Selection of Inertial Modes in Spherical Couette Flow

Spherical Couette flow involves fluid sheared between concentric coaxially rotating spheres. Its scientific relevance lies not only in the simplicity of the system but also in its applicability to astrophysical objects such as atmospheres, oceans, and planetary cores. One common behavior in all rotating flows, including spherical Couette flow, is the presence of inertial modes, which are linear wave modes restored by the Coriolis force. Building on a previous identification of inertial modes in a laboratory spherical Couette cell, here we propose selection mechanisms to explain the presence of the particular modes we have observed. Mode selection depends on both amplification and damping. Our experimental observations are consistent with amplification and selection by over-reflection at a shear layer, and we would expect other spherical Couette devices to behave similarly. Damping effects, due in part to the presence of an inner sphere, add further constraints which are likely to play a role in mode selection in planetary atmospheres and cores, including the core of earth.