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The shallow Water Equations! The shallow water equations are derived from equations of conservation of mass and conservation of linear momentum (the Navier–Stokes equations), which hold even when the assumptions of shallow water break down, such as across a hydraulic jump. In the case of a horizontal bed, no Coriolis forces, frictional or viscous forces. page 1: Here η is the total fluid column height (instantaneous fluid depth as a function of x, y and t), and the 2D vector (u,v) is the fluid's horizontal flow velocity, averaged across the vertical column. Further g is acceleration due to gravity and ρ is the fluid density. The first equation is derived from mass conservation, the second two from momentum conservation. page 2: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. page 3:Animation of the linearized shallow-water equations for a rectangular basin, without friction and Coriolis force. The water experiences a splash which generates surface gravity waves that propagate away from the splash location and reflect off the basin walls. #cfdlab #computationalfluiddynamics #laminar #turbulence #fluidmotion #equation#reynolds #validation #verification #openfoam #ansys #cfx #fluent #fluidmechanic #heattransfer #comsol #cfd #art #love #math #fortran #modeling #laminar #turbulence #experiment #Shallowwaterequations #math

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