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- Shallow_water_equations abstract "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.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 of the fluid is small. 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.While a vertical velocity term is not present in the shallow water equations, note that this velocity is not necessarily zero. This is an important distinction because, for example, the vertical velocity cannot be zero when the floor changes depth, and thus if it were zero only flat floors would be usable with the shallow water equations. Once a solution (i.e. the horizontal velocities and free surface displacement) has been found, the vertical velocity can be recovered via the continuity equation.Situations in fluid dynamics where the horizontal length scale is much greater than the vertical length scale are common, so the shallow water equations are widely applicable. They are used with Coriolis forces in atmospheric and oceanic modeling, as a simplification of the primitive equations of atmospheric flow.Shallow water equation models have only one vertical level, so they cannot directly encompass any factor that varies with height. However, in cases where the mean state is sufficiently simple, the vertical variations can be separated from the horizontal and several sets of shallow water equations can describe the state.".
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- Shallow_water_equations wikiPageExternalLink shallowgov.pdf.
- Shallow_water_equations wikiPageID "8631522".
- Shallow_water_equations wikiPageRevisionID "604118385".
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- Shallow_water_equations subject Category:Equations_of_fluid_dynamics.
- Shallow_water_equations subject Category:Partial_differential_equations.
- Shallow_water_equations subject Category:Water_waves.
- Shallow_water_equations type Abstraction100002137.
- Shallow_water_equations type Communication100033020.
- Shallow_water_equations type DifferentialEquation106670521.
- Shallow_water_equations type Equation106669864.
- Shallow_water_equations type EquationsOfFluidDynamics.
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- Shallow_water_equations type PartialDifferentialEquation106670866.
- Shallow_water_equations type PartialDifferentialEquations.
- Shallow_water_equations type PsychologicalFeature100023100.
- Shallow_water_equations type Statement106722453.
- Shallow_water_equations type WaterWaves.
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- Shallow_water_equations comment "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).".
- Shallow_water_equations label "Shallow water equations".
- Shallow_water_equations label "Уравнения мелкой воды".
- Shallow_water_equations sameAs m.027bs5n.
- Shallow_water_equations sameAs Q4476546.
- Shallow_water_equations sameAs Q4476546.
- Shallow_water_equations sameAs Shallow_water_equations.
- Shallow_water_equations wasDerivedFrom Shallow_water_equations?oldid=604118385.
- Shallow_water_equations depiction Shallow_water_waves.gif.
- Shallow_water_equations isPrimaryTopicOf Shallow_water_equations.
