Twisting of a fire vortex subject to gravity and Coriolis forces

A set of gas dynamics equations for an ideal polytropic gas is considered in the isentropic case subject to gravity and Coriolis forces. For this system a special characteristic Cauchy problem is formulated, the solution of which described the motion of air, which is originally motionless in the field of gravity, during smooth heating of a vertical cylinder placed in it. It is proved that the formulated problem in some neighborhood of a point under consideration has a unique analytical solution in the form of a convergent series subject to the analyticity of the basic data. Analysis of the first coefficients of this series showed that heating the cylinder in air causes a circular gas motion swirling in the negative direction in the Northern Hemisphere and in the positive direction in the Southern Hemisphere. The facts ascertained are mathematical justification of the direction of twisting of fire vortices.