DYNAMICS OF FINITE-DIFFERENCE MODELS OF THE SHALLOW-WATER EQUATIONS.

Abstract

Two simple numerical models of the shallow-water equations identical in all respects but for their conservation properties have been tested regarding their internal mixing processes. The experiments show that violation of entropy conservation results in a spurious accumulation of rotational energy in the smaller scales, reflected by an unrealistic increase of entropy, which ultimately produces a finite rate of energy dissipation in the zero viscosity limit, thus violating the well-known dynamics of two-dimensional flow. Further, the experiments show a tendency to equipartition of the kinetic energy of the divergent part of the flow in the inviscid limit, suggesting the possibility of a divergent energy cascade in the physical system, as well as a possible influence of the energy mixing on the process of adjustment toward balanced flow.