Acceleration of hydrodynamic vortices in open systems

Abstract

A new class of exact solutions of hydrodynamic equations for an incompressible fluid (gas) at the presence of a bulk sink and uprising vertical flows of matter is considered. The acceleration of the rotation velocity of classical non-stationary vortices is conditioned by the joint action of the convective and Coriolis hydrodynamic forces (accelerations), which appear due to the converging radial flows of the matter in the region of a bulk sink. It is shown that there exist velocity profiles that nullify viscous terms in the Navier-Stokes equations and represent a vortex structure with a "rigid-body" rotation of its core and converging radial flows. The concept of non-stationary vortices in open systems is applied to description of origination of power atmospheric vortices (whirlwinds, tornados, and typhoons). In the classical hydrodynamics a favorable condition for the origination and existence of such vortices is the exact nullification of the terms, which describe kinematic viscosity of an incompressible fluid. Such flows have the minimal rate of energy dissipation that corresponds to the "minimum entropy production principle", and therefore may relatively easily appear in favorable natural conditions.