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Original research

Linear Eсkman friction in the mechanism of the cyclone-anticyclone vortex asymmetry and in a new theory of rotating superfluid

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The observed experimental and natural phenomenon of cyclone-anticyclone vortex asymmetry implies that a relatively more stable and showing a longer life, as well as a relatively more intense mode of rotation with an anticyclonic circulation direction (opposite to the direction of rotation of the medium as a whole) is realized as compared with an oppositely directed rotation of the cyclonic vortex mode. Until now, however, it was not a success to identify a universal triggering mechanism responsible for the formation of the corresponding breaking of chiral vortex symmetry.

Materials and methods

In this paper we reveal the said linear universal instability mechanism of breaking of chiral symmetry in the sign of vortex circulation in the rotating medium in the presence of linear Eckman friction.


Obtained is a condition for the linear dissipative - centrifugal instability (DCI), which leads (only when considering the external linear Eckman friction for an abovethreshold value of rotation frequency of the underlying boundary surface of fluid) to the breaking of chiral symmetry in the Lagrangian fluid particle dynamics and the corresponding realization of the cyclone-anticyclone vortex asymmetry.


A new non-stationary solution to the problem for the disc which carries out weak axial-torsional oscillations in fluid with the frequency which are superimposed on its rotation with the previously considered frequency ω0 in connection with the experimental data on the rotating superfluid helium II has been found. It gives the possibility to conclude that the effects of external, linear on velocity, friction forces must be important to include into consideration for the solve of any fundamental problems of hydrodynamics in bounded systems (as for the blood dynamics in cardiovascular system, for example).


Sergey G. Chefranov. Linear Eсkman friction in the mechanism of the cycloneanticyclone vortex asymmetry and in a new theory of rotating superfluid; Cardiometry; No.4; May 2014; p.46-69; DOI:10.12710/cardiometry.2014.4.4669 Available from:


Dissipative centrifugal instability,  Rotating superfluid helium,  Surface friction,  Torsional oscillation,  Viscous incompressible fluid,  Vortex asymmetry
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