Related papers: Shallow-water models for a vibrating fluid
We study free surface water waves in a 2-D symmetric triangular channel with sides that have a 45o slope. We develop models for small amplitude nonlinear waves, extending earlier studies that have considered the linearized problem. We see…
In this paper a rotating two-fluid model for the propagation of internal waves is introduced. The model can be derived from a rotating-fluid problem by including gravity effects or from a nonrotating one by adding rotational forces in the…
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…
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 order to improve the frequency dispersion effects of irrotational shallow water models in coastal oceanography, several full dispersion versions of classical models were formally derived in the literature. The idea, coming from G.…
We study a system of forced viscous shallow water equations with nontrivial bathymetry in two spatial dimensions. We develop a well-posedness theory for small but arbitrary forcing data, as well as for a fixed data profile but large…
We study periodic, two-dimensional, gravity-capillary traveling wave solutions to a viscous shallow water system posed on an inclined plane. While thinking of the Reynolds and Bond numbers as fixed and finite, we vary the speed of the…
We derive transport equations for the propagation of water wave action in the presence of a static, spatially random surface drift. Using the Wigner distribution $\W(\x,\k,t)$ to represent the envelope of the wave amplitude at position $\x$…
In the linear approximation, we study a one-dimensional problem of the reflectionless wave propagation on a surface of a shallow duct with the spatially varying water depth, duct width, and current. We show that both global and bounded…
Our aim is to study the effect of a continuous prescribed density variation on the propagation of ocean waves. More precisely, we derive KdV-type shallow water model equations for unidirectional flows along the Equator from the full…
The purpose of this paper is to derive rigorously the so called viscous shallow water equations given for instance page 958-959 in [A. Oron, S.H. Davis, S.G. Bankoff, Rev. Mod. Phys, 69 (1997), 931?980]. Such a system of equations is…
Effective field theory descriptions of surface waves on flowing fluids have tended to assume that the flow is irrotational, but this assumption is often impractical due to boundary layer friction and flow recirculation. Here we develop an…
Stability of inviscid shear shallow water flows with free surface is studied in the framework of the Benney equations. This is done by investigating the generalized hyperbolicity of the integrodifferential Benney system of equations. It is…
We describe traveling waves in a basic model for three-dimensional water-wave dynamics in the weakly nonlinear long-wave regime. Small solutions that are periodic in the direction of translation (or orthogonal to it) form an…
We derive the dispersion relation for linearized small-amplitude gravity waves for various choices of non-constant vorticity. To the best of our knowledge, this relation is only known explicitly in the case of constant vorticity. We provide…
In this paper, we review the history and current state-of-the-art in the modelling of long nonlinear dispersive waves. For the sake of conciseness of this review, we omit the unidirectional models and focus especially on some classical and…
The asymptotic derivation of a new family of one-dimensional, weakly nonlinear and weakly dispersive equations that model the flow of an ideal fluid in an elastic vessel is presented. Dissipative effects due to the viscous nature of the…
In this paper we study the behavior of an incompressible viscous fluid moving between two very close surfaces also in motion. Using the asymptotic expansion method we formally justify two models, a lubrication model and a shallow water…
Viscous linear surface waves are studied at arbitrary wavelength, layer thickness, viscosity and surface tension. We find that in shallow enough fluids no surface waves can propagate. This layer thickness is determined for some fluids,…
In the linear approximation we study long wave scattering on an axially symmetric flow in a shallow water basin with a drain in the center. This classical problem can be considered as a model of wave scattering on a rotating black hole. For…