Space Evolution of Tornado-Like Vortex Core

Abstract

In a long-wave approximation, the motion of liquid in a vertical tornado-like vortex core is studied. An extension of the continuous solution to a finite or infinite height is established to be possible. Classification of nonextended solutions is made: the solution doesn’t exist either due to vanishing of a vertical velocity component or due to tending of derivatives to infinity (analogously to a “gradient catastrophe” in gas dynamics). For the first case, an analytical example is built, in which the height-finite solution propagates continuously over the whole half-space. A possibility of applying obtained results to calculate the height of a tornado-like vortex, to describe the process of its decay and effects observed in tornados and dust vortices in nature is discussed.