Related papers: Long ring waves in a stratified fluid over a shear…

We study long surface and internal ring waves propagating in a stratified fluid over a parallel shear flow. The far-field modal and amplitude equations for the ring waves are presented in dimensional form. We re-derive them from the…

Oceanic internal waves often have curvilinear fronts and propagate over various currents. We present the first study of long weakly-nonlinear internal ring waves in a three-layer fluid in the presence of a background linear shear current.…

We consider a two-layer fluid with a depth-dependent upper-layer current (e.g. a river inflow, an exchange flow in a strait, or a wind-generated current). In the rigid-lid approximation, we find the necessary singular solution of the…

Surface and interfacial weakly-nonlinear ring waves in a two-layer fluid are modelled numerically, within the framework of the recently derived 2+1-dimensional cKdV-type equation. In a case study, we consider concentric waves from a…

In this work, we study the nonlinear traveling waves in density stratified fluids with depth varying shear currents. Beginning the formulation of the water-wave problem due to [1], we extend the work of [4] and [18] to examine the interface…

We study dispersion properties of linear surface gravity waves propagating in an arbitrary direction atop a current profile of depth-varying magnitude using a piecewise linear approximation, and develop a robust numerical framework for…

The interaction of surface waves with Couette-type current with uniform vorticity is a well suited problem for students approaching the theory of surface waves. The problem, although mathematically simple, contains rich physics, and is…

We investigate the weakly nonlinear dynamics of transient gravity waves at infinite depth under the influence of a shear current varying linearly with depth. An analytical solution is permitted via integration of the Euler equations.…

Long waves in shallow water propagating over a background shear flow towards a sloping beach are being investigated. The classical shallow-water equations are extended to incorporate both a background shear flow and a linear beach profile,…

We analytically study a scattering of long linear surface waves on stationary currents in a duct (canal) of constant depth and variable width. It is assumed that the background velocity linearly increases or decreases with the longitudinal…

We report experimental observations of two canonical surface wave patterns --- ship waves and ring waves --- skewed by sub-surface shear, thus confirming effects predicted by recent theory. Observed ring waves on a still surface with…

By using the multiple scale method with the simultaneous introduction of multiple times, we study the propagation of long surface-waves in a shallow inviscid fluid. As a consequence of the requirements of scale invariance and absence of…

We present a large-amplitude existence theory for two-dimensional solitary waves propagating through a two layer body of water. The domain of the fluid is bounded below by an impermeable flat ocean floor and above by a free boundary at…

In the context of fluid flows, the coupled Ostrovsky equations arise when two distinct linear long wave modes have nearly coincident phase speeds in the presence of background rotation. In this paper, nonlinear waves in a stratified fluid…

In this paper we present an experimental study of the long surface wave instability that can develop when a granular material flows down a rough inclined plane. The threshold and the dispersion relation of the instability are precisely…

The currents in the ocean have a serious impact on ocean dynamics, since they affect the transport of mass and thus the distribution of salinity, nutrients and pollutants. In many physically important situations the current depends…

A coupled system composed of a Newtonian fluid located on a sinusoidally-forced elastic solid is studied analytically and numerically. The focus is on the transient evolution from the beginning of the forced oscillations and on the periodic…

Motivated by observations of turbulence in the strongly stratified ocean thermocline, we use direct numerical simulations to investigate the interaction of a sinusoidal shear flow and a large-amplitude internal gravity wave. Despite strong…

The aim of this paper is to give a detailed presentation of long wave instabilities of shear layers for Navier Stokes equations, and in particular to give a simple and easy to read presentation of the study of Orr Sommerfeld equation and to…

Variable-coefficient Korteweg - de Vries equation is applied to describe the interfacial wave transformation in two-layer fluid of variable depth. The soliton dynamics in this fluid is studied. The solitary wave breaks in two transient…