Release:2018, Vol. 4. №3
About the author:Irina Yu. Krutova, Cand. Sci. (Phys.-Math.), Head of the Department of Higher and Applied Mathematics, Snezhinsk Physic Institute of the National Research Nuclear University MEPhI; firstname.lastname@example.org
This article considers the differential form of physical conservation laws: a) the law of conservation of mass in the form of the continuity equation; b) the momentum conservation law is transferred by the vector equation of motion; c) and the law of conservation of energy is transferred by the energy equation, which in the case considered in the article is fulfilled identically. This relates to gas flows in at a constant value of entropy. The author studies the case of a gas with the equations of state corresponding to a polytropic gas. She has obtained a system of four nonlinear partial differential equations for the four unknown functions.
This paper deals with one gas-dynamic problem corresponding to flows in tornadoes and tropical cyclones: the problem of a radial inflow, which does not have a twist of gas both at the initial time and at the inflow boundary. The author shows that in the case of analyticity of all input data the problem posed falls under the action of the corresponding analogue of the Kowalevski theorem and, therefore, has a unique solution that can be represented as infinite convergent series. The properties of the solution are investigated in two cases: 1) neglecting the rotation of the Earth around its axis; and 2) accounting for it.
Thus, the author proves that the twist of the gas arising in the inflow problem is caused only by the rotation of the Earth around its axis. The direction of this twist is unequivocally established: anti-clockwise, if the gas flow is located in the Northern Hemisphere, and clockwise in the case of a current located in Southern hemisphere.
In addition, this article discusses the hypothesis adopted by many authors about the effect of the rotation of the Earth around its axis on the flow of a continuous medium on its surface.