A Mathematical Model of Tornado

Abstract

Abstract We propose a mathematical model of tornado in the framework of continuum mechanics. According to this model, the swirling upward air motion in a tornado can be explained even without taking into account the Coriolis force or the vertical convection of warm air. Our results show that for a tornado to appear two factors are necessary: a powerful rotational motion of air in the upper atmosphere and the growth of air pressure from the center to the periphery of an expected region of tornado. The characteristics of air flow in tornado can be found by solving a boundary value problem for a nonlinear parabolic integro-differential equation for an unknown complex-valued temperature. We formulate this problem, propose an algorithm for its numerical solution, and examine its stationary solutions by the stabilization method.