Evolution of assymetric swirl upward flows adjacent to vacuum

Abstract

The problems of modeling three-dimensional flows adjacent to vacuum were regarded earlier (see, for example, [1–5]). In works [1–3] onedimensional and multi-dimensional flows of polytropic and normal gas adjacent to vacuum were investigated. In works [4, 5] symmetric swirl upward flows of polytropic gas around of the vertical located contact characteristic separating the gas and vacuum were considered. It is shown that even in case the gas abuts vacuum, it swirls counterclockwise. It is also found that the vortex itself moves westward, shifting slightly northward. The present paper considers the evolution of the asymmetric gas flow at the initial time continuously adjacent to vacuum. An equation system of gas dynamics under the action of gravity and Coriolis force is adopted as a mathematical model. For the equation system of gas dynamics the initial boundary value problem is set on the multiplicity characteristic of four. The solution to the problem is created in the form of a power series and the existence and uniqueness theorem of the solution around the free surface «gas-vacuum» is proved.