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Shallow-water theory is based on the assumption of a thin layer of water. In dimensional units the fluid equations can be written as ∂h/∂t + ∇ · uh = p - I and Du/Dt = - g∇h + F(u, h) where D/Dt is the total (Lagrangian) derivative, g is the acceleration of gravity, u is the fluid velocity, F(u, h) is a phenomenological term representing bottom friction, and the other quantities have already been defined in the text The equation for h can be obtained from the shallow-water equations by discarding the fluid acceleration (Du/Dt = 0) and assuming a Rayleigh friction term F(u, h) = -Ku. The parameters K and g have been scaled out from the equation for h by rescaling the spatial coordinates.
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