Wave breaking for a shallow water equation - ScienceDirect
2004年4月1日 · In this paper, we consider the following shallow water equation: (1.1) u t −u xxt +3uu x =2u x u xx +uu xxx, t>0,x∈ R, u (x,0)=u 0 (x), x∈ R. System (1.1) models wave motion in shallow water with u denoting the height of the water above a flat bottom, cf. [2].
Shallow-water wave theory - Coastal Wiki
As waves approach a shoreline, their height and wavelength are altered by the processes of refraction and shoaling before breaking on the shore. Once waves have broken, they enter what is termed the surf zone.
Wave breaking to a shallow water wave equation involving the …
2023年1月25日 · A nonlinear shallow water wave model involving the Fornberg-Whitham equation is investigated. From the equation itself, we derive several estimates, which are helpful to study the dynamical properties of its solutions. Finally, we give conditions on …
High order shallow water equations: application to dam break …
6 天之前 · 1. INTRODUCTION. The initial formulation of the shallow water equations was presented by de Saint-Venant [].Shallow water models, also referred to as first-order long wave approximation models, are hyperbolic systems with a diverse range of applications, including dam break modeling, tsunami prediction, flood management, hydraulic jump …
Wave Breaking for a Nonlinear Shallow Water Equation
2022年7月24日 · In this paper, we mainly study wave breaking for a nonlinear shallow water equation which describes the surface water waves of moderate amplitude in shallow water regime. We present a sufficient condition on the initial data to lead to wave breaking.
Wave breaking in the Whitham equation - ScienceDirect
2017年9月7日 · We prove wave breaking — bounded solutions with unbounded derivatives — in the nonlinear nonlocal equation which combines the dispersion relation of water waves and a nonlinearity of the shallow water equations, provided that the slope of the initial datum is sufficiently negative, whereby we solve a Whitham's conjecture.
2007年3月13日 · This paper is devoted to the study of a recently derived periodic shallow water equation. We discuss in detail the blow-up scenario of strong solutions and present several conditions on the initial profile, which ensure the occurrence of wave breaking. We also present a family of global weak solutions, which may be viewed as global periodic shock
Wave breaking to a shallow water wave equation involving the …
2023年1月1日 · This paper focuses on obtaining traveling wave solutions of the Fornberg–Whitham model derived from Gilson–Pickering equations, which describe the prorogation of waves in crystal lattice theory and …
A Shallow Water Model: Analytical and Numerical Study for
5 天之前 · Jones, C.: Shallow water equations and floor topography on sea surface. ... Lencina, I.V.: Comparison between 1D and 2D models to analyze the dam break wave using the FEM method and the shallow water equations (2007). ISSN 1651-064X. Google Scholar COMSOL Multiphysics Reference Manual. https://doc.comsol.com. Download references ...
Wave-breaking phenomena for a weakly dissipative shallow water equation ...
2020年5月29日 · Consideration in the present paper is a weakly dissipative shallow water equation. The parameters take different values, which include several different important shallow water equations, such as CH equation, DP equation, Novikov equation and so on. The wave-breaking phenomena are investigated by three different kinds of method.