Some generalizations of the tornado model

Abstract

A possible mechanism of tornado generation is associated with the Schwarzschild criterion for convective instability. The supercooled cloud-air mixture near the axis starts to descend and, due to the super adiabatic temperature gradient, the overheated near-surface air mass rises. The complete system of equations for full model includes equations for the stream function, for the azimuthal velocity component, and for the change in density. The refined model considers rotating convection within the framework of ideal hydrodynamics. The simplest model uses a separate equation for the stream function and can be applied to the initial stage of vortex generation. Within the framework of the simplest model, an analytical solution is combined from 8 linear dependencies by height. Rotation increases due to the conservation of angular momentum. Within the framework of the refined model, some unidirectional differential rotation arises, but it depends on boundary conditions (can be local). The full model studies the tornado development as rotating convection from the very beginning to the quasi-stationary stage. Velocity components increase in a coordinated manner. Two cases are considered: a single whirlwind and a two-eyed tornado. Radial flows converge towards the central part of the tornado near the earth surface, and there is an outflow from the "wall" to the axis and to the periphery near the top of the tornado. The maximum vertical velocity component is achieved at a certain radial distance at a certain height. The maximum azimuthal velocity component is achieved in the tornado "wall". Tornado generation criteria are discussed.