Channel flow over curved boundaries and a new hydraulic theory

Dressler (1978) derived the St Venant long wave equations for two-dimensional irrotational flow over curved boundaries using orthogonal curvilinear coordinates based on the channel bottom. These equations are considerably more complicated than those in the cartesian system, but they do contain contributions to the pressure and the governing equations from the curvature of the bed, which does not occur in the cartesian formulation at the same level of approximation. Similarly, Chapman and Dressler (1984) obtained the shallow water equations for unsteady shallow groundwater flow with a free surface over a curved impermeable boundary. In both these cases, the flow was assumed to be irrotational, which is well-known to be justified in the case of seepage flow and for wave motion on otherwise quiescent fluid, but not so justified in the case of fast hydraulic flows such as over spillways.