Dissipative soliton vortices and tropical cyclones
- PDF / 180,488 Bytes
- 4 Pages / 612 x 792 pts (letter) Page_size
- 70 Downloads / 178 Views
TICAL, NONLINEAR, AND SOFT MATTER PHYSICS
Dissipative Soliton Vortices and Tropical Cyclones S. G. Chefranova,* and A. G. Chefranovb,** a
Obukhov Institute of Atmospheric Physics, Russian Academy of Sciences, Moscow, 119017 Russia b Eastern Mediterranean University, Famagusta, Northern Cyprus, Turkey *e-mail: [email protected] **e-mail: [email protected] Received May 7, 2017
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. DOI: 10.1134/S1063776117100053
1. INTRODUCTION In the classical hydrodynamics of a viscous incompressible liquid, the number of exact solutions is scarce, while obtaining new solutions, as well as analysis of their stability, is of fundamental and applied importance for many problems in physics, geophysics, and astrophysics [1–3]. In contrast to exact steadystate solutions considered in [2, 3], which exist only in the presence of external boundaries of the liquid, vortex stationary regimes of a viscous incompressible liquid in an unbounded liquid are also known and correspond to exact solutions obtained by Burgers [1] and Sullivan [4]. Such solutions exist not because of external boundaries, but due to the balance between 3D extension of vortex filaments, which leads to an explosive growth of the entropy [1, 5, 6] and is responsible for the stabilizing effect of bulk viscous dissipation. In this work, we obtain a new exact solution to the equations in the hydrodynamics of a viscous incompressible liquid, which generalizes the Sullivan solution [4] due to taking into account additionally the effect of external friction and rotation of the liquid as a single whole. We demonstrate the important role of not only the bulk friction, but also the external friction in the formation of the radial structure of the velocity field tangential component for the generalization of the Sullivan vortex (SV). On the other hand, it was shown in [7] that the inclusion of the external (Eckman) friction in the case of rotation of the system as a whole may affect the stability of solid-state rotation of the core and single-cell Burgers vortex (BV) as well as double-cell SV. For
example, in the case of super-threshold rotation velocity of the system, dissipative–centrifugal instability (DCI) of BV and SV c
Data Loading...
