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, Miao; Sheremet, Alex; Shrira, Victor
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.
Anomalous changes recorded by the borehole strainmeter at Guza station before the Wenchuan earthquake are characterized by pulses or steps of much contraction and little expansion with respect to areal strain. The relative weight of contraction to expansion does not appear evenly nor randomly during the time but seemingly reflects the preparation process of the seismic event and, after the first increasing stage, goes in a convergent trend toward the normal level at the main shock instant. Upon on the concepts of Overrun Rates both for number and strength of overrun points of standard deviation, some tentative approaches are tested in order to biuld a time-pointer for retrospectively forecasting the disastrous earthquake according to the trend. The results are fairly promising with proper working cutoff period of high-pass filter.
Spatially growing disturbances in an alongshore current are considered. In many other types of shear flows these spatially growing modes describe the initial development of instabilities more satisfactorily than do the more commonly considered temporally growing modes. Here the spatial stability theory is applied to these wave-driven, semi-infinite types of flows for the first time. Both model [Thornton and Guza, 1986] and measured [Reniers et al., 1994] longshore current and beach profiles are analyzed, using both the temporal and spatial theories. Results of the two theories are compared using the approximate relations of Gaster . For the Thornton and Guza profile, predictions of the spatial theory and those from the transformed temporal theory are seen to be extremely close. For the profile of Reniers et al., which exhibited destabilization and spatially growing instabilities, the two sets of predictions are again very close. This implies that the simpler temporal stability theory, which has been used exclusively in previous studies, may be applied even when the spatial theory would clearly be more appropriate (such as in the experimental study examined here) by transforming the temporal predictions via Gaster's relations. Moreover, it appears that the predicted wavelength and period of the fastest growing mode (FGM) of untransformed temporal theory will be fairly good indicators of the same quantities for spatial modes and perhaps may be used as such when estimates of the group velocity from the temporal theory cannot be made with much certainty, such as when points are very sparse. It is shown that the basic structure of the fastest growing disturbance or mode (FGM) is similar for both theories for the Reniers et al. profile, although it would be a mistake to rely on the details of the linear eigenfunctions given by temporal theory.
Dodd, N.; FalquéS, A.
The investigation of anomalously large amplitude surface gravity waves on the sea surface (rogue or freak waves), which can appear suddenly and disappear in the same abrupt way, is very extensive in the recent years (see e.g., book [Kharif, Pelinovsky, Slunyaev 2009] and references there). However, any sudden displacements of water level or changes in flow velocities can also appear in the ocean wave motions of other types, including geophysical large-scale fields. The number of observations of such waves is still very small, they are even almost absent, but the investigations of such possible processes seem to be important for the applications. In the present paper the problem of rogue waves is discussed for edge waves in the coastal zone. Such waves belong to the class of topographically trapped waves, which are supposed to play dominant role in the dynamics of oceanic coastal zone. The amplitude of the waves reaches a maximum at the edge, and they are attenuated offshore. Direct visual observations of such waves are difficult, but such waves have been detected instrumentally in the nearshore wave field many times (see e.g. [Huntley and Bowen 1973; Bryan, Hows and Bowen 1998]). Edge waves are often considered as the major factor of the long-term evolution of coastal line, forming the rhythmic crescentic bars [Dolan and Ferm 1968; Bowen and Inman 1971; Guza and Inman 1975; Guza and Bowen 1981; Holman and Bowen 1982; Komar 1998]. In the present paper we summarize the results of the study of the nonlinear mechanisms of possible freak edge wave appearance: nonlinear dispersion enhancement and modulation instability.
Polukhina, Oxana; Kurkin, Andrey; Pelinovsky, Efim
Infragravity waves become increasingly important as the water depth gets shallower and wind generated waves become saturated due to wave breaking. Infragravity wave energy is composed of wave-group forced long waves and reflected leaky waves and trapped edge waves. Typically conditions on a approximately alongshore uniform beach are consisdered (e.g. Herbers et al., 1994, van Dongeren et al., 2003). Here we examine the alongshore variability in the infragravity conditions induced by nearby canyons utilizing a 2D-surfbeat model (Reniers et al., 2004). The model simulates the propagation of both leaky and trapped infragravity waves that are generated by directionally spread wave groups. Model computations are used to examine the potential reflection (Inman et al., 1976, Huntley et al., 1981) of shore-trapped edge waves from the canyon walls by considering various model-scenarios with and without the canyons. Computational results will be compared with observations of infragravity conditons obtained from an alongshore array of pressure and velocity meters situated just north of the canyon (MacMahan et al., 2004, this conference). References Herbers, T.H.C., Steve Elgar and R.T. Guza, 1994: Infragravity-frequency (0.005 0.05 Hz) motions on the shelf. Part 1: Forced waves. J. Phys. Oc., 25, 1063-1079. Huntley, D. A., R. T. Guza and E. B. Thornton, 1981, "Field Observations of Surf Beat: Part I, Progressive Edge Waves", J. Geophys. Res., 86, 6451-6466. Inman, D.L., C.E. Nordstrom and R.E. Flick, 1976: Currents in sub-marine canyons: An air-sea-land interaction, Ann. Rev. Fluid Mech., 8, 275-310. MacMahan, J., E.B. Thornton, A. Reniers and T.P. Stanton, 2004, The Torrey Pines Rip-currents, this conference. Reniers, A.J.H.M., E.B. Thornton and J.A. Roelvink, 2004: Morphodynamic modeling of an embayed beach under wave-group forcing, J. Geophys. Res., 109, C01030, doi:10.1029/2002JC001586. Van Dongeren, A.R., A.J.H.M. Reniers, J.A. Battjes and I.A. Svendsen, 2003, "Numerical modeling of infragravity wave response during Delilah." J. Geoph. Res, 108 (C9), 4-1-19
Reniers, A.; Macmahan, J.; Thornton, E.; Stanton, T.
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. Zegarli?ski -- 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. Chici?ska & K. W?dkiewicz. 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.
Belavkin, V. P.; Gut?, M.
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.
Bennis, A.; Ardhuin, F.; Dumas, F.; Bonneton, P.
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.
Ludka, B. C.; Guza, R. T.; McNinch, J. E.; O'Reilly, W.