Particular solutions and Riemann problem for modified shallow water equations

In this article gas-dynamic analogy for shallow water equations is generalized in the case when initial conditions depend on vertical coordinate. Simple parameterization of advective term allowing full theoretical analysis of solutions of simple waves and 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.