. Introduction  Rhythmic bed topography is observed in a wide range of systems. On river beds, dunes incident and reflected long waves on a perturbed bathymetry [see Chen and Guza, 1998].  The second
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.
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
Both oceanic observations, even in very deep water, and seismic observations, anywhere on Earth, contain low frequency noise that can be related to ocean waves. Most of the recorded noise has been explained by a nonlinear wave-wave interaction mecanism. This noise can take the form of surface gravity (Herbers and Guza 1994), acoustic (Lloyd 1981) or seismic waves (Longuet-Higgins 1950), that can be free to propagate outside of their generation area, or forced to follow their forcing wave groups. All previous theoretical work on seismic waves has been related to Rayleigh modes, while acoustic studies have only considered an ocean of infinite depth. Here we show how all types of waves: seismic waves (including Rayleigh and body waves), acoustic waves in the ocean, and surface gravity waves can be produced and estimated from directional wave spectra, using one single theory. This theory gives the known and well-verified gravity wave result, derived for incompressible motions, when taking the limit of short wave numbers. This consistent approach makes it possible to reconcile noise measurements at sea with land-based seismic data, as illustrated with data acquired in 2010 in the the southern Indian Ocean. In particular, this new dataset shows very well the presence of at least the first 4 vertical modes in a water layer of 4500 m over a uniform solid half-space, as expected from the theory by Stoneley (1926). Based on this understanding, it is possible to validate the noise sources predicted by a numerical wave model (Ardhuin et al. 2011, Schimmel et al. 2011) using locally forced gravity modes, measured with pressure sensors at depths from 10 to 300 m (Herbers and Guza 1994). Because seismic waves are caused by this same noise source, but now integrated spatially, this better knowledge of the source can be used to focus on uncertainties in the noise propagation and attenuation. In particular, there is a clear evidence from seismic stations on land, that the seismic attenuation must vary spatially.
Ardhuin, F.; Herbers, T. H. C.; Mariť, L.; Royer, J. Y.; Obrebski, M.; Stutzmann, E.; Schimmel, M.