On the nonlinear dynamics of massive particles in tornadoes

The motion of inertial particles in intense vortices with a vertical axis in the field of gravity has been analytically studied. In this problem, the nonlinear nature of the hydrodynamic resistance–its dependence on the modulus of the particle’s velocity relative to the medium–is essential. Different components of the movement interact with each other, since each of them affects the coefficient of resistance. An effective method for an approximate solution of the problem is found. A number of general laws of particle dynamics are established. In particular, a regime is characteristic in which their tangential velocity is close to the velocity of the medium, while the radial velocity is substantially smaller (it is close in order of magnitude to the geometric mean of tangential velocity of the particle and the difference between the latter and the tangential velocity of the medium).