Instabilities of Steady Flow in a Rotating Spherical Cavity Excited by Inner Core Oscillation

Abstract

We experimentally investigated a stability of steady flow caused by inner core oscillation in a rotating spherical cavity with fluid. The inner core oscillation relative to the cavity is caused by steady external field, directed transversally to the rotation axis; thus, the oscillation frequency is equal to the rotation frequency of the system. Differential rotation of the core is deactivated, for that one of the core poles is connected with the nearest cavity pole by a torsionally elastic fish-line. It is found that the quasi-two-dimensional steady azimuthal flow is excited by the core oscillation; the flow intensity is proportional to the core oscillation amplitude squared. With increase of amplitude, the axially symmetrical flow loose stability; the instability mode is similar to the one found before in the case of free core oscillation, which was executing the mean differential rotation (Kozlov et al.: Eur. J. Mech. B-Fluid. 63(3), 39–46, 2017). The comparative analysis shows that the differential rotation of inner core is not an essential condition for the appearance of instabilities. The mechanism for the appearance of instabilities is related with inflection points in azimuthal velocity profile of the fluid flow caused by the core oscillation relative to the cavity.