Thermal convection into a swirling source/sink line vortex

Abstract

These last ten years, observations of atmospheric tornadoes knew a very large development. The main goal of this kind of exploration is to determine singular conditions that are responsible of the genesis of this variety of thunderstorms. These investigations made it possible to conclude that one of the essential mechanisms of this phenomenon is due to a thermomechanical process, resulting of a strong gradient of temperature, driving the fluid between the ground and the atmosphere. In this paper, we present exact solutions of Navier-Stokes equations linked with the energy equation, which modeled this type of thermomechanical process. Our model consists of stationary and axisymmetrical flows of a viscous fluid in a half-space, limited by a horizontal plane, in the Boussinesq approximation. These solutions, which satisfy the no-slip condition at the ground, belong to a family of fields of velocity and temperature that depends on five parameters. The mathematical problem we consider is derived by the streamfunction-vorticity method in order to substitute the classical formulation of Navier-Stokes equations