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Spherical Couette flow (flow between concentric rotating spheres) is one of flows under consideration for the laboratory magnetic dynamos. Recent experiments have shown that such flows may excite Coriolis restored inertial modes. The present work aims to better understand the properties of the observed modes and the nature of their excitation. Using numerical solutions describing forced inertial modes of a uniformly rotating fluid inside a spherical shell, we first identify the observed oscillations of the Couette flow with nonaxisymmetric, retrograde, equatorially antisymmetric inertial modes, confirming first attempts using a full sphere model. Although the model has no differential rotation, identification is possible because a large fraction of the fluid in a spherical Couette flow rotates rigidly. From the observed sequence of the excited modes appearing when the inner sphere is slowed down by step, we identify a critical Rossby number associated with a given mode, below which it is excited. The matching between this critical number and the one derived from the phase velocity of the numerically computed modes shows that these modes are excited by an instability likely driven by the critical layer that develops in the shear layer, staying along the tangent cylinder of the inner sphere.

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.