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We review various methods for the analysis of initial-value problems for integrable dispersive equations in the weak-dispersion or semiclassical regime. Some methods are sufficiently powerful to rigorously explain the generation of…
The formulation of a canonical deep-water breaking wave problem is introduced, and the results of a set of three-dimensional numerical simulations for deep-water breaking waves are presented. In this paper fully nonlinear progressive waves…
This paper deals with the dead-water phenomenon, which occurs when a ship sails in a stratified fluid, and experiences an important drag due to waves below the surface. More generally, we study the generation of internal waves by a…
In this paper, we want to understand the Proudman resonance. It is a resonant respond in shallow waters of a water body on a traveling atmospheric disturbance when the speed of the disturbance is close to the typical water wave velocity. We…
In classical tsunami-generation techniques, one neglects the dynamic sea bed displacement resulting from fracturing of a seismic fault. The present study takes into account these dynamic effects. Earth's crust is assumed to be a…
We present a novel numerical method for simulating the generation and propagation of surface gravity waves by vertical seabed displacements. The cornerstone of our method is the computation of a time dependent conformal map which…
We investigate the potential and limitations of the wave generation by disturbances moving at the bottom. More precisely, we assume that the wavemaker is composed of an underwater object of a given shape which can be displaced according to…
This paper addresses deep-water gravity waves of finite amplitude generated by an initial disturbance to the water. It is assumed that the horizontal dimensions of the initially disturbed body of the water are much larger than the magnitude…
Lee waves generated by stratified flow over rough bottom topography in the ocean extract momentum and energy from the geostrophic flow, causing drag and enhancing turbulence and mixing in the interior ocean when they break. Inviscid linear…
We discuss the scaling laws for the flow generated in a viscous fluid by a wave propagating along a solid boundary. This has applications to the displacement of tiny objects on solids, under the effect of progressive surface waves and for…
In the present manuscript, we consider the problem of dispersive wave simulation on a rotating globally spherical geometry. In this Part IV, we focus on numerical aspects while the model derivation was described in Part III. The algorithm…
It is shown that spatially periodic one-dimensional surface waves in shallow water behave almost linearly, provided large part of the energy is contained in sufficiently high frequencies. The amplitude is not required to be small (apart…
The impact of a turbulent flow on wind-driven oceanic near-inertial waves is examined using a linearised shallow-water model of the mixed layer. Modelling the flow as a homogeneous and stationary random process with spatial scales…
We review here the derivation of many of the most important models that appear in the literature (mainly in coastal oceanography) for the description of waves in shallow water. We show that these models can be obtained using various…
We study the propagation of two-dimensional tsunami waves triggered by a seaquake in the open sea in the presence of underlying wind-generated currents, corresponding to background flows of constant vorticity. A suitable scaling of the…
In this paper we describe a method for modeling the dynamic behavior of splashing fluids. The model simulates the behavior of a fluid when objects impact or float on its surface. The forces generated by the objects create waves and splashes…
Wave propagation phenomena in soils can be experimentally simulated using centrifuge scale models. An original excitation device (drop-ball arrangement) is proposed to generate short wave trains. Wave reflections on model boundaries are…
We develop a mechanism for the controlled conversion of ballistic to diffusive motion and vice versa. This process takes place at the interfaces of domains with different time-dependent forces in lattices of laterally oscillating barrier…
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…
The present article is the third part of a series of papers devoted to the shallow water wave modelling. In this part, we investigate the derivation of some long wave models on a deformed sphere. We propose first a suitable for our purposes…