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We investigate the integrability of a class of 1+1 dimensional models describing nonlinear dispersive waves in continuous media, e.g. cylindrical compressible hyperelastic rods, shallow water waves, etc. The only completely integrable cases…
We derive a simple algebraic form of the nonlinear wavenumber correction of surface gravity waves in deep water, based on temporal measurements of the water surface and the spatial Zakharov equation. This allows us to formulate an…
The objective of this work is to investigate the unexplored laminar-to-turbulent transition of a heated flat-plate boundary layer with a fluid at supercritical pressure. Two temperature ranges are considered: a subcritical case, where the…
This paper presents a novel method for obtaining the probability wave of breaking ($P_b$) of deep water, dominant wind-sea waves (that is, waves made of the energy within $\pm$30\% of the peak wave frequency) derived from Gaussian wave…
Large-scale simulations of the wave equation in electromagnetism, seismology, and acoustics, can be solved efficiently by finite difference methods. The accuracy of these numerical solutions usually depends on the minimization of…
This is a study of two-dimensional steady periodic travelling waves on the surface of an infinitely deep irrotational ocean, when the top streamline is in contact with a membrane which has a nonlinear response to stretching and bending, and…
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…
In this paper we consider fundamental processes of the disturbance and propagation of internal gravity waves in the ocean modeled as a vertically stratified, horizontally non-uniform, and non-stationary medium. We develop asymptotic methods…
We present a brief discussion on the nonlinear Schr{\"o}dinger equation for modeling the propagation of the deep-water wavetrains and a discussion on its doubly-localized breather solutions that can be connected to the sudden formation of…
Dispersive averaging effects are used to show that KdV equation with periodic boundary conditions possesses high frequency solutions which behave nearly linearly. Numerical simulations are presented which indicate high accuracy of this…
Water's density maximum at 4C makes it well suited to study internal gravity wave excitation by convection: an increasing temperature profile is unstable to convection below 4C, but stably stratified above 4C. We present numerical…
The weakly nonlinear dynamics of the free surface of a dielectric liquid in an electric field directed tangentially to the unperturbed boundary is investigated numerically. Within the framework of the strong field model, when the effects of…
The propagation of wave disturbances over a vertically oscillating liquid may form standing waves, known as Faraday waves. Here we present an alternative description of the generation and evolution of Faraday waves by nonlinear resonant…
Three-dimensional turbulence is usually studied experimentally by using a spatially localized forcing at large scales (e.g. via rotating blades or oscillating grids), often in a deterministic way. Here, we report an original technique where…
In this paper we discuss a theoretical model for the interfacial profiles of progressive non-linear waves which result from introducing a triangular obstacle, of finite height, attached to the bottom below the flow of a stratified, ideal,…
In this paper we construct a new solution which represents Pollard-like three-dimensional nonlinear geophysical internal water waves. The Pollard-like solution includes the effects of the rotation of Earth and describes the internal water…
This paper aims to give a refined wave breaking description of the Cauchy problem to the one-dimensional nonlinear shallow water equations providing a sharp estimate of the lifespan of the solutions depending on the amplitude and topography…
The impact of a plunging breaker on a partially submerged cube is explored experimentally in a wave tank equipped with a programable wave maker. The experiments are conducted with the cube (dimension $L=30.48$ cm) positioned at one…
Process of the nonlinear deformation of the surface wave in shallow water is studied. Main attention is paid to the relation between the Fourier-spectrum and wave steepness. It is shown that the spectral harmonics of the initially sine wave…
To investigate the formation mechanism of energy spectra of internal waves in the oceans, direct numerical simulations are performed. The simulations are based on the reduced dynamical equations of rotating stratified turbulence. In the…