Horizontal mixing layer in shallow water flows

Horizontal-shear thin-layer homogeneous fluid flow in the open channel is considered. A one-dimensional mathematical model of the development and evolution of the horizontal mixing layer is derived within the framework of the three-layer scheme. The steady-state solutions of the equations of motion are constructed and investigated. In particular, supercritical (subcritical)-in-average flow concepts are introduced and the problem of the mixing layer structure is solved. The proposed model is verified on the basis of comparison with a numerical solution of two-dimensional equations of shallow water theory.