Search results
Results from the WOW.Com Content Network
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 ...
Mild-slope equation – Physics phenomenon and formula; Shallow water equations – Set of partial differential equations that describe the flow below a pressure surface in a fluid; Stokes drift – Average velocity of a fluid parcel in a gravity wave; Undertow (water waves) – Return flow below nearshore water waves.
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 the right-hand sides of the above equations are set to zero, they reduce to the shallow water equations. Under some additional approximations, but at the same order of accuracy, the above set A can be reduced to a single partial differential equation for the free surface elevation η {\displaystyle \eta } :
In shallow water, the group velocity is equal to the shallow-water phase velocity. This is because shallow water waves are not dispersive. In deep water, the group velocity is equal to half the phase velocity: {{math|c g = 1 / 2 c p. [7] The group velocity also turns out to be the energy transport velocity.
Propagation of shoaling long waves, showing the variation of wavelength and wave height with decreasing water depth.. In fluid dynamics, Green's law, named for 19th-century British mathematician George Green, is a conservation law describing the evolution of non-breaking, surface gravity waves propagating in shallow water of gradually varying depth and width.
shallow-water waves with weakly non-linear restoring forces, long internal waves in a density-stratified ocean, ion acoustic waves in a plasma, acoustic waves on a crystal lattice. The KdV equation can also be solved using the inverse scattering transform such as those applied to the non-linear Schrödinger equation.