We present a study of inertial modes in a differentially rotating spherical shell (spherical Couette flow) experiment with a radius ratio of $\eta =1/3$. Inertial modes are Coriolis-restored linear wave modes which often arise in rapidly rotating fluids. Recent experimental work has shown that inertial modes exist in a spherical Couette flow for ${\mathrm{\Omega }}_i<{\mathrm{\Omega }}_o$, where ${\mathrm{\Omega }}_i$ and ${\mathrm{\Omega }}_o$ are the inner and outer sphere rotation rate. A finite number of particular inertial modes has previously been found. By scanning the Rossby number from $-2.5<\text{Ro}=({\mathrm{\Omega }}_i-{\mathrm{\Omega }}_o)/{\mathrm{\Omega }}_o<0$ at two fixed ${\mathrm{\Omega }}_o$, we report the existence of similar inertial modes. However, the behavior of the flow described here differs significantly from previous spherical Couette experiments. We show that the kinetic energy of the dominant inertial mode dramatically increases with decreasing Rossby number, which eventually leads to a wave breaking and an increase of small-scale structures at a critical Rossby number. Such a transition in a spherical Couette flow has not been described before. The critical Rossby number scales with the Ekman number as $E^{1/5}$. Additionally, the increase of small-scale features beyond the transition transfers energy to a massively enhanced mean flow around the tangent cylinder. In this context, we discuss an interaction between the dominant inertial modes with a geostrophic Rossby mode exciting secondary modes whose frequencies match the triadic resonance condition.

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• Flow instability
• Geophysical fluid dynamics
• Rotating geophysical flows
• Transition to turbulence