Dissipative soliton vortices and tropical cyclones

Abstract

We have obtained a new exact steady-state solution to the hydrodynamic equation for a viscous incompressible liquid, which is a generalization of the well-known Sullivan solution (1959), taking into account additionally the external (Eckman) friction and rotation of the system as a single whole. In contrast to the radial structure of a Sullivan vortex, different circulation directions of velocity field tangential component are possible in the new solution in the inner and outer cells. We have considered the correspondence of this solution to the radial vortex structure observed in tropical cyclones, where the precisely anticyclonic circulation always exists in the inner core (typhoon, hurricane eye), which is associated with descending vertical currents for the cyclonic direction of rotation (as well as ascending currents) outside this core.