Related papers: Near Critical Reflection of Internal Waves

Internal waves describe the (linear) response of an incompressible stably stratified fluid to small perturbations. The inclination of their group velocity with respect to the vertical is completely determined by their frequency. Therefore…

An experimental study is reported of the near-critical reflection of internal gravity waves over sloping topography in a stratified fluid. An overturning instability close to the slope and triggering the boundary-mixing process is observed…

The aim of this work is to make a further step towards the understanding of the near-critical reflection of internal gravity waves from a slope in the more general and realistic context where the size of viscosity $\nu$ and the size of…

A wave equation for a time-dependent perturbation about the steady shallow-water solution emulates the metric an acoustic white hole, even upon the incorporation of nonlinearity in the lowest order. A standing wave in the sub-critical…

Linear waves in bounded inviscid fluids do not generally form normal modes with regular eigenfunctions. Examples are provided by inertial waves in a rotating fluid contained in a spherical annulus, and internal gravity waves in a stratified…

Preservation of the angle of reflection when an internal gravity wave hits a sloping boundary generates a focusing mechanism if the angle between the direction of propagation of the incident wave and the horizontal is close to the slope…

We prove local higher-order asymptotics for extreme water waves with vorticity near stagnation points. We obtain that the behaviour of solutions and their regularity depend substantially on the vorticity. In particular, we show that extreme…

Bifurcations of solitary waves propagating along the interface between two ideal fluids are considered. The study is based on a Hamiltonian approach. It concentrates on values of the density ratio close to a critical one, where the…

Nonlinear acoustic evolution is often discussed in the context of wave-steepening that leads to shock formation, and is of special interest in applications where the shock continues to strengthen due to a narrowing of its channel or the…

A weakly nonlinear study is numerically conducted to determine the behaviour near the onset of convection in rotating spherical shells. The mathematical and numerical procedure is described in generality, with the results presented for an…

A reduced dynamical model is derived which describes the interaction of weak inertia-gravity waves with nonlinear vortical motion in the context of rotating shallow-water flow. The formal scaling assumptions are (i) that there is a…

Internal waves propagate obliquely through a stratified fluid with an angle that is fixed with respect to gravity. Upon reflection on a sloping bed, striking phenomena are expected to occur close to the slope. We present here laboratory…

This paper investigates the nonlinear dynamics of Newton's problem of minimal resistance in radial fields. We move beyond classical translational symmetry to analyze two non-equilibrium scenarios: a scale-invariant free expansion and an…

We study both analytically and numerically the nonlinear stage of the instability of one-dimensional solitons in a small vicinity of the transition point from supercritical to subcritical bifurcations in the framework of the generalized…

Internal gravity waves are an essential feature of stratified media, such as oceans and atmospheres. To investigate their dynamics, we perform simulations of the forced-dissipated kinetic equation describing the evolution of the energy…

The shear resulting from internal wave reflections can play a crucial role in the transport and resuspension of sediments in oceanic conditions. In particular, when these waves undergo a \textit{critical reflection} phenomenon, the…

In this article we consider the inviscid two-dimensional shallow water equations in a rectangle. The flow occurs near a stationary solution in the so called supercritical regime and we establish short term existence of smooth solutions for…

In this paper we construct small amplitude periodic internal waves traveling at the boundary region between two rotational and homogeneous fluids with different densities. Within a period, the waves we obtain have the property that the…

We investigate strongly nonlinear stationary gravity waves which experience refraction due to a thin vertical shear layer of horizontal background wind. The velocity amplitude of the waves is of the same order of magnitude as the background…

The present study focuses on the interaction of gravity waves in the atmosphere with the tropopause. As the vertical extent of the latter is small compared to the density scale height, wave propagation is described by the Taylor-Goldstein…