Unidirectional stratified flow through a non-rectangular channel

A self-similar solution describing stratified flow through a non-rectangular channel is derived. The solution shown here is an extension of Wood's (1968) solution for stratified withdrawal through a rectangular channel. We consider a restricted set of geometries (where the bottom of the channel is constrained to be flat) and calculate the flow, assuming first multi-layer stratification, and second continuous stratification. In the case of two-layer flow we prove that the self-similar solution is the only possible solution. The analytical solutions are corroborated by three-dimensional numerical model simulations.