Evolution of the horizontal mixing layer in shallow water

Horizontal shear motion of a homogeneous fluid in an open channel is considered in the approximation of the shallow water theory. The main attention is paid to studying the mixing process induced by the development of the Kelvin–Helmholtz instability and by the action of bottom friction. Based on a three-layer flow pattern, an averaged one-dimensional model of formation and evolution of the horizontal mixing layer is derived with allowance for friction. Steady solutions of the equations of motion are constructed, and the problem of the mixing layer structure is solved. If bottom friction is taken into account, the mixing process becomes slower and the width of the intermediate mixing layer does not increase. Verification of the proposed one-dimensional model is performed through comparisons with available experimental data and with the numerical solution of the two-dimensional equations of the shallow water theory.