Oblique nonlinear interaction of two incident solitary waves, or soliton resonance, is important because it can produce a third solitary wave that has an amplitude up to 4 times the incident wave amplitude. Although this process is well studied for surface waves and in other fields of physics such as plasma, it has not been well studied for internal solitary-like waves (ISWs) in the ocean. In t...

Abstract

Under suitable assumptions, the nonlinear dynamics of surface gravity waves can be modeled by the one-dimensional nonlinear Schrödinger equation. Besides traveling wave solutions like solitons, this model admits also breather solutions that are now considered as prototypes of rogue waves in ocean. We propose a novel technique to study the interaction between waves and ships/structures during ex...

A specific, genuinely three-dimensional mechanism of rogue wave formation, in a late stage of the modulational instability of a perturbed Stokes deep-water wave, is recognized through numerical experiments. The simulations are based on fully nonlinear equations describing weakly three-dimensional potential flows of an ideal fluid with a free surface in terms of conformal variables. Spontaneous ...

Interacting ocean surface waves force water column pressure fluctuations with spectral peaks at the same frequencies of primary microseisms (PM), double-frequency microseisms (DF), and seismic hum. Prior treatment of nonlinear ocean wave interactions has focused on the DF pressure fluctuations which, in the presence of opposing waves, do not decay with depth and hence are dominant in deep water...

We study the modulational instability in surface gravity waves with random phase spectra. Starting from the nonlinear Schrödinger equation and using the Wigner-Moyal transform, we study the stability of the narrow-banded approximation of a typical wind-wave spectrum, i.e., the JONSWAP spectrum. By performing numerical simulations of the nonlinear Schrödinger equation we show that in the unstabl...

Recent achievements of nonlinear acoustics concerning the realization of solitons and solitary waves in crystals and their surfaces attained by nanosecond and picosecond laser ultrasonics are discussed and compared. The corresponding pump-probe setups are described, which allow an all-optical contact-free excitation and detection of short strain pulses in the broad frequency range between 10 MH...

Three–wave nonlinear resonant interaction (TWRI) is typically encountered in the description of any conservative nonlinear medium where the nonlinear dynamics can be considered as a perturbation of the linear wave solution, the lowest–order nonlinearity is quadratic in the field amplitudes, the three–wave resonance can be satisfied [1]. Indeed TWRI is the lowest–order nonlinear effect for a sys...

Rogue waves is the name given by oceanographers to isolated large amplitude waves, that occur more frequently than expected for normal, Gaussian distributed, statistical events. Rogue waves are ubiquitous in nature and appear in a variety of different contexts. Besides water waves, they have been recently reported in liquid Helium, in nonlinear optics, microwave cavities, etc. The first part of...

It is demonstrated that nonlinear properties of a thin film coating a lrnear elastic substrate may lead to the creation of a new type of surface acoustic waves which may exist at the condition c: cc:, where c, and crare the velocities in the substrate and the film, respectively. These waves appear when the amplitude at the surface exceeds a certain threshold value and for a definite sign of the...