Shallow water equations

（重定向自Shallow water model）

Output from a shallow water equation model of water in a bathtub. The water experiences five splashes which generate surface gravity waves that propagate away from the splash locations and reflect off the bathtub walls.

Tsunami generation and propagation, as computed with the shallow water equations (red line; without frequency dispersion)), and with a Boussinesq-type model (blue line; with frequency dispersion). Observe that the Boussinesq-type model (blue line) forms a soliton with an oscillatory tail staying behind. The shallow water equations (red line) form a steep front, which will lead to bore formation, later on. The water depth is 100 meters.

The shallow water equations (also called Saint-Venant equations in its unidimensional form, after Adhémar Jean Claude Barré de Saint-Venant) are a set of hyperbolic partial differential equations (or parabolic if viscous shear is considered) that describe the flow below a pressure surface in a fluid (sometimes, but not necessarily, a free surface). The shallow water equations can also be simplified to the commonly used 1-D Saint-Venant equation.

单词	Shallow water model
释义	Shallow water model 英语百科 Shallow water equations （重定向自Shallow water model） The shallow water equations (also called Saint-Venant equations in its unidimensional form, after Adhémar Jean Claude Barré de Saint-Venant) are a set of hyperbolic partial differential equations (or parabolic if viscous shear is considered) that describe the flow below a pressure surface in a fluid (sometimes, but not necessarily, a free surface). The shallow water equations can also be simplified to the commonly used 1-D Saint-Venant equation.
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