Tian, Miao; Sheremet, Alex; Shrira, Victor
The observed spectra of nearshore infragravity waves are typically mixed, with a discrete component (edge waves, trapped waves, propagating parallel to the coast) and a continuous one (leaky waves, that propagate from, and radiate back into, the deep ocean. See e.g., Oltman-Shay and Guza, 1987). The evolution of infragravity spectrum is driven by three general processes: 1) edge-leaky interactions, that transfer energy to the system from shorter waves; 2) energy redistribution through edge-edge and edge-leaky interactions; 3) and energy dissipation due to processes such as bottom friction. Previous studies treated either the edge and leaky system, in isolation from the other one, and focused on phase-resolving dynamical equation. Following Whitham (1976), who derived the nonlinear edge-wave solutions for the shallow water equations, theoretical work on the nonlinear edge-edge interaction resulted in many significant extensions (e.g., Kirby et. al. 1998, Pelinovsky et. al. 2010). The interaction between standing edge waves and a normally incident wave has been investigated both within the framework of the shallow-water equation (Guza and Davis 1974) and full water wave theory (Minzoni and Whitham, 1977). Here, we derive a general dynamical equation for the full mixed edge-leaky spectrum over a laterally uniform beach based on Zakharov's (1968, 1999) Hamiltonian formalism. The introduction of canonical variables in this formalism significantly simplifies the complicated derivation of the nonlinear interaction coefficient in the previous work (Kirby et. al. 1998, Pelinovsky et. al. 2010). The subharmonic resonance mechanism for edge-wave excitation (Guza and Davis, 1974) is retrieved from the model equation as a special case. The effects of dissipation induced by bottom friction are included using a perturbation approach. A kinetic equation for Zakharov's (1999) canonical variables can be derived, that reduces to the stochastic nonlinear mild-slope model of Agnon and Sheremet (1997) for the leaky spectrum. Ongoing work focuses on the investigation of the dynamical properties of the edge wave spectrum. Future goals include the development of numerical implementation and validation of the model.
Tian, M.; Sheremet, A.; Shrira, V. I.
The observed spectra of nearshore infragravity waves are typically mixed, with a discrete component (edge waves, trapped waves, propagating parallel to the coast) and a continuous one (leaky waves, that propagate from, and radiate back into, the deep ocean. See e.g., Oltman-Shay and Guza, 1987). The evolution of infragravity spectrum is driven by three general processes: 1) edge-leaky interactions, that transfer energy to the system from shorter waves; 2) energy redistribution through edge-edge and edge-leaky interactions; 3) and energy dissipation due to processes such as bottom friction. Previous studies treated either the edge and leaky system, in isolation from the other one, and focused on phase-resolving dynamical equation. Following Whitham (1976), who derived the nonlinear edge-wave solutions for the shallow water equations, theoretical work on the nonlinear edge-edge interaction resulted in many significant extensions (e.g., Kirby et. al. 1998, Pelinovsky et. al. 2010). The interaction between standing edge waves and a normally incident wave has been investigated both within the framework of the shallow-water equation (Guza and Davis 1974) and full water wave theory (Minzoni and Whitham, 1977). Here, we derive a general dynamical equation for the full mixed edge-leaky spectrum over a laterally uniform beach based on Zakharov's (1968, 1999) Hamiltonian formalism. The introduction of canonical variables in this formalism significantly simplifies the complicated derivation of the nonlinear interaction coefficient in the previous work (Kirby et. al. 1998, Pelinovsky et. al. 2010). The subharmonic resonance mechanism for edge-wave excitation (Guza and Davis, 1974) is retrieved from the model equation as a special case. The effects of dissipation induced by bottom friction are included using a perturbation approach. A kinetic equation for Zakharov's (1999) canonical variables can be derived, that reduces to the stochastic nonlinear mild-slope model of Agnon and Sheremet (1997) for the leaky spectrum. Ongoing work focuses on the investigation of the dynamical properties of the edge wave spectrum and the development of numerical implementation and validation of the model.
The tenth Five-Year Project of China Earthquake Administration installed about 40 YRY-4 type high-resolution borehole strainmeters over the mainland China in order to enhance its capability of earthquake-forecasting attempt. The strainmeters are installed in rocks at a depth around 40m and resolve strain changes to the order of 10-11. Measurements are sampled every minute. There are four gauges horizontally placed, 45-degree apart, in an YRY-4 strainmeter, whose measurements are denoted as Si (i=1, 2, 3, 4) in our study. The similarity of the two curves of S1 +S3 and S2 +S4 of Guza recordings gives sufficient credit to the data. Among the sites, Guza is located the nearest (about 140km), from the epicentral area of the Wenchuan earthquake. Even months before the earthquake, it had already been noticed at Guza that the initially smooth curves had become badly interfered from time to time by minor steps or unsymmetrical pulses with periods of minutes~hours. The interferences were dominantly compressional and mostly on the order of 10-9. They were not corresponding to weather changes. Other sites are at least 300km away and did not observe such anomalies. A comparison of the interferences with the long-term and coseismic changes shows a good consistence in the sense of strain variety among them, which suggests a tectonic cause of the abnormal signals. High-passed data show obvious relevance of the abnormal signals to the Wenchuan quake in time. They became stronger as the great event approached, reached the highest at the main shock and diminishing while aftershocks have been dying away. We put forth an Overrun Rate Analysis (ORA) to give out a quantitative description of the interferences. The high-passed interferences can be depicted as positive or negative big values overrunning the normal level. Overrun Rate of Numbers, denoted as Ron, is defined as the total number of overrun points in one day, and Overrun Rate of Strength Ros the daily sum of amplitudes of overrun points. The graphs of Ron and Ros demonstrate more clearly the relevance of the interferences to the seismic event. Ron is analogous to the count rate of Acoustic Emission (AE) in rock failure experiments. According to Kaiser effect, the increase of Ron before the quake should reflect the increase of stress level. Few foreshocks had been recorded for the Wenchuan quake probably because there was not a dense seismological network over this area. However, the only remarkable Ms.45 event near Guza before the main shock brought about the biggest typical interference in the strain recording. It provides a direct evidence about the possible tectonic mechanism of the interferences. We have carried out a decompose of the recordings by means of Discrete Wavelet Transformation of dyadic scales. By comparing the component graphs of different levels we see a strengthening and a movement of weight center of the interferences towards the shock instant along with the increase of period. It can be readily attributed to the increase of fracture scale.
Keen, A. S.; Holman, R. A.
Parametric depth-induced-breaking dissipation models have shown great skill at predicting time averaged wave heights across the surf zone. First proposed by Battjes & Janssen (1978), these models balance the incoming wave energy flux with a roller dissipation term. This roller dissipation term is estimated by calculating the dissipation for one characteristic broken wave and then multiplying this quantity by the fraction of broken waves. To describe the fraction of broken waves, a typical assumption asserts that wave heights are nearly Rayleigh distributed [Thornton & Guza (1983)] allowing a sea state to be described by only a few parameters. While many experiments have validated the cross shore wave height profiles, few field experiments have been performed to analyze the probability distribution of breaking wave heights over a barred beach profile. The goal of the present research is to determine the distribution of broken and unbroken wave heights across a natural barred beach profile. Field data collected during the Surf Zone Optics experiment (a Multi-disciplinary University Research Initiative) in Duck, North Carolina, consisted of an array of in-situ pressure sensors and optical remote sensing cameras. Sea surface elevation time series from the in-situ pressure sensors are used here to resolve wave height distributions at multiple locations across the surf zone. Breaking wave height distributions are resolved based upon a combination of the pressure sensor and optically based breaker detection algorithm. Since breaking is easily able to be tracked by video imaging, breaking waves are flagged in the sea surface elevation series and binned into a broken wave height distribution. Results of this analysis are compared with model predictions based upon the Battjes & Janssen (1978), Thornton & Guza (1983) and Janssen & Battjes (2007) models to assess the validity of each wave height distribution model.
Contardo, Stephanie; Symonds, Graham; Segura, Laura
The occurrence of short period wind-sea associated with a diurnal sea breeze, superimposed on longer period swell in South West Western Australia provides an opportunity to observe the response of infragravity (0.01-0.05 Hz) waves, in the nearshore, to both wind-sea and swell forcing. An alongshore array of pressure sensors and a cross-shore array of current velocity and pressure sensors are deployed at Secret Harbour, a barred beach near Perth. The observations show a stronger infragravity response to longer period incident swell than to short period wind-sea. Infragravity waves at Secret Harbour are generated by two mechanisms: breakpoint forcing and bound wave release. Breakpoint forcing is observed with both swell and wind-sea forcing while bound wave release is only observed in the presence of swell. Two mechanisms generate free infragravity waves during swell periods while only one mechanism is in place during wind-sea periods, providing an explanation for the stronger response to swell than wind-sea. Free infragravity waves propagating offshore after reflection at the shoreline are called leaky waves; those which are trapped to the shoreline by refraction are called edge waves. At Secret Harbour, both edge waves and leaky waves are detected. Leaky waves dominate with swell forcing while edge waves dominate with wind-sea forcing. Amongst edge waves, mode 0 waves are found to dominate in the absence of wind-sea, while higher mode edge waves dominate when wind-sea is present. We calculate the expected wavenumber-frequency distribution of edge wave and leaky wave energy, based on resonance conditions, using wave period, incidence angle and directional spreading, as proposed by Bowen and Guza (1978). Observations and predictions are in good agreement. However the model can be improved by quantifying the infragravity energy generated by both infragravity wave generation mechanisms. Bowen, A. J., and R. T. Guza (1978), Edge waves and surf beat, Journal of Geophysical Research-Oceans and Atmospheres, 83(NC4), 1913-1920.
Abreu, M.; Larraza, A.; Thornton, E.
A shallow water, nonlinear spectral wave transformation model is developed for conditions of a mild sloping bottom (μ = ∇h/kh ≪ 1) and small amplitude effects (ɛ = ζ/h ≪ 1). Nonlinearities and combined shoaling and refraction effects act on the same time and length scales. The evolution equation of the wave action is prescribed by the wave Boltzmann equation, whereby resonant collinear triad interactions transfer energy among Fourier components. Combined shoaling and refraction effects are taken into account through the geometrical optics approximation. A numerical solution of the three-wave collision integral is presented, and the steady state wave Boltzmann equation is integrated using a piece wise ray method. The model is tested using the high-resolution frequency-directional wave spectra of Freilich, Guza, and Elgar (1990) that show nonlinear transfers of energy between both harmonic and nonharmonic frequencies. A digitized version of the measured frequency-directional spectrum at 10-m depth is evolved 246 m shoreward over a bathymetry of straight and parallel bottom contours to 4-m depth. The model predicts the prominent spectral features in the measured wave field. The model results are in general superior to estimates using linear, finite depth wave theory, and they compare well with the observations in the region of the spectrum dominated by nonlinear effects.
Haines, John W.; Sallenger, Asbury H., Jr.
Mean cross-shore currents observed across a barred surf zone are compared to model predictions. The model is based on a simplified momentum balance with a turbulent boundary layer at the bed. Turbulent exchange is parameterized by an eddy viscosity formulation, with the eddy viscosity Aυ independent of time and the vertical coordinate. Mean currents result from gradients due to wave breaking and shoaling, and the presence of a mean setup of the free surface. Descriptions of the wave field are provided by the wave transformation model of Thornton and Guza . The wave transformation model adequately reproduces the observed wave heights across the surf zone. The mean current model successfully reproduces the observed cross-shore flows. Both observations and predictions show predominantly offshore flow with onshore flow restricted to a relatively thin surface layer. Successful application of the mean flow model requires an eddy viscosity which varies horizontally across the surf zone. Attempts are made to parameterize this variation with some success. The data does not discriminate between alternative parameterizations proposed. The overall variability in eddy viscosity suggested by the model fitting should be resolvable by field measurements of the turbulent stresses. Consistent shortcomings of the parameterizations, and the overall modeling effort, suggest avenues for further development and data collection.
Belavkin, V. P.; Gutǎ, M.
pt. A. Quantum probability and analysis. Approximation via toy Fock space - the vacuum-adapted viewpoint / A. C. R. Belton. Regular solutions of quantum stochastic differential equations / F. Fagnola. From algebraic to analytic double product integrals / R. Hudson. Product systems; a survey with commutants in view / M. Skeide. Clifford algebras, random graphs, and quantum random variables / R. Schott & G. S. Staples. The set of density operators modelled on an Orlicz space / R. F. Streater. Quantum extensions of the classical domination principle / V. Umanità. Analysis in operator spaces / B. Zegarliński -- pt. B. Quantum statistics, filtering and control. Quantum filtering and optimal control / V. P. Belavkin & S. Edwards. On the separation principle in quantum control / L. Bouten & R. van Handel. Conciliation of Bayes and pointwise quantum state estimation / R. D. Gill. Optimal quantum feedback for canonical observables / J. Gough. Feedback control of quantum systems / M. James. Local asymptotic normality and optimal estimation for d-dimensional quantum systems / J. Kahn & M. Guza -- pt. C. Quantum measurements and information. Information gain in quantum continual measurements / A. Barchielli & G. Lupieri. Noisy qutrit channel / A. Chicińska & K. Włdkiewicz. Additivity of entangled channel capacity given quantum input states / V. P. Belavkin & X. Dai. Classical coding and the Cauchy-Schwarz inequality / B. Janssens. Note on information transmission in quantum systems / N. Watanabe.
Bennis, A.; Ardhuin, F.; Dumas, F.; Bonneton, P.
The interaction of waves with three-dimensional current structure is investigated using a two-way coupled modelling system combining MARS3D (Lazure and Dumas 2008) with WAVEWATCH III (Tolman 2008, Ardhuin et al. 2009) , a wave model (NOAA/NCEP, Tolman 2008). After a basic validation in two dimensions, the flow model MARS3D was adapted with three options that solve for the total momentum (Mellor 2003, 2008) or the quasi-Eulerian momentum (Ardhuin et al. 2008b). Adiabatic model results show that, as expected from theory (Ardhuin et al. 2008a), the total momentum fluxes parameterized by Mellor are not self-consistent and can lead to very large errors (Bennis and Ardhuin 2010). We thus use the model option to solve for the quasi-Eulerian momentum, including sources of momentum and turbulent kinetic energy (TKE). The influence of these TKE sources is investigated in the case of the NSTS experiment (Thornton and Guza, 1986). The feedback of the currents on the waves is negligible in this case. The sources of TKE from wave breaking and wave bottom friction are found to have strong influence on the bottom friction, in a way consistent with the parameterizations by Longuet-Higgins (1970) and Mellor (2002). The complete model is then applied to a real case of a large rip current on the South-West coast of France (Bruneau et al., Cont. Shelf Res. 2009). The breaking of waves on the opposed current generates a strong coupling on the rip current that partially controls the strength of the current and it three-dimensional shape.
Lopez, Mario; Iglesias, Gregorio
Long waves may cause significant disturbances for port operations. This paper is concerned with the long wave problems at Ferrol, a port in NW Spain. Long wave periods range between a few tens of seconds to several hours. In shallow water their wavelengths are on the order of hundreds of meters to kilometres. As a result, these waves can match the natural periods of oscillation of semi-enclosed bodies of water like gulfs, bays, fiords, or harbours, resulting in resonant oscillations. During resonance, the vertical displacement of the free surface increases until the energy input is balanced by losses due to friction, flow separation, boundary absorption, and radiation from the mouth (Okihiro et al., 1993). The induced horizontal displacements of the water mass are responsible for the large movements on ships. The non-linear interaction of long and wind waves and the direct atmospheric forcing are the main sources of long waves in the ocean. In the first case, the long waves are also known as infragravity waves and tend to have relatively small periods. In the second case, the atmospheric forced long waves, different mechanisms have been used to explain their generation. Atmospheric disturbances passing over the continental shelf (Sepic et al., 2008) or wind convection cells (de Jong and Battjes, 2004) are two of the causes for these 'meteorological' waves. Whatever their cause, they tend to have relatively large periods and, therefore, a significant potential to excite the first modes of oscillation of harbours. In addition, other different forcing mechanisms can generate long waves, including submerged landslides (Cecioni and Bellotti, 2010) and seisms (Candella et al., 2008). Disturbances to load and unload operations have been reported from 2005 at the Exterior Port of Ferrol (NW Spain). On-site measurements of sea-level oscillations revealed energy peaks possibly related to resonant processes (López et al., 2012; López and Iglesias, 2013). This work is focused on the long waves at the Port of Ferrol and their implications for the operations at the port. References Candella, R.N., Rabinovich, A.B., Thomson, R.E., 2008. The 2004 Sumatra tsunami as recorded on the Atlantic coast of South America. Adv. Geosci. 14, 117-128. Cecioni, C., Bellotti, G., 2010. Modeling tsunamis generated by submerged landslides using depth integrated equations. Appl. Ocean Res. 32(3), 343-350. de Jong, M.P.C., Battjes, J.A., 2004. Low-frequency sea waves generated by atmospheric convection cells. Journal of Geophysical Research-Oceans 109(C1), C01011. López, M., Iglesias, G., 2013. Artificial Intelligence for estimating infragravity energy in a harbour. Ocean Eng. 57(0), 56-63. López, M., Iglesias, G., Kobayashi, N., 2012. Long period oscillations and tidal level in the Port of Ferrol. Appl. Ocean Res. 38(0), 126-134. Okihiro, M., Guza, R.T., Seymour, R.J., 1993. Excitation of Seiche Observed in a Small Harbor. J. Geophys. Res. 98(C10), 18201-18211. Sepic, J., Orlic, M., Vilibic, I., 2008. The Bakar Bay seiches and their relationship with atmospheric processes. Acta Adriat. 49(2).
Ludka, B. C.; Guza, R. T.; McNinch, J. E.; O'Reilly, W.
Beach elevation change observations from the United States west and east coasts are used to identify statistically the dominant cross-shore patterns in sand level fluctuations, and these changes are related to equilibrium beach profile concepts. Three to seven years of observations at four beaches in Southern California include monthly surveys of the subaerial (near MSL) beach, and quarterly surveys from the backbeach to about 8m depth. At Duck, North Carolina, observations include 31 years of monthly surveys from the dunes to about 8m depth. On the Southern California beaches, the dominant seasonal pattern is subaerial erosion in winter and accretion in summer. Seasonal fluctuations of 3m in shoreline vertical sand levels, and 50m in subaerial beach width, are not uncommon. The sand eroded from the shoreline in winter is stored in an offshore sand bar and returns to the beach face in summer. Wave conditions in Southern California also vary seasonally, with energetic waves arriving from the north in winter, and lower energy, longer period southerly swell arriving in summer. A spectral refraction model, initialized with a regional network of directional wave buoys, is used to estimate hourly wave conditions, in 10m water depth. Using an equilibrium hypothesis, that the shoreline (defined as the cross-shore location of the MSL contour) change rate depends on the wave energy and the wave energy disequilibrium, Yates (2009) modeled the time-varying shoreline location at several Southern California beaches with significant skill. The four free model parameters were calibrated to fit observations. Following Yates (2009), we extend the equilibrium shoreline model to include the horizontal displacement of other elevation contours. At the Southern California sites, the modeled contour translation depends on the incident wave energy, the present contour configuration, and observation-based estimates of the contour behavior (based on EOF spatial amplitudes). At Duck, seasonal variations of the wave field (measured immediately offshore) are large, but shoreline changes (usually <30cm) are smaller than in Southern California. Maximum vertical variations occur just seaward of the shoreline and the nearshore bathymetry is often barred. Plant (1999) show that bar crest position at Duck has equilibrium-like behavior. We will present the results of equilibrium shoreline and profile modeling at Duck. At both sites, we diagnose sources (e.g. grain size and incident waves) of the sometimes strong observed alongshore variations in sand level change patterns. Funding was provided by the US Army Corps of Engineers and the California Department of Boating and Waterways. REFERENCES Plant, N. G., R. A. Holman, M. H. Freilich, and W. A. Birkemeier (1999), A simple model for interannual sandbar behavior, J. Geophys. Res., 104(C7), 15,755-15,776. Yates, M. L., R. T. Guza, and W. C. O'Reilly (2009), Equilibrium shoreline response: Observations and modeling, J. Geophys. Res., 114, C09014.