Modified shallow water equations. Simple waves and Riemann problem

Abstract

In this article gas-dynamic analogy for shallow water equations is generalized in the case when initial conditions depend on vertical coordinate. Simple parametrization of advective term allowing full theoretical analysis of solutions of simple waves of Riemann problem for modified shallow water equations is suggested. The simple wave solutions obtained have permitted to find dimensionless parameter, which restricts limits of applicability of classical shallow water equations and neglecting advective impulse transfer. Solution of the initial discontinuity decay problem for modified shallow water equations is found. © 2008 Springer.