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

Abstract

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, but, as the laboratory experiments show, such a mechanism should be closely interconnected with the presence of the rotation of the medium as a whole. 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 above-threshold 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. The condition for the DCI is found by considering such a generalization of the Kármán classic solution where the effect of linear external friction is taken into account. A new non-stationary solution to the problem for the disc which carries out weak axial-torsional oscillations in fluid in connection with the experimental data on the rotating superfluid helium-II has been found.

Eulerian derivation of non-inertial Navier–Stokes and boundary layer equations for incompressible flow in constant pure rotation

“…The differences between the numerical and analytical results are due to the formation of laminar instabilities. Instabilities associated with rotating disks are mostly of Type I and Type II ( [23], [24]). Type I instabilities occur due to inviscid The boundary characteristic properties in the radial and tangential directions were determined for the numerical and analytical results.…”