Concept information
Terme préférentiel
shallow water equation
Définition(s)
- The shallow-water equations (SWE) 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 in unidirectional form are also called Saint-Venant equations, after Adhémar Jean Claude Barré de Saint-Venant. The equations are derived from depth-integrating the Navier–Stokes equations, in the case where the horizontal length scale is much greater than the vertical length scale. Under this condition, conservation of mass implies that the vertical velocity scale of the fluid is small compared to the horizontal velocity scale. It can be shown from the momentum equation that vertical pressure gradients are nearly hydrostatic, and that horizontal pressure gradients are due to the displacement of the pressure surface, implying that the horizontal velocity field is constant throughout the depth of the fluid. Vertically integrating allows the vertical velocity to be removed from the equations. The shallow-water equations are thus derived. (Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Shallow_water_equations)
Concept(s) générique(s)
Synonyme(s)
- Shallow water model
- Shallow water system
Traductions
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français
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équation de Barré de Saint-Venant
URI
http://data.loterre.fr/ark:/67375/MDL-ZLVZ8KQN-T
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