Nonlinear dynamics of flows of a heavy compressible gas in the shallow water approximation

Abstract

The system of the equations of motion for a compressible gas in the gravitational field over a smooth underlying surface has been analyzed in the shallow water approximation. All continuous centered self similar solutions and all discontinuous self similar solutions have been obtained. The problem of the decay of an arbitrary discontinuity for the equations of motion of the compressible gas has been solved in the explicit form in the shallow water approximation. The existence of four different configurations implement ing the solution of the problem of the decay of an arbitrary discontinuity has been demonstrated. The condi tions necessary and sufficient for the implementation of each configuration have been determined.

Russian National Report: Meteorology and Atmospheric Sciences

“…Different aspects of planetary boundary layer described in the shallow-water approximation are studied in the frame of a finite-volume numerical method [Karelsky et al, 2012Chernyak et al, 2013].…”