Simple mathematical model of tornado

The paper proposes a mathematical model of tornado, based on the apparatus of continuum mechanics, according to which swirling flows of ascending air in a tornado take place without taking into account Coriolis force and vertical convection of warm air. According to the results obtained, the necessary conditions for the occurrence of a tornado are the presence of a powerful vortex motion in the upper atmosphere and an increase in air pressure with distance from the center of the tornado. Finding the parameters of air currents in a tornado reduces to solving a boundary value problem for a nonlinear parabolic integro-differential equation obtained in the work with respect to a complex “temperature”. An algorithm for solving the specified boundary value problem is proposed and its stationary solutions are investigated numerically by the method of establishment.