. We solve the single-fluid relativistic magnetohydrodynamic (RMHD) equations in conservative form using a scheme which is fourth order in space and time. To recover the primitive RMHD variables, we use a highly accurate, rapidly convergent algorithm which improves upon such schemes as the Newton-Raphson method. Although the exact RMHD equations are marginally stable, numerical discretization renders them unstable. We include numerical viscosity to restore numerical stability. In relativistic flows, diffusion can lead to a mathematical anomaly associated with frame transformations. However, in our KH studies, we remain in the rest frame of the system, and therefore do not encounter this anomaly. We use a two-dimensional slab geometry with periodic boundary conditions in both directions. The initial unperturbed velocity peaks along the central axis and vanishes asymptotically at the transverse boundaries. Remaining unperturbed quantities are uniform, with a flow-aligned unperturbed magnetic field. The early evolution in the nonlinear regime corresponds to the formation of counter-rotating vortices, connected by filaments, which persist in the absence of a magnetic field. A magnetic field inhibits the vortices through a series of stages, namely, field amplification, vortex disruption, turbulent breakdown, and an approach to a flow-aligned equilibrium configuration. Similar stages have been discussed in MHD literature. We examine how and to what extent these stages manifest in RMHD for a set of representative field strengths. To characterize field strength, we define a relativistic extension of the Alfvénic Mach number M(A). We observe close complementarity between flow and magnetic field behavior. Weaker fields exhibit more vortex rotation, magnetic reconnection, jet broadening, and intermediate turbulence
NASA Astrophysics Data System (ADS)
Juniper, Matthew; Qadri, Ubaid
2012-11-01
Four different physical mechanisms can cause or support instability in swirling shear flows (Gallaire and Chomaz 2003, PoF 15(9) 2622-2639). These are: axial shear, inertial waves, centrifugal instabilities, and azimuthal shear. In relatively simple flows, such as a Rankine vortex with plug axial flow, analytical methods can identify the physical mechanisms active in each region of the flow. In more complex flows, such as a vortex breakdown bubble, analytical methods cannot be applied and, in any case, regions of the flow are not easily delineated. When considering the stability of perturbations on top of a base flow, the structural sensitivity quantifies the effect of altering the feedback between the perturbation velocity vector and the perturbation momentum equation. We examine the nine components of this structural sensitivity, firstly for simple flows such as solid body rotation, secondly for complex swirling flows. The first analysis identifies the signature of each physical mechanism, such as the Kelvin-Helmholtz instability and the Coriolis mechanism. The second analysis compares these signatures with those found in different regions of the complex swirling flows. In this way, we identify the physical mechanisms that are active in each region of the more complex flow. Supported by the European Research Council and by Trinity College Cambridge.
Lyra, Wladimir; Mac Low, Mordecai-Mark E-mail: mordecai@amnh.org
2012-09-01
It has been suggested that the transition between magnetorotationally active and dead zones in protoplanetary disks should be prone to the excitation of vortices via Rossby wave instability (RWI). However, the only numerical evidence for this has come from alpha disk models, where the magnetic field evolution is not followed, and the effect of turbulence is parameterized by Laplacian viscosity. We aim to establish the phenomenology of the flow in the transition in three-dimensional resistive-magnetohydrodynamical models. We model the transition by a sharp jump in resistivity, as expected in the inner dead zone boundary, using the PENCIL CODE to simulate the flow. We find that vortices are readily excited in the dead side of the transition. We measure the mass accretion rate finding similar levels of Reynolds stress at the dead and active zones, at the {alpha} Almost-Equal-To 10{sup -2} level. The vortex sits in a pressure maximum and does not migrate, surviving until the end of the simulation. A pressure maximum in the active zone also triggers the RWI. The magnetized vortex that results should be disrupted by parasitical magneto-elliptic instabilities, yet it subsists in high resolution. This suggests that either the parasitic modes are still numerically damped or that the RWI supplies vorticity faster than they can destroy it. We conclude that the resistive transition between the active and dead zones in the inner regions of protoplanetary disks, if sharp enough, can indeed excite vortices via RWI. Our results lend credence to previous works that relied on the alpha-disk approximation, and caution against the use of overly reduced azimuthal coverage on modeling this transition.
Local parametric instability near elliptic points in vortex flows under shear deformation.
Koshel, Konstantin V; Ryzhov, Eugene A
2016-08-01
The dynamics of two point vortices embedded in an oscillatory external flow consisted of shear and rotational components is addressed. The region associated with steady-state elliptic points of the vortex motion is established to experience local parametric instability. The instability forces the point vortices with initial positions corresponding to the steady-state elliptic points to move in spiral-like divergent trajectories. This divergent motion continues until the nonlinear effects suppress their motion near the region associated with the steady-state separatrices. The local parametric instability is then demonstrated not to contribute considerably to enhancing the size of the chaotic motion regions. Instead, the size of the chaotic motion region mostly depends on overlaps of the nonlinear resonances emerging in the perturbed system. PMID:27586607
Excitation of instability waves in a two-dimensional shear layer by sound
NASA Technical Reports Server (NTRS)
Tam, C. K. W.
1978-01-01
The excitation of instability waves in a plane compressible shear layer by sound waves is studied. The problem is formulated mathematically as an inhomogeneous boundary-value problem. A general solution for abitrary incident sound wave is found by first constructing the Green's function of the problem. Numerical values of the coupling constants between incident sound waves and excited instability waves for a range of flow Mach number are calculated. The effect of the angle of incidence in the case of a beam of acoustic waves is analyzed. It is found that for moderate subsonic Mach numbers a narrow beam aiming at an angle between 50 to 80 deg to the flow direction is most effective in exciting instability waves.
Cowee, Misa M; Winske, Dan; Gary, S Peter
2009-01-01
Two-dimensional hybrid (kinetic ions, massless fluid electrons) simulations of the Kelvin Helmholtz Instability (KHI) for a magnetopause configuration with a magnetic shear across the boundary are carried out to examine how the transport of magnetosheath plasma into the magnetosphere is affected by the shear field. Low magnetic shear conditions where the magnetosheath magnetic field is within 30{sup o} of northward is included in the simulations because KHI is thought to be important for plasma transport only for northward or near-northward interplanetary magnetic field orientations. The simulations show that coherent vortices can grow for these near-northward angles, and that they are sometimes more coherent than for pure northward conditions because the turbulence which breaks-down these vortices is reduced when there are magnetic tension forces. With increasing magnetic shear angle, the growth rate is reduced, and the vortices do not grow to as large of size which reduces the plasma transport. By tracking the individual particle motions diffusion coefficients can be obtained for the system, where the diffusion is not classical in nature but instead has a time dependence resulting from both the increasingly large-scale vortex motion and the small-scale turbulence generated in the break-down of the instabilities. Results indicate that diffusion on the order of 10{sup 9} m{sup 2}/s could possibly be generated by KHI on the flanks of the magnetosphere.
NASA Astrophysics Data System (ADS)
Wareing, C. J.; Pittard, J. M.; Falle, S. A. E. G.; Van Loo, S.
2016-06-01
We have used the adaptive mesh refinement hydrodynamic code, MG, to perform idealized 3D magnetohydrodynamical simulations of the formation of clumpy and filamentary structure in a thermally unstable medium without turbulence. A stationary thermally unstable spherical diffuse atomic cloud with uniform density in pressure equilibrium with low density surroundings was seeded with random density variations and allowed to evolve. A range of magnetic field strengths threading the cloud have been explored, from β = 0.1 to 1.0 to the zero magnetic field case (β = ∞), where β is the ratio of thermal pressure to magnetic pressure. Once the density inhomogeneities had developed to the point where gravity started to become important, self-gravity was introduced to the simulation. With no magnetic field, clouds and clumps form within the cloud with aspect ratios of around unity, whereas in the presence of a relatively strong field (β = 0.1) these become filaments, then evolve into interconnected corrugated sheets that are predominantly perpendicular to the magnetic field. With magnetic and thermal pressure equality (β = 1.0), filaments, clouds and clumps are formed. At any particular instant, the projection of the 3D structure on to a plane parallel to the magnetic field, i.e. a line of sight perpendicular to the magnetic field, resembles the appearance of filamentary molecular clouds. The filament densities, widths, velocity dispersions and temperatures resemble those observed in molecular clouds. In contrast, in the strong field case β = 0.1, projection of the 3D structure along a line of sight parallel to the magnetic field reveals a remarkably uniform structure.
Kelvin-Helmholtz instability of magnetohydrodynamic waves propagating on solar surges
NASA Astrophysics Data System (ADS)
Zhelyazkov, I.; Chandra, R.; Srivastava, A. K.; Mishonov, T.
2015-04-01
In the present paper, we study the evolutionary conditions for Kelvin-Helmholtz (KH) instability in a high-temperature solar surge observed in NOAA AR 11271 using the Solar Dynamics Observatory data on 2011 August 25. The jet with speed of ≈100 km s-1, width of 7 Mm, and electron number density of 4.17×109 cm-3 is assumed to be confined in an untwisted/twisted magnetic flux tube with magnetic field of 10 G. The temperature of the plasma flow is 2×106 K while that of its environment, according to the observational data, is of the order of 106 K. The electron number density of surrounding magnetized plasma is evaluated to be equal to 1.15×109 cm-3. Under these conditions, the Alfvén speed inside the flux tube is 337.6 km s-1, the sound speed is around 166 km s-1, while these characteristic speeds of the environment are ≅719 km s-1 and ≅117 km s-1, respectively. We study the propagation of normal MHD modes in the flux tube considering the two cases, notably of untwisted magnetic flux tube and the twisted one. The numerical solution to the dispersion relation shows that the kink ( m=1) wave traveling in an untwisted flux tube becomes unstable if the jet speed exceeds 1060 km s-1—a speed which is inaccessible for solar surges. A weak twist (the ratio of azimuthal to longitudinal magnetic field component) of the internal magnetic field in the range of 0.025-0.2 does not change substantially the critical flow velocity. Thus, one implies that, in general, the kink mode is stable against the KH instability. It turns out, however, that the m=-2 and m=-3 MHD modes can become unstable when the twist parameter has values between 0.2 and 0.4. Therefore, the corresponding critical jet speed for instability onset lies in the range of 93.5-99.3 km s-1. The instability wave growth rate, depending on the value of the wavelength, is of the order of several dozen inverse milliseconds. It remains to be seen whether these predictions will be observationally validated in
Study on magnetohydrodynamic Kelvin-Helmholtz instability with mass transfer through porous media
NASA Astrophysics Data System (ADS)
Kumar Awasthi, Mukesh
2013-09-01
We study the linear analysis of Kelvin-Helmholtz instability of the interface between two viscous and magnetic fluids in a fully saturated porous medium using viscous potential flow theory, when the fluids are subjected to a constant tangential magnetic field, and when there is heat and mass transfer across the interface. The Darcy-Brinkman model has been used for the investigation. A dispersion relation has been derived and stability is discussed theoretically as well as numerically. The stability criterion is given in terms of a critical value of relative velocity as well as the critical value of applied magnetic field. It has been observed that both tangential magnetic field and vapor fraction have stabilizing effect on the stability of the system while heat and mass transfer destabilizes the interface. Porosity stabilizes the interface while the porous medium has destabilizing effect.
Separated shear-layer instability reproduction by a Reynolds stress model of turbulence
NASA Astrophysics Data System (ADS)
Jakirlic, Suad; Maduta, Robert
2013-11-01
A boundary layer separating from a solid wall transforms into a `separated shear layer' exhibiting a broader frequency range. Such a highly-unsteady shear layer separating the mean stream from the flow reversal is dominated by the organized, large-scale coherent structures, influencing to a large extent the overall flow behavior. Unlike in the case of a flat-plate boundary layer separating at a fixed point characterizing a backward-facing step geometry, which can be reasonably well captured by a statistical model of turbulence, the separation process pertinent to continuous curved surfaces as well as some fence- or rib-shaped configurations is beyond the reach of any RANS (Reynolds-Averaged Navier Stokes) model independent of the modeling level. The latter issue motivated the present work, dealing with an appropriate extension of a near-wall Second-Moment Closure (SMC) model towards an instability-sensitive formulation. The production term in the corresponding scale-supplying equation is selectively enhanced through introduction of the ratio of the first to the second derivative of the velocity field, the latter representing the integral part of the von Karman length scale, enabling appropriate capturing of the fluctuating turbulence and accordingly the reproduction of the separated shear-layer instability. The analysis is performed by simulating the flow separated from a fence, an axisymmetric hill and a cylinder configuration.
Numerical simulations of resistive magnetohydrodynamic instabilities in a poloidal divertor tokamak
NASA Astrophysics Data System (ADS)
Uchimoto, E.
1988-03-01
A new 3-D resistive MHD initial value code RPD has been successfully developed from scratch to study the linear and nonlinear evolution of long wavelength resistive MHD instabilities in a square cross-section tokamak with or without a poloidal divertor. The code numerically advances the full set of compressible resistive MHD equations in a toroidal geometry, with an important option of permitting the divertor separatrix and the region outside it to be in the computational domain. A severe temporal step size restriction for numerical stability imposed by the fast compressional waves was removed by developing and implementing a new, efficient semi-implicit scheme extending one first proposed by Harned and Kerner. As a result, the code typically runs faster than that with a mostly explicit scheme by a factor of about the aspect ratio. The equilibrium input for RPD is generated by a new 2-D code EQPD that is based on the Chodura-Schluter method. The RPD code, as well as the new semi-implicit scheme, has passed very extensive numerical tests in both divertor and divertorless geometries. Linear and nonlinear simulations in a divertorless geometry have reproduced the standard, previously known results. In a geometry with a four-node divertor the m = 2, n = 1 (2/1) tearing mode tends to be linearly stabilized as the q = 2 surface approaches the divertor separatrix. However, the m = 1, n = 1 (1/1) resistive kink mode remains relatively unaffected by the nearness of the q = 1 surface to the divertor separatrix. When plasma current is added to the region outside the divertor separatrix, the 2/1 tearing mode is linearly stabilized not by this current, but by the profile modifications induced near the q = 2 surface and the divertor separatrix. A similar stabilization effect is seen for the 1/1 resistive kink mode, but to a lesser extent.
Three-dimensional flow instability near ion selective membrane under shear flow
NASA Astrophysics Data System (ADS)
Kwon, Hyukjin J.; Pham, Sang Van; Kim, Bumjoo; Lim, Geunbae; White, Jacob; Han, Jongyoon
2015-11-01
Ion transport through ion selective membranes is critically determined by concentration polarization in bulk solutions near the membrane, which is a complicated multiphysics phenomena. For the first time, we report a full experimental and numerical characterization of three-dimensional electrokinetic instability near ion selective membrane under a DC bias and shear flow. A new pattern of instability vortex is found, which was shown to be critically affected by the confinement geometry of the system. It is also found that the onset of over-limiting current and over-limiting resistance can be controlled by geometry of the system, which has significant implications on the optimization of electrodialysis and other electrochemical systems. This work is supported by ARPA-E grant (DE-AR0000294), and also by Kuwait-MIT Center for Natural Resources and the Environment (CNRE), which was funded by Kuwait Foundation for the Advancement of Sciences (KFAS). V. S. Pham was partially supported by SMAR.
Kinetic shear Alfvén instability in the presence of impurity ions in tokamak plasmas
Lu, Gaimin; Shen, Y.; Xie, T.; He, Zhixiong; He, Hongda; Qi, Longyu; Cui, Shaoyan
2013-10-15
The effects of impurity ions on the kinetic shear Alfvén (KSA) instability in tokamak plasmas are investigated by numerically solving the integral equations for the KSA eigenmode in the toroidal geometry. The kinetic effects of hydrogen and impurity ions, including transit motion, finite ion Larmor radius, and finite-orbit-width, are taken into account. Toroidicity induced linear mode coupling is included through the ballooning-mode representation. Here, the effects of carbon, oxygen, and tungsten ions on the KSA instability in toroidal plasmas are investigated. It is found that, depending on the concentration and density profile of the impurity ions, the latter can be either stabilizing or destabilizing for the KSA modes. The results here confirm the importance of impurity ions in tokamak experiments and should be useful for analyzing experimental data as well as for understanding anomalous transport and control of tokamak plasmas.
Ion kinetic instabilities and turbulence of a parallel shearing flow of a plasma with hot ions
NASA Astrophysics Data System (ADS)
Mykhaylenko, Volodymyr St.; Mykhaylenko, Volodymyr; Lee, Hae June
2015-11-01
The results of the analytical and numerical investigations of the shear flow driven ion kinetic instabilities, excited due to the inverse ion Landau damping in the parallel shearing flow of plasmas with comparable ion and electron temperatures, that is the case relevant to a tokamak and space plasma, are presented. The levels of turbulence and the turbulent heating rates of ions and ion turbulent viscosity, resulted from the development of the electrostatic ion-temperature gradient and electromagnetic drift-Alfven turbulence, are determined and their consequences are discussed. This work was funded by National R&D Program through the National Research Foundation of Korea.Grants NRF-2014M1A7A1A03029878, NRF-2013R1A1A2005758.
NASA Technical Reports Server (NTRS)
Van Hoven, G.; Mok, Y.
1984-01-01
The condensation-mode growth rate of the thermal instability in an empirically motivated sheared field is shown to depend upon the existence of perpendicular thermal conduction. This typically very small effect (perpendicular conductivity/parallel conductivity less than about 10 to the -10th for the solar corona) increases the spatial-derivative order of the compressible temperature-perturbation equation, and thereby eliminates the singularities which appear when perpendicular conductivity = 0. The resulting growth rate is less than 1.5 times the controlling constant-density radiation rate, and has a clear maximum at a cross-field length of order 100 times and a width of about 0.1 the magnetic shear scale for solar conditions. The profiles of the observable temperature and density perturbations are independent of the thermal conductivity, and thus agree with those found previously. An analytic solution to the short-wavelength incompressible case is also given.
Experimental and numerical study of plastic shear instability under high-speed loading conditions
Sokovikov, Mikhail E-mail: naimark@icmm.ru; Chudinov, Vasiliy E-mail: naimark@icmm.ru; Bilalov, Dmitry E-mail: naimark@icmm.ru; Oborin, Vladimir E-mail: naimark@icmm.ru; Uvarov, Sergey E-mail: naimark@icmm.ru; Plekhov, Oleg E-mail: naimark@icmm.ru; Terekhina, Alena E-mail: naimark@icmm.ru; Naimark, Oleg E-mail: naimark@icmm.ru
2014-11-14
The behavior of specimens dynamically loaded during the split Hopkinson (Kolsky) bar tests in a regime close to simple shear conditions was studied. The lateral surface of the specimens was investigated in a real-time mode with the aid of a high-speed infra-red camera CEDIP Silver 450M. The temperature field distribution obtained at different time made it possible to trace the evolution of plastic strain localization. The process of target perforation involving plug formation and ejection was examined using a high-speed infra-red camera and a VISAR velocity measurement system. The microstructure of tested specimens was analyzed using an optical interferometer-profilometer and a scanning electron microscope. The development of plastic shear instability regions has been simulated numerically.
Sheared Flow Driven Drift Instability and Vortices in Dusty Plasmas with Opposite Polarity
NASA Astrophysics Data System (ADS)
Mushtaq, A.; Shah, AttaUllah; Ikram, M.; Clark, R. E. H.
2016-02-01
Low-frequency electrostatic drift waves are studied in an inhomogeneous dust magnetoplasma containing dust with components of opposite polarity. The drift waves are driven by the magnetic-field-aligned (parallel) sheared flows in the presence of electrons and ions. Due to sheared flow in the linear regime, the electrostatic dust drift waves become unstable. The conditions of mode instability, with the effects of dust streaming and opposite polarity, are studied. These are excited modes which gain large amplitudes and exhibit interactions among themselves. The interaction is governed by the Hasegawa-Mima (HM) nonlinear equation with vector nonlinearity. The stationary solutions of the HM equation in the form of a vortex chain and a dipolar vortex, including effects of dust polarity and electron (ion) temperatures, are studied. The relevance of the present work to space and laboratory four component dusty plasmas is noted.
Inflectional instabilities in the wall region of bounded turbulent shear flows
NASA Technical Reports Server (NTRS)
Swearingen, Jerry D.; Blackwelder, Ron F.; Spalart, Philippe R.
1987-01-01
The primary thrust of this research was to identify one or more mechanisms responsible for strong turbulence production events in the wall region of bounded turbulent shear flows. Based upon previous work in a transitional boundary layer, it seemed highly probable that the production events were preceded by an inflectional velocity profile which formed on the interface between the low-speed streak and the surrounding fluid. In bounded transitional flows, this unstable profile developed velocity fluctuations in the streamwise direction and in the direction perpendicular to the sheared surface. The rapid growth of these instabilities leads to a breakdown and production of turbulence. Since bounded turbulent flows have many of the same characteristics, they may also experience a similar type of breakdown and turbulence production mechanism.
NASA Astrophysics Data System (ADS)
Mixa, T.; Fritts, D. C.; Laughman, B.; Wang, L.; Kantha, L. H.
2015-12-01
Multiple observations provide compelling evidence that gravity wave dissipation events often occur in multi-scale environments having highly-structured wind and stability profiles extending from the stable boundary layer into the mesosphere and lower thermosphere. Such events tend to be highly localized and thus yield local energy and momentum deposition and efficient secondary gravity wave generation expected to have strong influences at higher altitudes [e.g., Fritts et al., 2013; Baumgarten and Fritts, 2014]. Lidars, radars, and airglow imagers typically cannot achieve the spatial resolution needed to fully quantify these small-scale instability dynamics. Hence, we employ high-resolution modeling to explore these dynamics in representative environments. Specifically, we describe numerical studies of gravity wave packets impinging on a sheet of high stratification and shear and the resulting instabilities and impacts on the gravity wave amplitude and momentum flux for various flow and gravity wave parameters. References: Baumgarten, Gerd, and David C. Fritts (2014). Quantifying Kelvin-Helmholtz instability dynamics observed in noctilucent clouds: 1. Methods and observations. Journal of Geophysical Research: Atmospheres, 119.15, 9324-9337. Fritts, D. C., Wang, L., & Werne, J. A. (2013). Gravity wave-fine structure interactions. Part I: Influences of fine structure form and orientation on flow evolution and instability. Journal of the Atmospheric Sciences, 70(12), 3710-3734.
Vortex formation in protoplanetary discs induced by the vertical shear instability
NASA Astrophysics Data System (ADS)
Richard, Samuel; Nelson, Richard P.; Umurhan, Orkan M.
2016-03-01
We present the results of 2D and 3D hydrodynamic simulations of idealized protoplanetary discs that examine the formation and evolution of vortices by the vertical shear instability (VSI). In agreement with recent work, we find that discs with radially decreasing temperature profiles and short thermal relaxation time-scales, are subject to the axisymmetric VSI. In three dimensions, the resulting velocity perturbations give rise to quasi-axisymmetric potential vorticity perturbations that break up into discrete vortices, in a manner that is reminiscent of the Rossby wave instability. Discs with very short thermal evolution time-scales (i.e. τ ≤ 0.1 local orbit periods) develop strong vorticity perturbations that roll up into vortices that have small aspect ratios (χ ≤ 2) and short lifetimes (˜ a few orbits). Longer thermal time-scales give rise to vortices with larger aspect ratios (6 ≤ χ ≤ 10), and lifetimes that depend on the entropy gradient. A steeply decreasing entropy profile leads to vortex lifetimes that exceed the simulation run times of hundreds of orbital periods. Vortex lifetimes in discs with positive or weakly decreasing entropy profiles are much shorter, being 10s of orbits at most, suggesting that the subcritical baroclinic instability plays an important role in sustaining vortices against destruction through the elliptical instability. Applied to the outer regions of protoplanetary discs, where the VSI is most likely to occur, our results suggest that vortices formed by the VSI are likely to be short-lived structures.
Experimental verification of the shear-modified ion-acoustic instability
NASA Astrophysics Data System (ADS)
Reynolds, E. W.; Teodorescu, C.; Koepke, M. E.
2002-11-01
The shear-modified ion-acoustic instability has been experimentally verified in double-ended Q-machine barium plasma containing shear in the magnetic-field-aligned (parallel) ion drift. The ion distribution function f(X,Vz) was measured directly and non-perturbatively with laser induced fluorescence. Measurements of the wave frequency (in the lab frame) and the wave-vector components show that, in the presence of shear, the wave phase velocity (in the ion frame) is greater than the ion-acoustic speed and out of the strong ion landau-damping regime. Measurements of the parallel electron drift yield values lower than the excitation threshold predicted by homogeneous theory but large enough for inverse electron landau damping to provide the free energy for the wave. We emphasize the ramifications on the mode properties of positive and negative values of shear. A quantitative comparison between experimental results and theoretical predictions is presented. Work supported by NASA and NSF. Useful discussions with V. Gavrishchaka and E. Scime are acknowledged.
Green, Harry W.
2007-01-01
Deep earthquakes have been a paradox since their discovery in the 1920s. The combined increase of pressure and temperature with depth precludes brittle failure or frictional sliding beyond a few tens of kilometers, yet earthquakes occur continually in subduction zones to ≈700 km. The expected healing effects of pressure and temperature and growing amounts of seismic and experimental data suggest that earthquakes at depth probably represent self-organized failure analogous to, but different from, brittle failure. The only high-pressure shearing instabilities identified by experiment require generation in situ of a small fraction of very weak material differing significantly in density from the parent material. This “fluid” spontaneously forms mode I microcracks or microanticracks that self-organize via the elastic strain fields at their tips, leading to shear failure. Growing evidence suggests that the great majority of subduction zone earthquakes shallower than 400 km are initiated by breakdown of hydrous phases and that deeper ones probably initiate as a shearing instability associated with breakdown of metastable olivine to its higher-pressure polymorphs. In either case, fault propagation could be enhanced by shear heating, just as is sometimes the case with frictional sliding in the crust. Extensive seismological interrogation of the region of the Tonga subduction zone in the southwest Pacific Ocean provides evidence suggesting significant metastable olivine, with implication for its presence in other regions of deep seismicity. If metastable olivine is confirmed, either current thermal models of subducting slabs are too warm or published kinetics of olivine breakdown reactions are too fast. PMID:17468397
Jayakumar, R.J.; Austin, M.E.; Brennan, D.P.; Chu, M.S.; Luce, T.C.; Strait, E.J.; Turnbull, A.D.
2002-07-01
In DIII-D plasmas with L-mode edge and negative central shear (q{sub axis}-q{sub min} {approx}0.3 to 0.5), an interchange-like instability has been observed [1]. The instability and a subsequent tearing mode cause reduction of the core electron temperature and plasma rotation, and therefore the instability affects discharge evolution and the desired high performance is not achieved. Stability analyses indicate robust ideal stability, while the Resistive Interchange Mode criterion is marginal and the instability appears to be localized initially. Based on this, we believe that the mode is, most likely, a Resistive Interchange Mode. The amplitude of the instability is correlated with the location of the q{sub min} surface and inversely with the fast-ion pressure. There is indication that the interchange-like instability may be ''seeding'' the tearing mode that sometimes follows the interchange-like instability.
Linear analysis of the vertical shear instability: outstanding issues and improved solutions
NASA Astrophysics Data System (ADS)
Umurhan, O. M.; Nelson, R. P.; Gressel, O.
2016-02-01
Context. The vertical shear instability is one of several known mechanisms that are potentially active in the so-called dead zones of protoplanetary accretion disks. A recent analysis of the instability mechanism indicates that a subset of unstable modes shows unbounded growth - both as resolution is increased and when the nominal lid of the atmosphere is extended. This trend suggests that, possibly, the model system is ill-posed. Aims: This research note both examines the energy content of these modes and questions the legitimacy of assuming separable solutions for a problem whose linear operator is fundamentally inseparable. Methods: The reduced equations governing the instability are revisited and the generated solutions are examined using both the previously assumed separable forms and an improved non-separable solution form that is introduced in this paper. Results: Reconsidering the solutions of the reduced equations by using the separable form shows that, while the low-order body modes have converged eigenvalues and eigenfunctions (for both variations in the model atmosphere's vertical boundaries and radial numerical resolution). It is also confirmed that the corresponding high-order body modes and the surface modes indeed show unbounded growth rates. The energy contained in both the higher order body modes and surface modes diminishes precipitously due to the disk's Gaussian density profile. Most of the energy of the instability is contained in the low-order modes. An inseparable solution form is introduced to filter out the inconsequential surface modes, leaving only body modes (both low- and high-order ones). The analysis predicts a fastest growing mode with a specific radial length scale. The growth rates associated with the fundamental corrugation and breathing modes match the growth and length scales observed in previous nonlinear studies of the instability. Conclusions: Linear stability analysis of the vertical shear instability should be done
Shear-driven instabilities and shocks in the atmospheres of hot Jupiters
NASA Astrophysics Data System (ADS)
Fromang, Sébastien; Leconte, Jeremy; Heng, Kevin
2016-07-01
Context. General circulation models of the atmosphere of hot Jupiters have shown the existence of a supersonic eastward equatorial jet. These results have been obtained using numerical schemes that filter out vertically propagating sound waves and assume vertical hydrostatic equilibrium, or were acquired with fully compressive codes that use large dissipative coefficients. Aims: We remove these two limitations and investigate the effects of compressibility on the atmospheric dynamics by solving the standard Euler equations. Methods: This was done by means of a series of simulations performed in the framework of the equatorial β-plane approximation using the finite-volume shock-capturing code RAMSES. Results: At low resolution, we recover the classical results described in the literature: we find a strong and steady supersonic equatorial jet of a few km s-1 that displays no signature of shocks. We next show that the jet zonal velocity depends significantly on the grid meridional resolution. When this resolution is fine enough to properly resolve the jet, the latter is subject to a Kelvin-Helmholtz instability. The jet zonal mean velocity displays regular oscillations with a typical timescale of a few days and a significant amplitude of about 15% of the jet velocity. We also find compelling evidence for the development of a vertical shear instability at pressure levels of a few bars. It seems to be responsible for an increased downward kinetic energy flux that significantly affects the temperature of the deep atmosphere and appears to act as a form of drag on the equatorial jet. This instability also creates velocity fluctuations that propagate upward and steepen into weak shocks at pressure levels of a few mbars. Conclusions: We conclude that hot-Jupiter equatorial jets are potentially unstable to both a barotropic Kelvin-Helmholtz instability and a vertical shear instability. Upon confirmation using more realistic models, these two instabilities could result in
The Effects of Contact Conditions on the Onset of Shear Instability in Cold-Spray
NASA Astrophysics Data System (ADS)
Meng, Fanchao; Aydin, Huseyin; Yue, Stephen; Song, Jun
2015-04-01
Using ABAQUS/Explicit, the effects of contact conditions between the particle and substrate, including tangential friction, normal constraint, and contact geometry on the plastic deformation during the cold-spray process are studied. It was found that the onset of shear instability, an event often used to indicate the establishment of bonding, is very sensitive to the choice of contact conditions. This suggests that the onset of shear instability does not serve as an accurate means to identify the plasticity threshold responsible for bonding. On the other hand, it is demonstrated that the evolution of the overall equivalent plastic strain (i.e., ) and the overall von Mises stress, being linearly proportional to each other, are both independent of contact conditions. Furthermore, it is shown that an energy value, defined as the product of the and the von Mises stress integrated over all particle elements, can quantitatively represent the energy dissipated via plastic deformation while being independent of contact conditions. The and associated energy value as defined may provide robust tools to assess the plasticity and the consequent bonding during cold-spray.
Turbulent mixing due to Holmboe wave instability in stratified shear flows at high Reynolds numbers
NASA Astrophysics Data System (ADS)
Salehipour, Hesam; Caulfield, Colm-Cille; Peltier, W. Richard
2015-11-01
We consider numerically the transition to turbulence and associated mixing in parallel stratified shear flows with hyperbolic tangent initial velocity and density distributions. When the characteristic length scale of density variation is sufficiently sharper than that of the velocity variation, this flow is primarily susceptible to Holmboe wave instability (HWI) which perturbs the interface to exhibit characteristic cusped interfacial waves. Unlike previous low- Re experimental and numerical studies, in the high- Re regime in which our DNS analyses are performed, the primary HWI triggers a vigorous yet markedly more long-lived turbulent event compared to its better known relative, the Kelvin-Helmholtz instability (KHI). HWI `scours' the primary density interface, leading to substantial irreversible mixing and vertical transport of density displaced above and below the (robust) primary density interface which is comparable in both absolute terms and relative efficiency to the mixing associated with an equivalent KHI. Our results establish categorically that, provided the Reynolds number is high enough, shear layers with sharp density interfaces and associated locally high values of the gradient Richardson number are sites of substantial and efficient irreversible mixing. H.S. is grateful to the David Crighton Fellowship from DAMTP, University of Cambridge.
Mikhailenko, V. V.; Mikhailenko, V. S.; Lee, Hae June; Koepke, M. E.
2014-07-15
The cross-magnetic-field (i.e., perpendicular) profile of ion temperature and the perpendicular profile of the magnetic-field-aligned (parallel) plasma flow are sometimes inhomogeneous for space and laboratory plasma. Instability caused either by a gradient in the ion-temperature profile or by shear in the parallel flow has been discussed extensively in the literature. In this paper, (1) hydrodynamic plasma stability is investigated, (2) real and imaginary frequency are quantified over a range of the shear parameter, the normalized wavenumber, and the ratio of density-gradient and ion-temperature-gradient scale lengths, and (3) the role of inverse Landau damping is illustrated for the case of combined ion-temperature gradient and parallel-flow shear. We find that increasing the ion-temperature gradient reduces the instability threshold for the hydrodynamic parallel-flow shear instability, also known as the parallel Kelvin-Helmholtz instability or the D'Angelo instability. We also find that a kinetic instability arises from the coupled, reinforcing action of both free-energy sources. For the case of comparable electron and ion temperature, we illustrate analytically the transition of the D'Angelo instability to the kinetic instability as (a) the shear parameter, (b) the normalized wavenumber, and (c) the ratio of density-gradient and ion-temperature-gradient scale lengths are varied and we attribute the changes in stability to changes in the amount of inverse ion Landau damping. We show that near a normalized wavenumber k{sub ⊥}ρ{sub i} of order unity (i) the real and imaginary values of frequency become comparable and (ii) the imaginary frequency, i.e., the growth rate, peaks.
NASA Technical Reports Server (NTRS)
Hawley, John F.; Balbus, Steven A.
1992-01-01
The nonlinear evolution of the recently identified accretion disk magnetic shear instability is investigated through a series of numerical simulations. Finite-difference computations of the equations of compressible MHD are carried out on an axisymmetric shearing sheet system with periodic boundary conditions designed to approximate a local region within an accretion disk. Initial field configurations that include some net vertical component evolve into a nonlinear, exponentially growing solution with large poloidal velocities and magnetic fields with energies comparable to the thermal energy density. The stability of a purely azimuthal field configuration is examined, and it is found that nonaxisymmetric instability is present, but with a growth time measured in tens of orbital periods. In general, the most rapid growth occurs for very small radial and azimuthal wavenumbers, leading to coherent magnetic field structure in planes parallel to the disk. It is suggested that this instability is a key ingredient for the generation of magnetic fields in disks.
Free MHD Shear Layers In The Presence Of Rotation And Magnetic Field
Spence, E. J.; Roach, A. H.; Edlund, E. M.; Sloboda, P.; Ji, H.
2012-03-20
We present an experimental and numerical study of hydrodynamic and magnetohydrodynamic free shear layers and their stability. We first examine the experimental measurement of globally unstable hydrodynamic shear layers in the presence of rotation, and their range of instability. These are compared to numerical simulations, which are used to explain the modification of the shear layer and thus the critical Rossby number for stability. Magnetic fields are then applied to these scenarios, and globally unstable magnetohydrodynamic shear layers generated. These too are compared to numerical simulations, showing behavior consistent with the hydrodynamic case and previously reported measurements.
Schnack, D. D.; Cheng, J.; Parker, S. E.; Barnes, D. C.
2013-06-15
We perform linear stability studies of the ion temperature gradient (ITG) instability in unsheared slab geometry using kinetic and extended magnetohydrodynamics (MHD) models, in the regime k{sub ∥}/k{sub ⊥}≪1. The ITG is a parallel (to B) sound wave that may be destabilized by finite ion Larmor radius (FLR) effects in the presence of a gradient in the equilibrium ion temperature. The ITG is stable in both ideal and resistive MHD; for a given temperature scale length L{sub Ti0}, instability requires that either k{sub ⊥}ρ{sub i} or ρ{sub i}/L{sub Ti0} be sufficiently large. Kinetic models capture FLR effects to all orders in either parameter. In the extended MHD model, these effects are captured only to lowest order by means of the Braginskii ion gyro-viscous stress tensor and the ion diamagnetic heat flux. We present the linear electrostatic dispersion relations for the ITG for both kinetic Vlasov and extended MHD (two-fluid) models in the local approximation. In the low frequency fluid regime, these reduce to the same cubic equation for the complex eigenvalue ω=ω{sub r}+iγ. An explicit solution is derived for the growth rate and real frequency in this regime. These are found to depend on a single non-dimensional parameter. We also compute the eigenvalues and the eigenfunctions with the extended MHD code NIMROD, and a hybrid kinetic δf code that assumes six-dimensional Vlasov ions and isothermal fluid electrons, as functions of k{sub ⊥}ρ{sub i} and ρ{sub i}/L{sub Ti0} using a spatially dependent equilibrium. These solutions are compared with each other, and with the predictions of the local kinetic and fluid dispersion relations. Kinetic and fluid calculations agree well at and near the marginal stability point, but diverge as k{sub ⊥}ρ{sub i} or ρ{sub i}/L{sub Ti0} increases. There is good qualitative agreement between the models for the shape of the unstable global eigenfunction for L{sub Ti0}/ρ{sub i}=30 and 20. The results quantify how far
NASA Technical Reports Server (NTRS)
Blackaby, Nicholas D.; Choudhari, Meelan
1993-01-01
We consider the inviscid instability of three-dimensional boundary-layer flows with a small crossflow over locally concave or convex walls, along with the inviscid instability of stratified shear flows. We show how these two problems are closely related through the forms of their governing equations. A proposed definition of a generalized Richardson number for the neutrally stable inviscid vortex motions is given. Implications of the similarity between the two problems are discussed.
Coupling of the Okuda-Dawson model with a shear current-driven wave and the associated instability
NASA Astrophysics Data System (ADS)
Masood, W.; Saleem, H.; Saleem
2013-12-01
It is pointed out that the Okuda-Dawson mode can couple with the newly proposed current-driven wave. It is also shown that the Shukla-Varma mode can couple with these waves if the density inhomogeneity is taken into account in a plasma containing stationary dust particles. A comparison of several low-frequency electrostatic waves and instabilities driven by shear current and shear plasma flow in an electron-ion plasma with and without stationary dust is also presented.
NASA Astrophysics Data System (ADS)
Mikhailenko, V. V.; Mikhailenko, V. S.; Lee, Hae June
2016-06-01
The temporal evolution of the kinetic ion temperature gradient driven instability and of the related anomalous transport of the ion thermal energy of plasma shear flow across the magnetic field is investigated analytically. This instability develops in a steady plasma due to the inverse ion Landau damping and has the growth rate of the order of the frequency when the ion temperature is equal to or above the electron temperature. The investigation is performed employing the non-modal methodology of the shearing modes which are the waves that have a static spatial structure in the frame of the background flow. The solution of the governing linear integral equation for the perturbed potential displays that the instability experiences the non-modal temporal evolution in the shearing flow during which the unstable perturbation becomes very different from a canonical modal form. It transforms into the non-modal structure with vanishing frequency and growth rate with time. The obtained solution of the nonlinear integral equation, which accounts for the random scattering of the angle of the ion gyro-motion due to the interaction of ions with ensemble of shearing waves, reveals similar but accelerated process of the transformations of the perturbations into the zero frequency structures. It was obtained that in the shear flow the anomalous ion thermal conductivity decays with time. It is a strictly non-modal effect, which originates from the temporal evolution of the shearing modes turbulence.
NASA Astrophysics Data System (ADS)
Zhai, Xiang; Bellan, Paul M.
2016-03-01
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 at 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.
Khan, Arshad; Khan, Ilyas; Shafie, Sharidan
2014-06-19
This article studies the radiation and porosity effects on the unsteady magnetohydrodynamic free convection flow of an incompressible viscous fluid past an infinite vertical plate that applies a shear stress f(t) to the fluid. Conjugate phenomenon of heat and mass transfer is considered. General solutions of the dimensionless governing equations along with imposed initial and boundary conditions are determined using Laplace transform technique. The solution of velocity is presented as a sum of mechanical and non mechanical parts. These solutions satisfy all imposed initial and boundary conditions and reduce to some known solutions from the literature as special cases. The results for embedded parameters are shown graphically. Numerical results for skin friction, Nusselt number and Sherwood number are computed and presented in tabular forms.
The study of adiabatic shear band instability in a pearlitic 4340 steel using a dynamic punch test
Zurek, A.K. )
1994-11-01
At low strain rates and moderate levels of strain, slip and twinning are the most common deformation mechanisms in metals and alloys. Both mechanisms are highly correlated with the crystallography of the material. At higher strain rates and levels of strain, deformation instabilities, such as adiabatic shear bands (ASB), may develop. These bands are planar in nature, and their formation is related more to the specimen geometry, deformation process, and mechanical properties of a material than to its local crystallography. The formation of adiabatic shear band instabilities in a pearlitic 4340 steel using a dynamic punch test has been studied. The dynamic punch-impact test produced white-etching adiabatic shear bands. The average strain of 0.5 was sufficient to produce adiabatic shear bands in this steel at an average strain rate of 18,000 s[sup [minus]1]. Nanohardness variations found across the adiabatic shear at an average strain rate of 18,000 s[sup [minus]1]. Nanohardness variations found across the adiabatic shear band are thought to be caused by the fragmentation and spheriodization of the Fe[sub 3]C and the overall deformation and work hardening of the pearlitic microstructure. The cracks formed at the termination of the adiabatic shear band caused the sample to fracture in a ductile mode.
Earthquakes initiation and thermal shear instability in the Hindu Kush intermediate depth nest
NASA Astrophysics Data System (ADS)
Poli, Piero; Prieto, German; Rivera, Efrain; Ruiz, Sergio
2016-02-01
Intermediate depth earthquakes often occur along subducting lithosphere, but despite their ubiquity the physical mechanism responsible for promoting brittle or brittle-like failure is not well constrained. Large concentrations of intermediate depth earthquakes have been found to be related to slab break-off, slab drip, and slab tears. The intermediate depth Hindu Kush nest is one of the most seismically active regions in the world and shows the correlation of a weak region associated with ongoing slab detachment process. Here we study relocated seismicity in the nest to constraint the geometry of the shear zone at the top of the detached slab. The analysis of the rupture process of the Mw 7.5 Afghanistan 2015 earthquake and other several well-recorded events over the past 25 years shows an initially slow, highly dissipative rupture, followed by a dramatic dynamic frictional stress reduction and corresponding large energy radiation. These properties are typical of thermal driven rupture processes. We infer that thermal shear instabilities are a leading mechanism for the generation of intermediated-depth earthquakes especially in presence of weak zone subjected to large strain accumulation, due to ongoing detachment process.
Transition to asymmetry in pipe flow of shear-thinning fluids: a linear instability?
NASA Astrophysics Data System (ADS)
Dennis, David; Wen, Chaofan; Poole, Robert
2015-11-01
Previous studies of shear-thinning fluids in pipe flow discovered that, although the time-averaged velocity profile was axisymmetric when the flow was laminar or fully turbulent, contrary to expectations it was asymmetric in the laminar-turbulent transition regime. We reveal that in fact the asymmetry is not induced by the laminar-turbulent transition process, but is an instability of the laminar state. Furthermore, the transition process is responsible for returning symmetry to the flow (i.e. the opposite to what was previously believed), which explains why the fully turbulent case is axisymmetric. The experiment was performed using an aqueous solution of xanthan gum (0.15%), an essentially inelastic shear-thinning polymer solution. Stereoscopic particle image velocimetry was used to measure the 3C velocity vectors over the entire circular cross-section of the pipe, 220 pipe diameters downstream of the inlet. The deviation from the axisymmetric laminar state is observed to develop in the form of a supercritical bifurcation with square-root dependence on Reynolds number. The asymmetry is non-hysteretic and reversible, not only having a favoured location, but a preferred route between axisymmetry and asymmetry, which it adheres to regardless of the direction of the transition.
Mikhailenko, V. V. Mikhailenko, V. S.; Lee, Hae June
2015-10-15
The developed kinetic theory for the stability of a magnetic-field-aligned (parallel) shear flow with inhomogeneous ion temperature [Mikhailenko et al., Phys. Plasmas 21, 072117 (2014)] predicted that a kinetic instability arises from the coupled reinforcing action of the flow velocity shear and ion temperature gradient in the cases where comparable ion and electron temperatures exist. In the present paper, the nonlinear theory was developed for the instability caused by the combined effects of ion-temperature-gradient and shear-flow (ITG–SF). The level of the electrostatic turbulence is determined for the saturation state of the instability on the basis of the nonlinear dispersion equation, which accounts for a nonlinear scattering of ions by the developed turbulence in a sheared flow. The renormalized quasilinear equation for the ion distribution function, which accounts for the turbulent scattering of ions by ITG–SF driven turbulence, was derived and employed for the estimation of the turbulent ion viscosity, the anomalous ion thermal conductivity, and anomalous ion heating rate at the saturation state of the instability.
Ashwin, J.; Ganesh, R.
2010-10-15
Using a generalized hydrodynamic (GH) model, the growth rate spectra of Kelvin-Helmholtz (KH) instability has been obtained analytically for a step shear profile in strongly coupled Yukawa liquids. The class of shear flows studied is assumed to be incompressible in nature. The growth rate spectra calculated exhibit viscous damping at high mode numbers, destabilization at stronger coupling, and in the limit {tau}{sub m} (viscoelastic relaxation time){yields}0, reduce to the regular Navier-Stokes growth rate spectra. A direct comparison is made with previous molecular dynamics (MD) simulations [Ashwin J. and R. Ganesh, Phys. Rev. Lett. 104, 215003 (2010)] of KH instability. We find that for a given value of Reynolds number R and coupling parameter 1<{Gamma}<100, the GH and MD growth rates are in a qualitative agreement. The inclusion of the effect of shear heating as an effective coupling parameter {Gamma}{sub e} appears to improve the quantitative comparison as well.
Lao, L.L.; Burrell, K.H.; Casper, T.S.
1996-08-01
The confinement and the stability properties of the DIII-D tokamak high performance discharges are evaluated in terms of rotational and magnetic shear with emphasis on the recent experimental results obtained from the negative central magnetic shear (NCS) experiments. In NCS discharges, a core transport barrier is often observed to form inside the NCS region accompanied by a reduction in core fluctuation amplitudes. Increasing negative magnetic shear contributes to the formation of this core transport barrier, but by itself is not sufficient to fully stabilize the toroidal drift mode (trapped- electron-{eta}{sub i}mode) to explain this formation. Comparison of the Doppler shift shear rate to the growth rate of the {eta}{sub i} mode suggests that the large core {bold E x B} flow shear can stabilize this mode and broaden the region of reduced core transport . Ideal and resistive stability analysis indicates the performance of NCS discharges with strongly peaked pressure profiles is limited by the resistive interchange mode to low {Beta}{sub N} {lt} 2.3. This mode is insensitive to the details of the rotational and the magnetic shear profiles. A new class of discharges which has a broad region of weak or slightly negative magnetic shear (WNS) is described. The WNS discharges have broader pressure profiles and higher values than the NCS discharges together with high confinement and high fusion reactivity.
Nonlinear magnetohydrodynamic stability
NASA Technical Reports Server (NTRS)
Bauer, F.; Betancourt, O.; Garabedian, P.
1981-01-01
The computer code developed by Bauer et al. (1978) for the study of the magnetohydrodynamic equilibrium and stability of a plasma in toroidal geometry is extended so that the growth rates of instabilities may be estimated more accurately. The original code, which is based on the variational principle of ideal magnetohydrodynamics, is upgraded by the introduction of a nonlinear formula for the growth rate of an unstable mode which acts as a quantitative measure of instability that is important in estimating numerical errors. The revised code has been applied to the determination of the nonlinear saturation, ballooning modes and beta limits for tokamaks, stellarators and torsatrons.
NASA Astrophysics Data System (ADS)
Choi, M. J.; Park, H. K.; Yun, G. S.; Nam, Y. B.; Choe, G. H.; Lee, W.; Jardin, S.
2016-01-01
The electron cyclotron emission imaging (ECEI) instrument is widely used to study the local electron temperature (Te) fluctuations by measuring the ECE intensity IECE ∝ Te in tokamak plasmas. The ECEI measurement is often processed in a normalized fluctuation quantity against the time averaged value due to complication in absolute calibration. In this paper, the ECEI channels are relatively calibrated using the flat Te assumption of the sawtooth crash or the tearing mode island and a proper extrapolation. The 2-D relatively calibrated electron temperature (Te,rel) images are reconstructed and the displacement amplitude of the magnetohydrodynamic modes can be measured for the accurate quantitative growth analysis.
Choi, M J; Park, H K; Yun, G S; Nam, Y B; Choe, G H; Lee, W; Jardin, S
2016-01-01
The electron cyclotron emission imaging (ECEI) instrument is widely used to study the local electron temperature (Te) fluctuations by measuring the ECE intensity IECE ∝ Te in tokamak plasmas. The ECEI measurement is often processed in a normalized fluctuation quantity against the time averaged value due to complication in absolute calibration. In this paper, the ECEI channels are relatively calibrated using the flat Te assumption of the sawtooth crash or the tearing mode island and a proper extrapolation. The 2-D relatively calibrated electron temperature (Te,rel) images are reconstructed and the displacement amplitude of the magnetohydrodynamic modes can be measured for the accurate quantitative growth analysis. PMID:26827320
NASA Technical Reports Server (NTRS)
Hyun, J. M.
1981-01-01
Quasi-geostrophic disturbance instability characteristics are studied in light of a linearized, two-layer Eady model in which both the static stability and the zonal current shear are uniform but different in each layer. It is shown that the qualitative character of the instability is determined by the sign of the basic-state potential vorticity gradient at the layer interface, and that there is a qualitative similarity between the effects of Richardson number variations due to changes in static stability and those due to changes in shear. The two-layer model is also used to construct an analog of the Williams (1974) continuous model of generalized Eady waves, the basic state in that case having zero potential vorticity gradient in the interior. The model results are in good agreement with the earlier Williams findings.
Sharif, M.; Yousaf, Z. E-mail: zeeshan.math@pu.edu.pk
2014-06-01
This paper investigates stability regions for a non-static restricted class of axially symmetric geometry filled with anisotropic, heat radiating and shearing viscous fluid that collapses non-adiabatically. In this context, dynamical equations as well as collapse equation are constructed through perturbation scheme with f(R) = R+εR{sup 2} model. We then develop dynamical instability regions at Newtonian and post-Newtonian eras. It is concluded that pressure anisotropy and heat dissipation increases the instability regions of the collapsing system while shearing viscosity as well as f(R) dark sourced terms decrease them during collapse. Finally, we calculate our results under constant curvature condition and GR limit, i.e., f(R)→R.
Ortiz, Aurélie U; Boutin, Anne; Fuchs, Alain H; Coudert, François-Xavier
2013-06-01
We provide the first molecular dynamics study of the mechanical instability that is the cause of pressure-induced amorphization of zeolitic imidazolate framework ZIF-8. By measuring the elastic constants of ZIF-8 up to the amorphization pressure, we show that the crystal-to-amorphous transition is triggered by the mechanical instability of ZIF-8 under compression, due to shear mode softening of the material. No similar softening was observed under temperature increase, explaining the absence of temperature-induced amorphization in ZIF-8. We also demonstrate the large impact of the presence of adsorbate in the pores on the mechanical stability and compressibility of the framework, increasing its shear stability. This first molecular dynamics study of ZIF mechanical properties under variations of pressure, temperature, and pore filling opens the way to a more comprehensive understanding of their mechanical stability, structural transitions, and amorphization. PMID:26283122
Experimental study of small-scale instabilities in Rayleigh-Bénard convection driven by a shear flow
NASA Astrophysics Data System (ADS)
Vidal, Valerie; Davaille, Anne; Crambes, Christine
2003-11-01
Small-scale convection appears under a cold thermal boundary layer when the local Rayleigh number exceeds a critical value Ra_δ. We have studied experimentally the interaction of this small-scale instabilities with a shear flow. Experiments are performed in a tank heated from one side and cooled from above. Rayleigh numbers are between 10^4 and 10^8, and Prandtl numbers are high (≥ 1000). Fluids are polymer solutions (constant viscosity), sugar or corn syrups (viscosity depending on temperature) or wax (phase transition). Two scales of motion are observed: a large convection cell (whole tank) and, for sufficiently high Rayleigh numbers, small-scale instabilities that remain trapped in the shear zone, following an helicoidal path with axis parallel to the shear. The intermittency of the associated temperature time series has been analyzed. The temporal periodicity scales as τ ˜ Ra-2/3. The presence of these instabilities under the lithosphere could explain some geophysical observations, such as small-wavelength lineations in the terrestrial gravity field.
Mazur, V. A. Chuiko, D. A.
2013-12-15
The coefficient of reflection of a fast magnetosonic wave incident on the magnetosphere from the solar wind is studied analytically in the framework of a plane-stratified model of the medium with allowance for the transverse inhomogeneity of the magnetosphere and a jump of the plasma parameters at the magnetopause. Three factors decisively affecting the properties of reflection are taken into account: the shear flow of the solar wind plasma relative to the magnetosphere; the presence of a magnetospheric magnetohydrodynamic waveguide caused by the transverse plasma inhomogeneity; and the presence of an Alfvén resonance deep in the magnetosphere, where the oscillation energy dissipates. If the solar wind velocity exceeds the wave phase velocity along the magnetopause, then the wave energy in the solar wind is negative and such a wave experiences overreflection. In the opposite case, the wave energy is positive and the wave is reflected only partially. The wave reflection has a pronounced resonant character: the reflection coefficient has deep narrow minima or high narrow maxima at the eigenfrequencies of the magnetospheric waveguide. For other frequencies, the reflection coefficient only slightly differs from unity. The wave energy influx into the magnetosphere is positive for waves with both positive and negative energies. For waves with a negative energy, this is a consequence of their overreflection, because the flux of negative energy carried away by the reflected wave exceeds the incident flux of negative energy.
NASA Astrophysics Data System (ADS)
Chen, Yu; Wen, Lianxing
2015-08-01
We apply a multiple source inversion method to systematically study the source processes of 25 large deep-focus (depth >400 km) earthquakes with Mw > 7.0 from 1994 to 2012, based on waveform modeling of P, pP, SH and sSH wave data. The earthquakes are classified into three categories based on spatial distributions and focal mechanisms of the inferred sub-events: 1) category one, with non-planar distribution and variable focal mechanisms of sub-events, represented by the 1994 Mw 8.2 Bolivia earthquake and the 2013 Mw 8.3 Okhotsk earthquake; 2) category two, with planar distribution but focal mechanisms inconsistent with the plane, including eighteen earthquakes; and 3) category three, with planar distribution and focal mechanisms consistent with the plane, including six earthquakes. We discuss possible physical mechanisms for earthquakes in each category in the context of plane rupture, transformational faulting and shear thermal instability. We suggest that the inferred source processes of large deep-focus earthquakes can be best interpreted by cascading failure of shear thermal instabilities in pre-existing weak zones, with the perturbation of stress generated by a shear instability triggering another and focal mechanisms of the sub-events controlled by orientations of the pre-existing weak zones. The proposed mechanism can also explain the observed great variability of focal mechanisms, the presence of large values of CLVD (Compensated Linear Vector Dipole) and the super-shear rupture of deep-focus earthquakes in the previous studies. In addition, our studies suggest existence of relationships of seismic moment ∼ (source duration)3 and moment ∼ (source dimension)3 in large deep-focus earthquakes.
NASA Astrophysics Data System (ADS)
García-Muñoz, M.; Fahrbach, H.-U.; Zohm, H.; ASDEX Upgrade Team
2009-05-01
A scintillator based detector for fast-ion losses has been designed and installed on the ASDEX upgrade (AUG) tokamak [A. Herrmann and O. Gruber, Fusion Sci. Technol. 44, 569 (2003)]. The detector resolves in time the energy and pitch angle of fast-ion losses induced by magnetohydrodynamics (MHD) fluctuations. The use of a novel scintillator material with a very short decay time and high quantum efficiency allows to identify the MHD fluctuations responsible for the ion losses through Fourier analysis. A Faraday cup (secondary scintillator plate) has been embedded behind the scintillator plate for an absolute calibration of the detector. The detector is mounted on a manipulator to vary its radial position with respect to the plasma. A thermocouple on the inner side of the graphite protection enables the safety search for the most adequate radial position. To align the scintillator light pattern with the light detectors a system composed by a lens and a vacuum-compatible halogen lamp has been allocated within the detector head. In this paper, the design of the scintillator probe, as well as the new technique used to analyze the data through spectrograms will be described. A last section is devoted to discuss the diagnosis prospects of this method for ITER [M. Shimada et al., Nucl. Fusion 47, S1 (2007)].
Garcia-Munoz, M.; Fahrbach, H.-U.; Zohm, H.; Collaboration: ASDEX Upgrade Team
2009-05-15
A scintillator based detector for fast-ion losses has been designed and installed on the ASDEX upgrade (AUG) tokamak [A. Herrmann and O. Gruber, Fusion Sci. Technol. 44, 569 (2003)]. The detector resolves in time the energy and pitch angle of fast-ion losses induced by magnetohydrodynamics (MHD) fluctuations. The use of a novel scintillator material with a very short decay time and high quantum efficiency allows to identify the MHD fluctuations responsible for the ion losses through Fourier analysis. A Faraday cup (secondary scintillator plate) has been embedded behind the scintillator plate for an absolute calibration of the detector. The detector is mounted on a manipulator to vary its radial position with respect to the plasma. A thermocouple on the inner side of the graphite protection enables the safety search for the most adequate radial position. To align the scintillator light pattern with the light detectors a system composed by a lens and a vacuum-compatible halogen lamp has been allocated within the detector head. In this paper, the design of the scintillator probe, as well as the new technique used to analyze the data through spectrograms will be described. A last section is devoted to discuss the diagnosis prospects of this method for ITER [M. Shimada et al., Nucl. Fusion 47, S1 (2007)].
García-Muñoz, M; Fahrbach, H-U; Zohm, H
2009-05-01
A scintillator based detector for fast-ion losses has been designed and installed on the ASDEX upgrade (AUG) tokamak [A. Herrmann and O. Gruber, Fusion Sci. Technol. 44, 569 (2003)]. The detector resolves in time the energy and pitch angle of fast-ion losses induced by magnetohydrodynamics (MHD) fluctuations. The use of a novel scintillator material with a very short decay time and high quantum efficiency allows to identify the MHD fluctuations responsible for the ion losses through Fourier analysis. A Faraday cup (secondary scintillator plate) has been embedded behind the scintillator plate for an absolute calibration of the detector. The detector is mounted on a manipulator to vary its radial position with respect to the plasma. A thermocouple on the inner side of the graphite protection enables the safety search for the most adequate radial position. To align the scintillator light pattern with the light detectors a system composed by a lens and a vacuum-compatible halogen lamp has been allocated within the detector head. In this paper, the design of the scintillator probe, as well as the new technique used to analyze the data through spectrograms will be described. A last section is devoted to discuss the diagnosis prospects of this method for ITER [M. Shimada et al., Nucl. Fusion 47, S1 (2007)]. PMID:19499603
Mazur, V. A. Chuiko, D. A.
2013-06-15
Oscillations of the 'magnetosphere-solar wind' system are studied analytically in the framework of a plane-stratified model of the medium. The properties of oscillations are determined by three phenomena: Kelvin-Helmholtz instability on the tangential discontinuity (magnetopause) separating the magnetosphere and the solar wind, the presence of a waveguide for fast magnetosonic waves in the magnetosphere, and the Alfven resonance-a sharp increase in the amplitude of oscillations having the properties of Alfven waves-in the inner magnetosphere. The oscillations of the system form a discrete spectrum of eigenmodes. Analytical expressions are obtained for the frequency and growth rate of instability of each mode, as well as for the functions describing the spatial structure of these modes. All these characteristics of the eigenmodes are shown to depend on the velocity of the solar wind as a parameter. The dependences of the main mode characteristics (such as the instability thresholds, the points of the maximum and minimum growth rate, and the spatial distributions of the oscillation energy) on this parameter are determined for each eigenmode.
Influence of equilibrium shear flow on peeling-ballooning instability and edge localized mode crash
Xi, P. W.; Xu, X. Q.; Wang, X. G.; Xia, T. Y.
2012-09-15
The E Multiplication-Sign B shear flow plays a dual role on peeling-ballooning modes and their subsequently triggered edge localized mode (ELM) crashes. On one hand, the flow shear can stabilize high-n modes and twist the mode in the poloidal direction, constraining the mode's radial extent and reducing the size of the corresponding ELM. On the other hand, the shear flow also introduces the Kelvin-Helmholtz drive, which can destabilize peeling-ballooning modes. The overall effect of equilibrium shear flow on peeling-ballooning modes and ELM crashes depends on the competition between these two effects. When the flow shear is either small or very large, it can reduce ELM size. However, for moderate values of flow shear, the destabilizing effect from the Kelvin-Helmholtz term is dominant and leads to larger ELM crashes.
Wall-mode instability in plane shear flow of viscoelastic fluid over a deformable solid.
Chokshi, Paresh; Bhade, Piyush; Kumaran, V
2015-02-01
The linear stability analysis of a plane Couette flow of an Oldroyd-B viscoelastic fluid past a flexible solid medium is carried out to investigate the role of polymer addition in the stability behavior. The system consists of a viscoelastic fluid layer of thickness R, density ρ, viscosity η, relaxation time λ, and retardation time βλ flowing past a linear elastic solid medium of thickness HR, density ρ, and shear modulus G. The emphasis is on the high-Reynolds-number wall-mode instability, which has recently been shown in experiments to destabilize the laminar flow of Newtonian fluids in soft-walled tubes and channels at a significantly lower Reynolds number than that for flows in rigid conduits. For Newtonian fluids, the linear stability studies have shown that the wall modes become unstable when flow Reynolds number exceeds a certain critical value Re(c) which scales as Σ(3/4), where Reynolds number Re=ρVR/η,V is the top-plate velocity, and dimensionless parameter Σ=ρGR(2)/η(2) characterizes the fluid-solid system. For high-Reynolds-number flow, the addition of polymer tends to decrease the critical Reynolds number in comparison to that for the Newtonian fluid, indicating a destabilizing role for fluid viscoelasticity. Numerical calculations show that the critical Reynolds number could be decreased by up to a factor of 10 by the addition of small amount of polymer. The critical Reynolds number follows the same scaling Re(c)∼Σ(3/4) as the wall modes for a Newtonian fluid for very high Reynolds number. However, for moderate Reynolds number, there exists a narrow region in β-H parametric space, corresponding to very dilute polymer solution (0.9≲β<1) and thin solids (H≲1.1), in which the addition of polymer tends to increase the critical Reynolds number in comparison to the Newtonian fluid. Thus, Reynolds number and polymer properties can be tailored to either increase or decrease the critical Reynolds number for unstable modes, thus providing
NASA Astrophysics Data System (ADS)
Sassenberg, Karl; Richardson, Andrew S.; Brennan, Dylan P.; Finn, John M.
2012-03-01
Confinement times of fusion plasmas can be greatly enhanced through access to flexible and reliable control of both resistive and ideal plasma modes. Numerical studies are presented of magnetohydrodynamic instability control through sensing and proportional feedback in Reversed Field Pinches (RFPs) with two resistive walls. The feedback signal incorporates all three components of the magnetic field perturbation, each with its own gain factor. This study extends the work of Richardson & Finn (Phys. Plasmas vol. 17, p. 112511 (2010)) and includes an important feature of the RFX-mod experiment, namely two resistive walls with external measurements. In particular, when a single resistive wall scenario is considered, feedback based on sensing the first tangential component (the derivative of the helical flux) inside the wall is found to perform better than when the same component is measured outside the wall. Furthermore, the effect of feedback control on the magnetosonic (MS) mode with two walls is compared to the single resistive wall scenario with the first tangential component measured outside. In the latter case feedback of the second tangential component (the helical field) was found to drive the MS mode unstable.
NASA Technical Reports Server (NTRS)
Massaglia, S.; Ferrari, A.; Bodo, G.; Kalkofen, W.; Rosner, R.
1985-01-01
The stability of current-driven filamentary modes in magnetic flux tubes embedded in a plane-parallel atmosphere in LTE and in hydrostatic equilibrium is discussed. Within the tube, energy transport by radiation only is considered. The dominant contribution to the opacity is due to H- ions and H atoms (in the Paschen continuum). A region in the parameter space of the equilibrium configuration in which the instability is effective is delimited, and the relevance of this process for the formation of structured coronae in late-type stars and accretion disks is discussed.
Machado, Anaïs; Bodiguel, Hugues; Beaumont, Julien; Clisson, Gérald; Colin, Annie
2016-07-01
We study flows of hydrolized polyacrylamide solutions in two dimensional porous media made using microfluidics, for which elastic effects are dominant. We focus on semi-dilute solutions (0.1%-0.4%) which exhibit a strong shear thinning behavior. We systematically measure the pressure drop and find that the effective permeability is dramatically higher than predicted when the Weissenberg number is greater than about 10. Observations of the streamlines of the flow reveal that this effect coincides with the onset of elastic instabilities. Moreover, and importantly for applications, we show using local measurements that the mean flow is modified: it appears to be more uniform at high Weissenberg number than for Newtonian fluids. These observations are compared and discussed using pore network simulations, which account for the effect of disorder and shear thinning on the flow properties. PMID:27478522
Large-Amplitude Long-Wave Instability of a Supersonic Shear Layer
NASA Technical Reports Server (NTRS)
Messiter, A. F.
1995-01-01
For sufficiently high Mach numbers, small disturbances on a supersonic vortex sheet are known to grow in amplitude because of slow nonlinear wave steepening. Under the same external conditions, linear theory predicts slow growth of long-wave disturbances to a thin supersonic shear layer. An asymptotic formulation is given here which adds nonzero shear-layer thickness to the weakly nonlinear formulation for a vortex sheet. Spatial evolution is considered, for a spatially periodic disturbance having amplitude of the same order, in Reynolds number, as the shear-layer thickness. A quasi-equilibrium inviscid nonlinear critical layer is found, with effects of diffusion and slow growth appearing through nonsecularity condition. Other limiting cases are also considered, in an attempt to determine a relationship between the vortex-sheet limit and the long-wave limit for a thin shear layer; there appear to be three special limits, corresponding to disturbances of different amplitudes at different locations along the shear layer.
Nonlinear evolution of resistive tearing mode instability with shear flow and viscosity
NASA Technical Reports Server (NTRS)
Ofman, L.; Morrison, P. J.; Steinolfson, R. S.
1993-01-01
The effect of shear flow on the nonlinear evolution of the tearing mode is investigated via numerical solutions of the resistive MHD equations in slab geometry, using a finite-difference alternative-direction implicit method. It was found that, when the shear flow is small (V less than 0.3), the tearing mode saturates within one resistive time, whereas for larger flows the nonlinear saturation develops on longer time scales. The magnetic energy release decreases and the saturation time increases with increasing values of V for both small and large resistivity. Shear flow was found to decrease the saturated magnetic island width and to generate currents far from the tearing layer. Results suggest that equilibrium shear flow may improve the confinement of tokamak plasma.
NASA Astrophysics Data System (ADS)
Jo, Young Hyun; Lee, Hae June; Mikhailenko, Vladimir V.; Mikhailenko, Vladimir S.
2016-01-01
It was derived that the drift-Alfven instabilities with the shear flow parallel to the magnetic field have significant difference from the drift-Alfven instabilities of a shearless plasma when the ion temperature is comparable with electron temperature for a finite plasma beta. The velocity shear not only modifies the frequency and the growth rate of the known drift-Alfven instability, which develops due to the inverse electron Landau damping, but also triggers a combined effect of the velocity shear and the inverse ion Landau damping, which manifests the development of the ion kinetic shear-flow-driven drift-Alfven instability. The excited unstable waves have the phase velocities along the magnetic field comparable with the ion thermal velocity, and the growth rate is comparable with the frequency. The development of this instability may be the efficient mechanism of the ion energization in shear flows. The levels of the drift--Alfven turbulence, resulted from the development of both instabilities, are determined from the renormalized nonlinear dispersion equation, which accounts for the nonlinear effect of the scattering of ions by the electromagnetic turbulence. The renormalized quasilinear equation for the ion distribution function, which accounts for the same effect of the scattering of ions by electromagnetic turbulence, is derived and employed for the analysis of the ion viscosity and ions heating, resulted from the interactions of ions with drift-Alfven turbulence. In the same way, the phenomena of the ion cyclotron turbulence and anomalous anisotropic heating of ions by ion cyclotron plasma turbulence has numerous practical applications in physics of the near-Earth space plasmas. Using the methodology of the shearing modes, the kinetic theory of the ion cyclotron turbulence of the plasma with transverse current with strong velocity shear has been developed.
Shear waves in the diamond-anvil cell reveal pressure-induced instability in (Mg,Fe)O.
Jacobsen, Steven D; Spetzler, Hartmut; Reichmann, Hans J; Smyth, Joseph R
2004-04-20
The emerging picture of Earth's deep interior from seismic tomography indicates more complexity than previously thought. The presence of lateral anisotropy and heterogeneity in Earth's mantle highlights the need for fully anisotropic elasticity data from mineral physics. A breakthrough in high-frequency (gigahertz) ultrasound has resulted in transmission of pure-mode elastic shear waves into a high-pressure diamond-anvil cell using a P-to-S elastic-wave conversion. The full elastic tensor (c(ij)) of high-pressure minerals or metals can be measured at extreme conditions without optical constraints. Here we report the effects of pressure and composition on shear-wave velocities in the major lower-mantle oxide, magnesiowüstite-(Mg,Fe)O. Magnesiowüstite containing more than approximately 50% iron exhibits pressure-induced c(44) shear-mode softening, indicating an instability in the rocksalt structure. The oxide closer to expected lower-mantle compositions ( approximately 20% iron) shows increasing shear velocities more similar to MgO, indicating that it also should have a wide pressure-stability field. A complete sign reversal in the c(44) pressure derivative points to a change in the topology of the (Mg,Fe)O phase diagram at approximately 50-60% iron. The relative stability of Mg-rich (Mg,Fe)O and the strong compositional dependence of shear-wave velocities (and partial differential c(44)/ partial differential P) in (Mg,Fe)O implies that seismic heterogeneity in Earth's lower mantle may result from compositional variations rather than phase changes in (Mg,Fe)O. PMID:15079080
Shear waves in the diamond-anvil cell reveal pressure-induced instability in (Mg,Fe)O
Jacobsen, Steven D.; Spetzler, Hartmut; Reichmann, Hans J.; Smyth, Joseph R.
2004-01-01
The emerging picture of Earth's deep interior from seismic tomography indicates more complexity than previously thought. The presence of lateral anisotropy and heterogeneity in Earth's mantle highlights the need for fully anisotropic elasticity data from mineral physics. A breakthrough in high-frequency (gigahertz) ultrasound has resulted in transmission of pure-mode elastic shear waves into a high-pressure diamond-anvil cell using a P-to-S elastic-wave conversion. The full elastic tensor (cij) of high-pressure minerals or metals can be measured at extreme conditions without optical constraints. Here we report the effects of pressure and composition on shear-wave velocities in the major lower-mantle oxide, magnesiowüstite-(Mg,Fe)O. Magnesiowüstite containing more than ≈50% iron exhibits pressure-induced c44 shear-mode softening, indicating an instability in the rocksalt structure. The oxide closer to expected lower-mantle compositions (≈20% iron) shows increasing shear velocities more similar to MgO, indicating that it also should have a wide pressure-stability field. A complete sign reversal in the c44 pressure derivative points to a change in the topology of the (Mg,Fe)O phase diagram at ≈50–60% iron. The relative stability of Mg-rich (Mg,Fe)O and the strong compositional dependence of shear-wave velocities (and ∂c44/∂P) in (Mg,Fe)O implies that seismic heterogeneity in Earth's lower mantle may result from compositional variations rather than phase changes in (Mg,Fe)O. PMID:15079080
Instability of settling non-spherical particle in a vertical shear flow
NASA Astrophysics Data System (ADS)
Qi, Dewei; Koch, Donald; Subramanian, Ganesh
2010-11-01
Two mechanisms are attributed to the cross-stream migration when fiber settles in a vertical shear flow. First, a particle may migrate toward streamlines of the imposed shear flow with smaller downward fluid velocities, due to relative translation of the particle and fluid, called the Saffman effect. Second, a non-spherical particle at finite Reynolds number will attempt to rotate with its long body along the horizontal direction due to inertial torque. On the other hand, the torque due to the imposed weak vertical shear flow rotates the non-spherical in the opposite direction. The dynamic balance between the two torques may lead to a small angle between the particle long body and horizontal plane and may drive the particle migrate toward the streamlines of the shear flow with the large downward fluid velocity. The second mechanism was recently proposed by Shin, Koch and Subramanian.A fiber with aspect ratio κ=2, 1.6, 1.2 1.1 and 0 is used to study the lateral migration. It is shown that at a given shear and aspect ratio, fiber lateral migration can be divided into three phases depending on the Reynolds number. The simulation results identified the lateral migration phase diagram and confirm the second mechanism.
Is the Oort A-value a universal growth rate limit for accretion disk shear instabilities?
NASA Technical Reports Server (NTRS)
Balbus, Steven A.; Hawley, John F.
1992-01-01
A weak-field local MHD instability that is of importance to accretion disks is examined. The maximum growth rate of the instability is found to be not only independent of the magnetic field strength but independent of field geometry as well. In particular, all Keplerian disks are unstable in the presence of any weak poloidal field, with the ratio of the maximum growth rate to disk angular velocity given by 3/4. The maximum growth rate of any weak field configuration that is not purely toroidal is given by the local Oort A-value of the disk. The behavior is studied by using a form of the dynamical Hill equations. It is conjectured that the Oort A-value is an upper bound to the growth rate of any instability feeding upon the free energy of differential rotation.
Magnetohydrodynamic Turbulence
NASA Astrophysics Data System (ADS)
Montgomery, David C.
2004-01-01
Magnetohydrodynamic (MHD) turbulence theory is modeled on neutral fluid (Navier-Stokes) turbulence theory, but with some important differences. There have been essentially no repeatable laboratory MHD experiments wherein the boundary conditions could be controlled or varied and a full set of diagnostics implemented. The equations of MHD are convincingly derivable only in the limit of small ratio of collision mean-free-paths to macroscopic length scales, an inequality that often goes the other way for magnetofluids of interest. Finally, accurate information on the MHD transport coefficients-and thus, the Reynolds-like numbers that order magnetofluid behavior-is largely lacking; indeed, the algebraic expressions used for such ingredients as the viscous stress tensor are often little more than wishful borrowing from fluid mechanics. The one accurate thing that has been done extensively and well is to solve the (strongly nonlinear) MHD equations numerically, usually in the presence of rectangular periodic boundary conditions, and then hope for the best when drawing inferences from the computations for those astrophysical and geophysical MHD systems for which some indisputably turbulent detailed data are available, such as the solar wind or solar prominences. This has led to what is perhaps the first field of physics for which computer simulations are regarded as more central to validating conclusions than is any kind of measurement. Things have evolved in this way due to a mixture of the inevitable and the bureaucratic, but that is the way it is, and those of us who want to work on the subject have to live with it. It is the only game in town, and theories that have promised more-often on the basis of some alleged ``instability''-have turned out to be illusory.
Palermo, F.; Garbet, X.; Cartier-Michaud, T.; Ghendrih, P.; Grandgirard, V.; Sarazin, Y.; Ghizzo, A.
2015-04-15
One important issue in turbulence self-organization is the interplay between the Kelvin–Helmholtz (KH) instability and streamers and/or zonal flows. This question has been debated for a long time. The effects of the KH instability and its position in the sequence of events between streamers, turbulence, and zonal flows have been investigated with a reduced gyro-bounce averaged kinetic code devoted to study the primary ion temperature gradient (ITG) instability linked to trapped ion modes (TIM). In toroidal geometry, the specific dynamics of TIM linked to trapped particles becomes important when the frequency of ITG modes falls below the ion bounce frequency, allowing one to average on both the cyclotron and bounce motion fast time scales. This reduction of the number of degrees of freedom leads to a strong reduction of computer resources (memory and computation time). Bounce-averaged gyrokinetic code can be considered as a toy model able to describe basic structures of turbulent transport in tokamak devices. In particular, by means of this code, we have observed that the energy injected in the system by the TIM instability is exchanged between streamers and zonal flows by means of KH vortices that grow along these structures in the nonlinear phase. The energy transfer occurs throughout the relaxation phase of the streamer growth leading to a modification of the KH modes and to the generation of the zonal flows.
NASA Astrophysics Data System (ADS)
Palermo, F.; Garbet, X.; Ghizzo, A.; Cartier-Michaud, T.; Ghendrih, P.; Grandgirard, V.; Sarazin, Y.
2015-04-01
One important issue in turbulence self-organization is the interplay between the Kelvin-Helmholtz (KH) instability and streamers and/or zonal flows. This question has been debated for a long time. The effects of the KH instability and its position in the sequence of events between streamers, turbulence, and zonal flows have been investigated with a reduced gyro-bounce averaged kinetic code devoted to study the primary ion temperature gradient (ITG) instability linked to trapped ion modes (TIM). In toroidal geometry, the specific dynamics of TIM linked to trapped particles becomes important when the frequency of ITG modes falls below the ion bounce frequency, allowing one to average on both the cyclotron and bounce motion fast time scales. This reduction of the number of degrees of freedom leads to a strong reduction of computer resources (memory and computation time). Bounce-averaged gyrokinetic code can be considered as a toy model able to describe basic structures of turbulent transport in tokamak devices. In particular, by means of this code, we have observed that the energy injected in the system by the TIM instability is exchanged between streamers and zonal flows by means of KH vortices that grow along these structures in the nonlinear phase. The energy transfer occurs throughout the relaxation phase of the streamer growth leading to a modification of the KH modes and to the generation of the zonal flows.
Ng Sheungwah; Hassam, A.B.
2005-06-15
Finite Larmor radius (FLR) effects, originally shown to stabilize magnetized plasma interchange modes at short wavelength, are shown to assist velocity shear stabilization of long wavelength interchanges. It is shown that the FLR effects result in stabilization with roughly the same efficacy as the stabilization from dissipative (resistive and viscous) effects found earlier.
Robust control of linear global instability in models of non-parallel shear flows
NASA Astrophysics Data System (ADS)
Lauga, Eric; Bewley, Thomas
2000-11-01
The present study investigates the control of self-excited oscillations in spatially developing flows such as jets and wakes using H_∞ control theory on a linear complex Ginzburg Landau model. The coefficients of this 1D model equation, which is known to exhibit a generic hydrodynamic instability behavior, are those scaled by Roussopoulos & Monkewitz ( Physica D, 1996) to display behavior modeling that of the near-wake of a circular cylinder, in which a large pocket of local absolute instability is embedded within a convectively unstable flow. Based on noisy measurements at a point sensor typically located inside the wake, the compensator uses an \\cal H_∞ filter to construct a state estimate. This estimate is then used to compute \\cal H_∞ control feedback at a point actuator location, which is typically located upstream of the sensor. The goal of the control scheme is to stabilize the system by minimizing a weighted average of the ``system response'' and the ``control effort'' (both appropriately defined) while rigorously bounding the response of the controlled system to external disturbances. The application of such modern control rules leads to better performance than the control feedback proposed by previous studies by delaying the Reynolds number at which the onset of global instability appears by a factor of 3 and substantially decreasing the sensitivity of the system to external perturbations.
Magnetohydrodynamic Simulations of Barred Galaxies
NASA Astrophysics Data System (ADS)
Kim, W.-T.
2013-04-01
Magnetic fields are pervasive in barred galaxies, especially in gaseous substructures such as dust lanes and nuclear rings. To explore the effects of magnetic fields on the formation of the substructures as well as on the mass inflow rates to the galaxy center, we run two-dimensional, ideal magnetohydrodynamic simulations. We use a modified version of the Athena code whose numerical magnetic diffusivity is shown to be of third order in space. In the bar regions, magnetic fields are compressed and abruptly bent around the dust-lane shocks. The associated magnetic stress not only reduces the peak density of the dust-lane shocks but also removes angular momentum further from the gas that is moving radially in. Nuclear rings that form at the location of centrifugal barrier rather than resonance with the bar are smaller and more radially distributed, and the mass flow rate to the galaxy center is correspondingly larger in models with stronger magnetic fields. Outside the bar regions, the bar potential and strong shear conspire to amplify the field strength near the corotation resonance. The amplified fields transport angular momentum outward, producing trailing magnetic arms with strong fields and low density. The base of the magnetic arms are found to be unstable to a tearing-mode instability of magnetic reconnection. This produces numerous magnetic islands that eventually make the outer regions highly chaotic.
NASA Astrophysics Data System (ADS)
Wang, Meng; Huerre, Patrick; Jiang, Chung-Hsiang; Pei, Suyang; Rui, Maryann; Marcus, Philip
2015-11-01
It has been found recently that baroclinic critical layers are responsible for a new finite-amplitude instability, called the Zombie Vortex Instability (ZVI), in stratified (with Brunt-Väisälä frequency N) flows, rotating with angular velocity Ω and shear σ. ZVI occurs via baroclinic critical layers that create linearly unstable vortex layers, which roll-up into vortices. Those vortices excite new baroclinic critical layers, which form new generations of vortices, resulting in ``vortex self-replication'' that fills the fluid with turbulent vortices. To understand the role of baroclinic critical layers in ZVI, we analyze their structures with matched asymptotic expansions, assuming viscosity determines the magnitude and thickness of the critical layer. We verify our analytically obtained leading order inner and outer layer solutions with numerical simulations. In addition, maps of the control parameter space (Reynolds number, N/ Ω and σ/ Ω) are presented that show two regimes where ZVI occurs, and the physics that determines the boundaries of the two regimes is interpreted. The parameter map and its underlying physics provide guidance for designing practical laboratory experiments in which ZVI could be observed.
NASA Astrophysics Data System (ADS)
Rogister, André L.; Singh, Raghvendra
2005-11-01
By keeping account of the trapped electron ∇B and curvature drifts, it is found that the spatial decay of the collisionless electron drift wave is governed either by the trapped electron response or by the resonant interaction of ions with the sidebands of the primary oscillation. In the former case, pairs of spatially bounded unstable and damped solutions are obtained for negative magnetic shear (ŝ<0) if, as usual, LTe=1/∂rlnTe<0; there are no bounded solutions if ŝLTe<0. In the latter case, there is either a set of bounded damped solutions if ηi>0 or a set of bounded unstable solutions if ηi<0. The unstable modes have a radiating character and the growth rates are γ ˜(2n+1)√1+2q2 ∣ŝ∣∣LNωe*/qR∣ (n is the Hermite polynomial solution index, q the safety factor, ŝ the magnetic shear parameter, R the major radius, ωe* the electron diamagnetic frequency, LN=1/∂rlnNe, and ηi=LN/LTi).The sidebands are responsible for unusually large ratios Qe/TeΓe, where Qe and Γe are the anomalous electron energy flux and the particle flux. These results may explain the box-type Te profile observed in lower hybrid current drive reversed magnetic shear plasmas on the Japan Atomic Energy Research Institute Tokamak 60 Upgrade (JT-60U) [H. Ninomiya and the JT-60U Team, Phys. Fluids B 4, 2070 (1992)]. It is finally demonstrated that the ballooning hypothesis generally leads to conflicting requirements: it is thus hardly relevant for the electron drift branch! The "radiating" boundary condition that has formerly been imposed on the slab solution is finally discussed.
Magnetic viscosity by localized shear flow instability in magnetized accretion disks
Matsumoto, R.; Tajima, T.
1995-01-01
Differentially rotating disks are subject to the axisymmetric instability for perfectly conducting plasma in the presence of poloidal magnetic fields. For nonaxisymmetric perturbations, the authors find localized unstable eigenmodes whose eigenfunction is confined between two Alfven singularities at {omega}{sub d} = {+-} {omega}{sub A}, where {omega}{sub d} is the Doppler-shifted wave frequency, and {omega}{sub A} = k{parallel}v{sub A} is the Alfven frequency. The radial width of the unstable eigenfunction is {Delta}x {approximately} {omega}{sub A}/(Ak{sub y}), where A is the Oort`s constant, and k{sub y} is the azimuthal wave number. The growth rate of the fundamental mode is larger for smaller value of k{sub y}/k{sub z}. The maximum growth rate when k{sub y}/k{sub z} {approximately} 0.1 is {approximately} 0.2{Omega} for the Keplerian disk with local angular velocity {Omega}. It is found that the purely growing mode disappears when k{sub y}/k{sub z} > 0.12. In a perfectly conducting disk, the instability grows even when the seed magnetic field is infinitesimal. Inclusion of the resistivity, however, leads to the appearance of an instability threshold. When the resistivity {eta} depends on the instability-induced turbulent magnetic fields {delta}B as {eta}([{delta}B{sup 2}]), the marginal stability condition self-consistently determines the {alpha} parameter of the angular momentum transport due to the magnetic stress. For fully ionized disks, the magnetic viscosity parameter {alpha}{sub B} is between 0.001 and 1. The authors` three-dimensional MHD simulation confirms these unstable eigenmodes. It also shows that the {alpha} parameter observed in simulation is between 0.01 and 1, in agreement with theory. The observationally required smaller {alpha} in the quiescent phase of accretion disks in dwarf novae may be explained by the decreased ionization due to the temperature drop.
Modeling shear instability and fracture in dynamically deformed Al/W granular composites
NASA Astrophysics Data System (ADS)
Olney, Karl; Benson, David; Nesterenko, Vitali F.
2012-03-01
Aluminum/Tungsten granular composites are materials which combine high density and strength with bulk distributed fracture of Al matrix into small particles under impact or shock loading. They are processed using cold and hot isostatic pressing of W particles/rods in the matrix of Al powder. Numerical models were used to elucidate the dynamic behavior of these materials under dynamic conditions simulating low velocity high energy impact in drop weight test (10 m/s). It was demonstrated that arrangement of W components and bonding between Al particles dramatically affect the samples shear localization and mode of fracture of the Al matrix in agreement with experiments.
NASA Astrophysics Data System (ADS)
Rouhnia, M.; Strom, K.
2015-12-01
Sediment removal rates from buoyant river discharges are typically scaled with particle settling velocity. However, some field and laboratory data suggest that removal can take place at rates higher than those predicted by individual particle settling. It is possible that these enhanced removal rates could potentially be due, at least in part, to mass settling of fluid and sediment near the fresh and saltwater interface. Fluid shear at the interface can mix the freshwater and sediment with the underlying saltwater and lead to pockets or bands of saltwater and sediment that are more dense than the underlying clear saltwater; resulting in an unstable configuration that can lead to rapid vertical transport of sediment. In this study, we perform laboratory experiments to study the enhancement of sediment removal from buoyant plumes under the effect of shear-driven gravitational instabilities. To do this, we ran a 5 cm deep layer of freshwater with flocculated kaolinite over a 50 cm deep basin of clear saltwater in a 1 m long glass flume under a range of upper layer velocities, concentrations, and initial stratification ratios. A Vectrino profiler is placed such that it constantly records velocity profiles from 2 cm above to 2 cm below the original interface. The velocity of the buoyant layer is controlled using a vertical head pipe at the flume inlet, and the Richardson number is varied from 0.05 to 0.25. The interface is monitored with a digital camera and a laser sheet, and Rhodamine B is added to the buoyant layer for better visualization. Snapshots from the video are used to observe the overall dynamics and developments of instabilities at the interface. The sediment concentration of the inflow and outflow of the system are continuously measured with a pair of OBS sensors, and floc size is measured with a floc imaging system and converted to a floc settling velocity. The difference in sediment concentration between the two OBS sensors is used along with a mass
[Nonlinear magnetohydrodynamics
Not Available
1994-01-01
Resistive MHD equilibrium, even for small resistivity, differs greatly from ideal equilibrium, as do the dynamical consequences of its instabilities. The requirement, imposed by Faraday`s law, that time independent magnetic fields imply curl-free electric fields, greatly restricts the electric fields allowed inside a finite-resistivity plasma. If there is no flow and the implications of the Ohm`s law are taken into account (and they need not be, for ideal equilibria), the electric field must equal the resistivity times the current density. The vanishing of the divergence of the current density then provides a partial differential equation which, together with boundary conditions, uniquely determines the scalar potential, the electric field, and the current density, for any given resistivity profile. The situation parallels closely that of driven shear flows in hydrodynamics, in that while dissipative steady states are somewhat more complex than ideal ones, there are vastly fewer of them to consider. Seen in this light, the vast majority of ideal MHD equilibria are just irrelevant, incapable of being set up in the first place. The steady state whose stability thresholds and nonlinear behavior needs to be investigated ceases to be an arbitrary ad hoc exercise dependent upon the whim of the investigator, but is determined by boundary conditions and choice of resistivity profile.
Modeling shear instability and fracture in dynamically deformed Al/W granular composites
NASA Astrophysics Data System (ADS)
Olney, Karl; Benson, David; Nesterenko, Vitali
2011-06-01
Aluminum/Tungsten granular composites are materials which combine high density and strength with bulk distributed fracture of Al matrix into small particles under impact or shock loading. They are processed using cold and hot isostatic pressing of W particles/rods in the matrix of Al powder. The presentation will describe modeling of these materials under dynamic conditions simulating low velocity high energy impact in drop weight test (10 m/s) and also behavior following impact with velocities up to 1200 m/s. It will be demonstrated that morphology of W component and bonding between Al particles dramatically affects their strength, shear localization and mode of fracture of Al matrix. The support for this project provided by the Office of Naval Research Multidisciplinary University Research Initiative Award N00014-07-1-0740 (Program Officer Dr. Clifford Bedford).
Flow Shear Effects in the Onset Physics of Resistive MHD Instabilities in Tokamaks. Final report
Brennan, Dylan P.
2013-04-24
The progress in this research centers around the computational analysis of flow shear effects in the onset of a 3/2 mode driven by a 1/1 mode in DIII-D equilibria. The initial idea was to try and calculate, via nonlinear simulations with NIMROD, the effects of rotation shear on driven 3/2 and 2/1 seed island physics, in experimentally relevant DIIID equilibria. The simulations indicated that very small seed islands were directly driven, as shielding between the sawtooth and the surfaces is significant at the high Lundquist numbers of the experiment. Instead, long after the initial crash the difference in linear stability of the 3/2, which remained prevalent despite the flattening of the core profiles from the sawtooth, contributed to a difference in the eventual seed island evolution. Essentially the seed islands grew or decayed long after the sawtooth crash, and not directly from it. Effectively the dominant 1/1 mode was found to be dragging the coupled modes surrounding it at a high rate through the plasma at their surfaces. The 1/1 mode is locked to the local frame of the plasma in the core, where the flow rate is greatest. The resonant perturbations at the surrounding surfaces propagate in the 'high slip regime' in the language of Fitzpatrick. Peaked flux averaged jxb forces (see Figs. 1 and 2) agree with localized flow modifications at the surfaces in analogy with Ebrahimi, PRL 2007. We track the mode into nonlinear saturation and have found oscillatory states in the evolution. During a visit (11/09) to Tulsa by R.J. LaHaye (GA), it became clear that similar oscillatory states are observed in DIII-D for these types of discharges.
MHD simulation studies of z-pinch shear flow stabilization
NASA Astrophysics Data System (ADS)
Paraschiv, I.; Bauer, B. S.; Sotnikov, V. I.; Makhin, V.; Siemon, R. E.
2003-10-01
The development of the m=0 instability in a z-pinch in the presence of sheared plasma flows is investigated with the aid of a two-dimensional magnetohydrodynamic (MHD) simulation code (MHRDR). The linear growth rates are compared to the results obtained by solving the ideal MHD linearized equations [1] and to the results obtained using a 3D hybrid simulation code [2]. The instability development is followed into the nonlinear regime where its growth and saturation are examined. [1] V.I. Sotnikov, I. Paraschiv, V. Makhin, B.S. Bauer, J.-N. Leboeuf, and J.M. Dawson, "Linear analysis of sheared flow stabilization of global magnetohydrodynamic instabilities based on the Hall fluid mode", Phys. Plasmas 9, 913 (2002). [2] V.I. Sotnikov, V. Makhin, B.S. Bauer, P. Hellinger, P. Travnicek, V. Fiala, J.-N. Leboeuf, "Hybrid Simulations of Current-Carrying Instabilities in Z-pinch Plasmas with Sheared Axial Flow", AIP Conference Proceedings, Volume 651, Dense Z-Pinches: 5th International Conference on Dense Z-Pinches, edited by J. Davis et al., page 396, June 2002.
NASA Astrophysics Data System (ADS)
Shi, Ji-Ming; Stone, James M.; Huang, Chelsea X.
2016-03-01
Previous studies of the non-linear regime of the magnetorotational instability in one particular type of shearing box model - unstratified with no net magnetic flux - find that without explicit dissipation (viscosity and resistivity) the saturation amplitude decreases with increasing numerical resolution. We show that this result is strongly dependent on the vertical aspect ratio of the computational domain Lz/Lx. When Lz/Lx ≲ 1, we recover previous results. However, when the vertical domain is extended Lz/Lx ≳ 2.5, we find the saturation level of the stress is greatly increased (giving a ratio of stress to pressure α ≳ 0.1), and moreover the results are independent of numerical resolution. Consistent with previous results, we find that saturation of the magnetorotational (MRI) in this regime is controlled by a cyclic dynamo which generates patches of strong toroidal field that switches sign on scales of Lx in the vertical direction. We speculate that when Lz/Lx ≲ 1, the dynamo is inhibited by the small size of the vertical domain, leading to the puzzling dependence of saturation amplitude on resolution. We show that previous toy models developed to explain the MRI dynamo are consistent with our results, and that the cyclic pattern of toroidal fields observed in stratified shearing box simulations (leading to the so-called butterfly diagram) may also be related. In tall boxes the saturation amplitude is insensitive to whether or not explicit dissipation is included in the calculations, at least for large magnetic Reynolds and Prandtl number. Finally, we show MRI turbulence in tall domains has a smaller critical Pmc, and an extended lifetime compared to Lz/Lx ≲ 1 boxes.
MHD Instabilities at the Heliopause
Dasgupta, B.; Florinski, V.; Heerikhuisen, J.; Zank, G. P.
2006-09-26
The heliopause (HP) is the outer edge of the heliosphere which separates the tenuous and hot heliosheath plasma on one side and the relatively dense and cool magnetized interstellar plasma on the other side. As a surface of tangential discontinuity, the HP is subjected to both Rayleigh-Taylor (RT) and Kelvin-Helmholtz (KH) instabilities. The coupling between plasma ions and neutral atoms through the process of charge exchange provides an ''effective gravity'' at the HP, while a shear flow exists across it. We derive analytically the linearized dispersion relation for waves propagating along the surface of this discontinuity, which represents a combined RT/KH analysis. We investigate both the purely hydrodynamic, as well as magnetohydrodynamic, cases, and find that interstellar and heliospheric magnetic fields can help stabilize the HP for RT and KH-type instabilities.
NASA Astrophysics Data System (ADS)
Xu, Changjian; Li, Dechang; Cheng, Yuan; Liu, Ming; Zhang, Yongwei; Ji, Baohua
2015-06-01
Anti-parallel -sheet crystallite as the main component of silk fibroin has attracted much attention due to its superior mechanical properties. In this study, we examine the processes of pulling a peptide chain from -sheet crystallite using steered molecular dynamics simulations to investigate the rupture behavior of the crystallite. We show that the failure of -sheet crystallite was accompanied by a propagation of instability of hydrogen-bonds (H-bonds) in the crystallite. In addition, we find that there is an optimum size of the crystallite at which the H-bonds can work cooperatively to achieve the highest shear strength. In addition, we find that the stiffness of loading device and the loading rates have significant effects on the rupture behavior of -sheet crystallite. The stiff loading device facilitates the rebinding of the H-bond network in the stick-slip motion between the chains, while the soft one suppresses it. Moreover, the rupture force of -sheet crystallites decreases with loading rate. Particularly, when the loading rate decreases to a critical value, the rupture force of the -sheet crystallite becomes independent of the loading rates. This study provides atomistic details of rupture behaviors of -sheet crystallite, and, therefore, sheds valuable light on the underlying mechanism of the superior mechanical properties of silk fibroin.
Lattice Boltzmann model for resistive relativistic magnetohydrodynamics.
Mohseni, F; Mendoza, M; Succi, S; Herrmann, H J
2015-08-01
In this paper, we develop a lattice Boltzmann model for relativistic magnetohydrodynamics (MHD). Even though the model is derived for resistive MHD, it is shown that it is numerically robust even in the high conductivity (ideal MHD) limit. In order to validate the numerical method, test simulations are carried out for both ideal and resistive limits, namely the propagation of Alfvén waves in the ideal MHD and the evolution of current sheets in the resistive regime, where very good agreement is observed comparing to the analytical results. Additionally, two-dimensional magnetic reconnection driven by Kelvin-Helmholtz instability is studied and the effects of different parameters on the reconnection rate are investigated. It is shown that the density ratio has a negligible effect on the magnetic reconnection rate, while an increase in shear velocity decreases the reconnection rate. Additionally, it is found that the reconnection rate is proportional to σ-1/2, σ being the conductivity, which is in agreement with the scaling law of the Sweet-Parker model. Finally, the numerical model is used to study the magnetic reconnection in a stellar flare. Three-dimensional simulation suggests that the reconnection between the background and flux rope magnetic lines in a stellar flare can take place as a result of a shear velocity in the photosphere. PMID:26382548
Lattice Boltzmann model for resistive relativistic magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Mohseni, F.; Mendoza, M.; Succi, S.; Herrmann, H. J.
2015-08-01
In this paper, we develop a lattice Boltzmann model for relativistic magnetohydrodynamics (MHD). Even though the model is derived for resistive MHD, it is shown that it is numerically robust even in the high conductivity (ideal MHD) limit. In order to validate the numerical method, test simulations are carried out for both ideal and resistive limits, namely the propagation of Alfvén waves in the ideal MHD and the evolution of current sheets in the resistive regime, where very good agreement is observed comparing to the analytical results. Additionally, two-dimensional magnetic reconnection driven by Kelvin-Helmholtz instability is studied and the effects of different parameters on the reconnection rate are investigated. It is shown that the density ratio has a negligible effect on the magnetic reconnection rate, while an increase in shear velocity decreases the reconnection rate. Additionally, it is found that the reconnection rate is proportional to σ-1 / 2, σ being the conductivity, which is in agreement with the scaling law of the Sweet-Parker model. Finally, the numerical model is used to study the magnetic reconnection in a stellar flare. Three-dimensional simulation suggests that the reconnection between the background and flux rope magnetic lines in a stellar flare can take place as a result of a shear velocity in the photosphere.
NASA Technical Reports Server (NTRS)
Davis, J. G.; Scoggins, J. R.
1981-01-01
Data from the Fourth Atmospheric Variability Experiment were used to investigate conditions/factors responsible for the development (local time rate-of-change) of convective instability, wind shear, and vertical motion in areas with varying degrees of convective activity. AVE IV sounding data were taken at 3 or 6 h intervals during a 36 h period on 24-25 April 1975 over approximately the eastern half of the United States. An error analysis was performed for each variable studied.
NASA Technical Reports Server (NTRS)
1943-01-01
This is the sixth of a series of reports covering an investigation of the general instability problem by the California Institute of Technology. The first five reports of this series cover investigations of the general instability problem under the loading conditions of pure bending and were prepared under the sponsorship of the Civil Aeronautics Administration. This report and the succeeding reports of this series cover the work done on other loading conditions under the sponsorship of the National Advisory Committee for Aeronautics. This report summarizes the work that has been carried on in the experimental investigation of the problem of general instability of stiffened metal cylinders subjected to combined bending and transverse shear at the C.I.T. This part of the investigation includes tests on 55 sheet-covered specimens.
NASA Astrophysics Data System (ADS)
Wan, Xiaoliang; Yu, Haijun; Weinan, E.
2015-05-01
In this work, we study the nonlinear instability of two-dimensional (2D) wall-bounded shear flows from the large deviation point of view. The main idea is to consider the Navier-Stokes equations perturbed by small noise in force and then examine the noise-induced transitions between the two coexisting stable solutions due to the subcritical bifurcation. When the amplitude of the noise goes to zero, the Freidlin-Wentzell (F-W) theory of large deviations defines the most probable transition path in the phase space, which is the minimizer of the F-W action functional and characterizes the development of the nonlinear instability subject to small random perturbations. Based on such a transition path we can define a critical Reynolds number for the nonlinear instability in the probabilistic sense. Then the action-based stability theory is applied to study the 2D Poiseuille flow in a short channel.
NASA Astrophysics Data System (ADS)
Teodorescu, C.; Koepke, M. E.; Reynolds, E. W.
2002-05-01
Broadband ion-acoustic waves have been observed in the Earth's ionosphere, where the electron and ion temperatures are equal, propagating obliquely to the magnetic field lines. Explaining these waves with the current-driven ion-acoustic instability in homogeneous plasma requires an unusually large ratio of electron to ion temperature. We investigate in a Q machine oblique ion-acoustic waves, excited by the combination of magnetic-field-aligned (parallel) current and sheared parallel ion flow, at almost equal ion and electron temperatures. Direct measurements of the parallel and perpendicular ion temperatures, parallel and perpendicular ion drift velocities, electron temperature and parallel electron drift velocity, parallel and perpendicular wavevector components, and mode frequency and growth rate are used to elucidate the shear-modified ion-acoustic instability mechanism and document an observed correlation between ion-temperature anisotropy and wave-propagation angle. Experimental measurements show how anisotropy significantly influences this propagation angle. These results may support the ion-acoustic wave interpretation of broadband waves in the auroral energization region where shear and anisotropy are known to exist. Although the results were obtained from an investigation of shear-modified ion-acoustic waves, our conclusions pertain to the general subject of oblique ion-acoustic waves and thus have ramifications for many space plasmas. * Work supported by NSF and NASA.
Magnetogenesis through Relativistic Velocity Shear
NASA Astrophysics Data System (ADS)
Miller, Evan
Magnetic fields at all scales are prevalent in our universe. However, current cosmological models predict that initially the universe was bereft of large-scale fields. Standard magnetohydrodynamics (MHD) does not permit magnetogenesis; in the MHD Faraday's law, the change in magnetic field B depends on B itself. Thus if B is initially zero, it will remain zero for all time. A more accurate physical model is needed to explain the origins of the galactic-scale magnetic fields observed today. In this thesis, I explore two velocity-driven mechanisms for magnetogenesis in 2-fluid plasma. The first is a novel kinematic 'battery' arising from convection of vorticity. A coupling between thermal and plasma oscillations, this non-relativistic mechanism can operate in flows that are incompressible, quasi-neutral and barotropic. The second mechanism results from inclusion of thermal effects in relativistic shear flow instabilities. In such flows, parallel perturbations are ubiquitously unstable at small scales, with growth rates of order with the plasma frequency over a defined range of parameter-space. Of these two processes, instabilities seem far more likely to account for galactic magnetic fields. Stable kinematic effects will, at best, be comparable to an ideal Biermann battery, which is suspected to be orders of magnitude too weak to produce the observed galactic fields. On the other hand, instabilities grow until saturation is reached, a topic that has yet to be explored in detail on cosmological scales. In addition to investigating these magnetogenesis sources, I derive a general dispersion relation for three dimensional, warm, two species plasma with discontinuous shear flow. The mathematics of relativistic plasma, sheared-flow instability and the Biermann battery are also discussed.
Boquist, Carl W.; Marchant, David D.
1978-01-01
A ceramic-metal composite suitable for use in a high-temperature environment consists of a refractory ceramic matrix containing 10 to 50 volume percent of a continuous high-temperature metal reinforcement. In a specific application of the composite, as an electrode in a magnetohydrodynamic generator, the one surface of the electrode which contacts the MHD fluid may have a layer of varying thickness of nonreinforced refractory ceramic for electrode temperature control. The side walls of the electrode may be coated with a refractory ceramic insulator. Also described is an electrode-insulator system for a MHD channel.
Adaptive wavelets and relativistic magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Hirschmann, Eric; Neilsen, David; Anderson, Matthe; Debuhr, Jackson; Zhang, Bo
2016-03-01
We present a method for integrating the relativistic magnetohydrodynamics equations using iterated interpolating wavelets. Such provide an adaptive implementation for simulations in multidimensions. A measure of the local approximation error for the solution is provided by the wavelet coefficients. They place collocation points in locations naturally adapted to the flow while providing expected conservation. We present demanding 1D and 2D tests includingthe Kelvin-Helmholtz instability and the Rayleigh-Taylor instability. Finally, we consider an outgoing blast wave that models a GRB outflow.
Merritt, E. C.; Doss, F. W.; Loomis, E. N.; Flippo, K. A.; Kline, J. L.
2015-06-24
Counter-propagating shear experiments conducted at the OMEGA Laser Facility have been evaluating the effect of target initial conditions, specifically the characteristics of a tracer foil located at the shear boundary, on Kelvin-Helmholtz instability evolution and experiment transition toward nonlinearity and turbulence in the high-energy-density (HED) regime. Experiments are focused on both identifying and uncoupling the dependence of the model initial turbulent length scale in variable-density turbulence models of k-ϵ type on competing physical instability seed lengths as well as developing a path toward fully developed turbulent HED experiments. We present results from a series of experiments controllably and independently varyingmore » two initial types of scale lengths in the experiment: the thickness and surface roughness (surface perturbation scale spectrum) of a tracer layer at the shear interface. We show that decreasing the layer thickness and increasing the surface roughness both have the ability to increase the relative mixing in the system, and thus theoretically decrease the time required to begin transitioning to turbulence in the system. In addition, we also show that we can connect a change in observed mix width growth due to increased foil surface roughness to an analytically predicted change in model initial turbulent scale lengths.« less
Merritt, E. C.; Doss, F. W.; Loomis, E. N.; Flippo, K. A.; Kline, J. L.
2015-06-24
Counter-propagating shear experiments conducted at the OMEGA Laser Facility have been evaluating the effect of target initial conditions, specifically the characteristics of a tracer foil located at the shear boundary, on Kelvin-Helmholtz instability evolution and experiment transition toward nonlinearity and turbulence in the high-energy-density (HED) regime. Experiments are focused on both identifying and uncoupling the dependence of the model initial turbulent length scale in variable-density turbulence models of k-ϵ type on competing physical instability seed lengths as well as developing a path toward fully developed turbulent HED experiments. We present results from a series of experiments controllably and independently varying two initial types of scale lengths in the experiment: the thickness and surface roughness (surface perturbation scale spectrum) of a tracer layer at the shear interface. We show that decreasing the layer thickness and increasing the surface roughness both have the ability to increase the relative mixing in the system, and thus theoretically decrease the time required to begin transitioning to turbulence in the system. In addition, we also show that we can connect a change in observed mix width growth due to increased foil surface roughness to an analytically predicted change in model initial turbulent scale lengths.
Merritt, E. C. Doss, F. W.; Loomis, E. N.; Flippo, K. A.; Kline, J. L.
2015-06-15
Counter-propagating shear experiments conducted at the OMEGA Laser Facility have been evaluating the effect of target initial conditions, specifically the characteristics of a tracer foil located at the shear boundary, on Kelvin-Helmholtz instability evolution and experiment transition toward nonlinearity and turbulence in the high-energy-density (HED) regime. Experiments are focused on both identifying and uncoupling the dependence of the model initial turbulent length scale in variable-density turbulence models of k-ϵ type on competing physical instability seed lengths as well as developing a path toward fully developed turbulent HED experiments. We present results from a series of experiments controllably and independently varying two initial types of scale lengths in the experiment: the thickness and surface roughness (surface perturbation scale spectrum) of a tracer layer at the shear interface. We show that decreasing the layer thickness and increasing the surface roughness both have the ability to increase the relative mixing in the system, and thus theoretically decrease the time required to begin transitioning to turbulence in the system. We also show that we can connect a change in observed mix width growth due to increased foil surface roughness to an analytically predicted change in model initial turbulent scale lengths.
Marchant, David D.; Killpatrick, Don H.
1978-01-01
An electrode capable of withstanding high temperatures and suitable for use as a current collector in the channel of a magnetohydrodynamic (MHD) generator consists of a sintered powdered metal base portion, the upper surface of the base being coated with a first layer of nickel aluminide, an intermediate layer of a mixture of nickel aluminide - refractory ceramic on the first layer and a third or outer layer of a refractory ceramic material on the intermediate layer. The sintered powdered metal base resists spalling by the ceramic coatings and permits greater electrode compliance to thermal shock. The density of the powdered metal base can be varied to allow optimization of the thermal conductivity of the electrode and prevent excess heat loss from the channel.
NASA Astrophysics Data System (ADS)
Tarasov, Boris G.
2014-05-01
Today, frictional shear resistance along pre-existing faults is considered to be the lower limit on rock shear strength for confined conditions corresponding to the seismogenic layer. This paper introduces a recently identified shear rupture mechanism providing a paradoxical feature of hard rocks - the possibility of shear rupture propagation through the highly confined intact rock mass at shear stress levels significantly less than frictional strength. In the new mechanism, the rock failure associated with consecutive creation of small slabs (known as ‘domino-blocks') from the intact rock in the rupture tip is driven by a fan-shaped domino structure representing the rupture head. The fan-head combines such unique features as: extremely low shear resistance, self-sustaining stress intensification, and self-unbalancing conditions. Due to this the failure process caused by the mechanism is very dynamic and violent. This makes it impossible to directly observe and study the mechanism and can explain why the mechanism has not been detected before. This paper provides physical motivation for the mechanism, based upon side effects accompanying the failure process. Physical and mathematical models of the mechanism presented in the paper explain unique and paradoxical features of the mechanism. The new shear rupture mechanism allows a novel point of view for understanding the nature of spontaneous failure processes in hard rocks including earthquakes.
Nonlinear evolution of the Kelvin-Helmholtz instability in the double current sheet configuration
NASA Astrophysics Data System (ADS)
Mao, Aohua; Li, Jiquan; Liu, Jinyuan; Kishimoto, Yasuaki
2016-03-01
The nonlinear evolution of the Kelvin-Helmholtz (KH) instability driven by a radially antisymmetric shear flow in the double current sheet configuration is numerically investigated based on a reduced magnetohydrodynamic model. Simulations reveal different nonlinear fate of the KH instability depending on the amplitude of the shear flow, which restricts the strength of the KH instability. For strong shear flows far above the KH instability threshold, the linear electrostatic-type KH instability saturates and achieves a vortex flow dominated quasi-steady state of the electromagnetic (EM) KH turbulence with large-amplitude zonal flows as well as zonal fields. The magnetic surfaces are twisted significantly due to strong vortices but without the formation of magnetic islands. However, for the shear flow just over the KH instability threshold, a weak EM-type KH instability is saturated and remarkably damped by zonal flows through modifying the equilibrium shear flow. Interestingly, a secondary double tearing mode (DTM) is excited subsequently in highly damped KH turbulence, behaving as a pure DTM in a flowing plasma as described in Mao et al. [Phys. Plasmas 21, 052304 (2014)]. However, the explosive growth phenomenon is replaced by a gradually growing oscillation due to the extremely twisted islands. As a result, the release of the magnetic energy becomes slow and the global magnetic reconnection tends to be gentle. A complex nonlinear interaction between the EM KH turbulence and the DTMs occurs for the medium shear flows above the KH instability threshold, turbulent EM fluctuations experience oscillatory nonlinear growth of the DTMs, finally achieves a quasi-steady state with the interplay of the fluctuations between the DTMs and the EM KH instability.
Single-fluid stability of stationary plasma equilibria with velocity shear and magnetic shear
Miura, Akira
2009-10-15
By using incompressible single-fluid equations with a generalized Ohm's law neglecting the electron inertia, a linear eigenmode equation for a magnetic field perturbation is derived for stationary equilibria in a slab geometry with velocity and magnetic shears. The general eigenmode equation contains a fourth-order derivative of the perturbation in the highest order and contains Alfven and whistler mode components for a homogeneous plasma. The ratio of the characteristic ion inertia length to the characteristic inhomogeneity scale length is chosen as a small parameter for expansion. Neglecting whistler mode in the lowest order, the eigenmode equation becomes a second-order differential equation similar to the ideal magnetohydrodynamic eigenmode equation except for the fact that the unperturbed perpendicular velocity contains both electric and ion diamagnetic drifts. A sufficient condition for stability against the Kelvin-Helmholtz instability driven by shear in the ion diamagnetic drift velocity is derived and then applied to tokamaks.
NASA Astrophysics Data System (ADS)
Erdélyi, R.
2007-07-01
The heating of solar atmosphere from chromosphere to corona is one of the key fundamental and yet unresolved questions of modern space and plasma physics. In spite of the multi-fold efforts spanning over half a century including the many superb technological advances and theoretical developments (both analytical and computational) the unveiling of the subtle of coronal heating still remains an exciting job for the 21st century! In the present paper I review the various popular heating mechanisms put forward in the existing extensive literature. The heating processes are, somewhat arbitrarily, classified as hydrodynamic (HD), magnetohydrodynamic (MHD) or kinetic based on the model medium. These mechanisms are further divided based on the time scales of the ultimate dissipation involved (i.e. AC and DC heating, turbulent heating). In particular, attention is paid to discuss shock dissipation, Landau damping, mode coupling, resonant absorption, phase mixing, and, reconnection. Finally, I briefly review the various observational consequences of the many proposed heating mechanisms and confront them with high-resolution ground-based and satellite data currently available.
DISCO: A 3D Moving-mesh Magnetohydrodynamics Code Designed for the Study of Astrophysical Disks
NASA Astrophysics Data System (ADS)
Duffell, Paul C.
2016-09-01
This work presents the publicly available moving-mesh magnetohydrodynamics (MHD) code DISCO. DISCO is efficient and accurate at evolving orbital fluid motion in two and three dimensions, especially at high Mach numbers. DISCO employs a moving-mesh approach utilizing a dynamic cylindrical mesh that can shear azimuthally to follow the orbital motion of the gas. The moving mesh removes diffusive advection errors and allows for longer time-steps than a static grid. MHD is implemented in DISCO using an HLLD Riemann solver and a novel constrained transport (CT) scheme that is compatible with the mesh motion. DISCO is tested against a wide variety of problems, which are designed to test its stability, accuracy, and scalability. In addition, several MHD tests are performed which demonstrate the accuracy and stability of the new CT approach, including two tests of the magneto-rotational instability, one testing the linear growth rate and the other following the instability into the fully turbulent regime.
NASA Astrophysics Data System (ADS)
Johnson, P. A.; Carmeliet, J.; Savage, H. M.; Scuderi, M.; Carpenter, B. M.; Guyer, R. A.; Daub, E. G.; Marone, C.
2015-12-01
We investigate dynamic-wave triggered slip under laboratory shear conditions. The experiment is comprised of a 3-block system containing two gouge layers composed of glass beads and held in place by a fixed load in a bi-axial configuration. When the system is sheared under steady state conditions at loads from 3-8 MPa, stick-slip exhibiting a characteristic recurrence time is observed. Under these load conditions, we find that shear failure may be instantaneously triggered by a brief dynamical wave if the system is in a critical shear-stress state, near failure. Dynamic triggering is only observed when the dynamic wave amplitude exceeds strains of 10^(-7). Following triggering, the gouge material remains in an unstable state for long periods of time as manifest by unique slip characteristics not observed during spontaneous events: the measured physical characteristics—the gouge material strength recovery, the gouge layer thickness, the gouge shear modulus and the stick-slip recurrence time recover over many stick-slip cycles following triggering. This work suggests that faults must be critically stressed to trigger under dynamic conditions and that the recovery process following a dynamically triggered event differs from the recovery following a spontaneous event.
Feedback instability in the magnetosphere-ionosphere coupling system: Revisited
Watanabe, T.-H.
2010-02-15
A coupled set of the reduced magnetohydrodynamic and the two-fluid equations is applied to the magnetosphere-ionosphere (M-I) feedback interactions in relation to growth of quite auroral arcs. A theoretical analysis revisiting the linear feedback instability reveals asymptotic behaviors of the dispersion relation and a non-Hermite property in the M-I coupling. A nonlinear simulation of the feedback instability in the M-I coupling system manifests growth of the Kelvin-Helmholtz-like mode in the magnetosphere as the secondary instability. The distorted vortex and field-aligned current profiles propagating as the shear Alfven waves lead to spontaneous deformation of ionospheric density and current structures associated with auroral arcs.