Related papers: Serre-type equations in deep water
A model for the wave motion of an internal wave in the presence of current in the case of intermediate long wave approximation is studied. The lower layer is considerably deeper, with a higher density than the upper layer. The flat surface…
The classical system of shallow-water (Saint--Venant) equations describes long surface waves in an inviscid incompressible fluid of a variable depth. Although shock waves are expected in this quasilinear hyperbolic system for a wide class…
During the past decade a number of attempts to formulate a continuum description of complex states of matter have been proposed to circumvent more cumbersome many-body and simulation methods. Typically these have been quantum systems (e.g.,…
A recently developed method has been extended to a nonlocal equation arising in steady water wave propagation in two dimensions. We obtain analyic approximation of steady water wave solution in two dimensions with rigorous error bounds for…
The Serre-Green-Naghdi (SGN) equations provide a valuable framework for modelling fully nonlinear and weakly dispersive shallow-water flows. However, their elliptic formulation can considerably increase the computational cost compared to…
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…
The multiscale patch scheme is built from given small micro-scale simulations of complicated physical processes to empower large macro-scale simulations. By coupling small patches of simulations over unsimulated spatial gaps, large savings…
In this work, we study the generalized shallow water wave equation to obtain novel solitary wave solutions. The application of this non-linear model can be found in tidal waves, weather simulations, tsunami prediction, river and irrigation…
This article provides a reduced-order modelling framework for turbulent compressible flows discretized by the use of finite volume approaches. The basic idea behind this work is the construction of a reduced-order model capable of providing…
We focus here on the water waves problem for uneven bottoms in the long-wave regime, on an unbounded two or three-dimensional domain. In order to derive asymptotic models for this problem, we consider two different regimes of bottom…
We consider Euler's equations for free surface waves traveling on a body of density stratified water in the scenario when gravity and surface tension act as restoring forces. The flow is continuously stratified, and the water layer is…
The evolution of random wave fields on the free surface is a complex process which is not completely understood nowadays. For the sake of simplicity in this study we will restrict our attention to the 2D physical problems only (i.e. 1D wave…
Equations for the wave-averaged three-dimensional momentum equations have been published in this journal. It appears that these equations are not consistent with the known depth-integrated momentum balance, especially over a sloping bottom.…
We propose the use of physics-informed neural networks for solving the shallow-water equations on the sphere in the meteorological context. Physics-informed neural networks are trained to satisfy the differential equations along with the…
We present a theoretical and numerical framework -- which we dub the Direct Integration Method (DIM) -- for simple, efficient and accurate evaluation of surface wave models allowing presence of a current of arbitrary depth dependence, and…
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 formulate a new approach to solving the initial value problem of the shallow water-wave equations utilizing the famous Carrier-Greenspan transformation [G. Carrier and H. Greenspan, J. Fluid Mech. 01, 97 (1957)]. We use a Taylor series…
In this article we consider the multi-layer shallow water system for the propagation of gravity waves in density-stratified flows, with additional terms introduced by the oceanographers Gent and McWilliams in order to take into account…
In the framework of the canonical model of hydrodynamics, where fluid is assumed to be ideal and incompressible, waves are potential, two-dimensional, and symmetric, the authors have recently reported the existence of a new type of gravity…
We explore the utility of the recently proposed alpha equations in providing a subgrid model for fluid turbulence. Our principal results are comparisons of direct numerical simulations of fluid turbulence using several values of the…