Quasi-linear equations of dynamics of internal solitary waves in multilayer shallow water

A non-homogeneous system of one-dimensional conservation laws is proposed, which describes propagation of large-amplitude bottom (subsurface) internal waves in multilayer stratified shallow water in the Boussinesq approximation. The model can be applied to layered flows of a stably stratified fluid and is hyperbolic for moderate velocity shear in the layers. Steady solutions of equations of motion are studied, and conditions for the formation of solitary waves of the first mode are formulated. The model is verified by means of comparing the results predicted by this model with the results of actual observations and calculations of two-dimensional equations of motion. Propagation of unsteady nonlinear wave packets in a multilayer fluid is numerically simulated.