THE ELLIPTICITY CONDITION OF THE MONGE-AMPERE EQUATION IN THE SOLENOIDAL MODEL

摘要

The aim of the present paper is to discuss the influence of the ellipticity condition of the momentum divergence equation on the solution of non-divergent equation of the solenoidal or geostrophic models in the barotropic approaches. The equation considered is a nonlinear differential equation of Monge-Ampere type used for determining a streamfunction field if the geopotential field is known. It is obtained by transforming the governing equations and assuming that the divergence of wind field is equal to zero. The nonlinear balance equation is a part of the general system equations describing quasi-solenoidal or quasi-geostrophic models. Making use of the real aerological measurement data furnished by the international GRID network, the Monge-Ampere equation has been solved numerically together with the solenoidal model in barotropic approximation (a forecast for 12 hours). The results may be treated as a stage in the search for a relation between the numerical results and the processes observed in the satellite pictures. The position of the prognostic relative rotation contour line of zero (Ω = 0) may be used for determining the direction of movement of a front cloud belt.