# Cyclone–Anticyclone Vortex Asymmetry Mechanism and Linear Ekman Friction

S. G. Chefranov*

Obukhov Institute of Atmospheric Physics, Russian Academy of Sciences,
Pyzhevskii per. 3, Moscow, 119017 Russia

*e-mail: schefranov@mail.ru

Received 24 September, 2015

**Abstract—**Allowance for the linear Ekman friction has been found to ensure a threshold (in rotation frequency) realization of the linear dissipative–centrifugal instability and the related chiral symmetry breaking in the dynamics of Lagrangian particles, which leads to the cyclone–anticyclone vortex asymmetry. An excess of the fluid rotation rate ω_{0} over some threshold value determined by the fluid eigenfrequency ω (i.e., ω_{0} > ω) is shown to be a condition for the realization of such an instability. A new generalization of the solution of the Karman problem to determine the steady-state velocity field in a viscous incompressible fluid above a rotating solid disk of large radius, in which the linear Ekman friction was additionally taken into account, has been obtained. A correspondence of this solution and the conditions for the realization of the dissipative–centrifugal instability of a chiral-symmetric vortex state and the corresponding cyclone–anticyclone vortex asymmetry has been shown. A generalization of the well-known spiral velocity distribution in an “Ekman layer” near a solid surface has been established for the case where the fluid rotation frequency far from the disk ω differs from the disk rotation frequency ω_{0}.

**DOI: **10.1134/S1063776116040038