Hyperbolic model of strongly nonlinear waves in two-layer flows of an inhomogeneous fluid

A mathematical model of propagation of nonlinear long waves in a two-layer shear flow of an inhomogeneous liquid with a free boundary is proposed, taking into account the effects of dispersion and mixing. The equations of fluid motion are presented in the form of a hyperbolic system of quasi-linear equations of the first order. Solutions describing damped oscillations of the internal interface are constructed in the class of traveling waves. The parameters of a two-layer flow at which the formation of large-amplitude waves is possible are found. Numerical simulation of nonstationary flows arising during the flow around a local obstacle is performed. It is shown that, depending on the velocity of the incoming flow and the shape of the obstacle, disturbances propagate upstream in the form of a monotone or wave boron.