The effect of oscillating force field on the dynamics of free inner core in a rotating fluid-filled spherical cavity

Abstract

This research involves experimental studies of the dynamics of a free spherical core in a fluid-filled spherical cavity rotating around the horizontal axis and subject to vibration perpendicular to the rotation axis. The core stays in the center of the cavity under the action of a centrifugal force (the core density is less than the fluid density). The vibration manifests itself in resonance regions when the vibration frequency coincides with one of the core’s natural frequencies. The amplitude of the core oscillations and generation of its intensive differential rotation rise steeply, with the differential rotation lagging or leading, depending on the frequency of the core oscillations. Excitation of leading rotation is accompanied by the core shift from the cavity center to one of the poles with the core rotation axis deviated from the cavity rotation axis. The research shows that the superposition of different force fields, oscillating vibrational field, and static gravitational force field determines the differential rotation rate of the core. The gravity field causes the lagging circular oscillations of the core with respect to the cavity, and consequently its steady lagging differential rotation, which decreases as the cavity rotation rate increases. The research shows that 2D steady flow in the form of a Taylor-Proudman column accompanies the differential rotation of the core. The resulting flow is a linear superposition of flows excited independently by gravity and vibration. The instability of the flow manifests itself, as an azimuthal two-dimensional wave is propagating on the Taylor-Proudman column boundary, and depends on the flow structure.