Stewartson layer instability and triadic resonances in rotating sphere with oscillating inner core

Abstract

This work is devoted to an experimental study of the stability of a steady flow in a rotating spherical cavity with an oscillating core. The case of circular core oscillations in a plane perpendicular to the rotation axis is considered. The steady flow structure strongly depends on the dimensionless oscillation frequency. In the frequency range where there are no inertial waves, the flow resembles a classical Taylor column with an almost uniform distribution of the angular velocity. With an increase in the oscillation amplitude above a certain threshold level, a two-dimensional azimuthal wave is excited at the column boundary. The wave velocity is determined by the intensity of the liquid differential rotation and does not depend on the Ekman number. In the case of oscillation with a frequency less than twice the rotation rate, the inertial waves propagate in fluid bulk and introduce a significant correction to the steady velocity profile. At high amplitudes, the triadic subharmonic resonance of inertial waves is excited. The triadic interactions simultaneously manifest themselves in two regions of the spherical shell, generating secondary waves with the same frequencies, but different wavenumbers: subharmonic waves with shorter (respectively, longer) wavelengths are observed in outer (respectively, inner) regions of the shell. In some cases, the third (intermediate) region with subharmonic waves of intermediate wavelength can be observed. The development of the triadic resonance leads to a strongly nonlinear response in the form of a system of steady vortices with well-defined azimuthal periodicity.