A NEW MATHEMATICAL-MODEL APPLIED TO TORNADO GENESIS

One of the most important topics in fluid mechanics research is the vortex genesis and the vortex stability. Tornadoes are directly related to these studies: a tornado can be represented by an infinite vortex line in a viscous fluid interacting with a plane boundary surface at right angles to the line. The purpose of this paper is to derive an analytical model which can describe the genesis of these vortex lines in agreement with meteorological mechanisms. This model is built upon a bifurcation process. We consider an axisymmetric non-rotating updraft satisfying an adherence condition at the ground. We show that this flow is unstable and bifurcates to a stationary tornado flow. The startup of a tornado is then modeled.