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The shallow-water equations in unidirectional form are also called (de) Saint-Venant equations, after Adhémar Jean Claude Barré de Saint-Venant (see the related section below). The equations are derived [ 2 ] from depth-integrating the Navier–Stokes equations , in the case where the horizontal length scale is much greater than the vertical ...
It 2D hydrodynamics module, TELEMAC-2D, solves the so-called shallow water equations, also known as the Saint Venant equations.TELEMAC-2D solves the Saint-Venant equations using the finite-element or finite-volume method and a computation mesh of triangular elements.
#!/usr/bin/env python2.7 """ Make an animation of the linear shallow-water equations in 2D Based on the exact solution for axisymmetrical waves in: G. F. Carrier and H. Yeh (2005) Tsunami propagation from a finite source.
The mathematical model is the 2D shallow water wave equation. As such it cannot resolve vertical convection and consequently not breaking waves or 3D turbulence (e.g. vorticity). All spatial coordinates are assumed to be UTM (meters). As such, ANUGA is unsuitable for modelling flows in areas larger than one and half UTM zones (9 degrees wide).
His later paper in 1940 [5] relaxed this theory from 2D flow to quasi-2D shallow water equations on a beta plane. In this system, the atmosphere is separated into several incompressible layers stacked upon each other, and the vertical velocity can be deduced from integrating the convergence of horizontal flow.
Boussinesq approximation (water waves) – nonlinear theory for waves in shallow water. Capillary wave – surface waves under the action of surface tension; Cnoidal wave – nonlinear periodic waves in shallow water, solutions of the Korteweg–de Vries equation; Mild-slope equation – refraction and diffraction of surface waves over varying ...
The Camassa–Holm equation can be written as the system of equations: [2] + + =, = + + (), with p the (dimensionless) pressure or surface elevation. This shows that the Camassa–Holm equation is a model for shallow water waves with non-hydrostatic pressure and a water layer on a horizontal bed.
When considering a relatively thin layer of fluid of constant density, with on the bottom a topography and on top a free surface, the shallow water approximation can be used. Using this approximation, Rossby showed in 1939, [3] by integrating the shallow water equations over the depth of the fluid, that