  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 $\Omega_{i}<\Omega_{o}$, where $\Omega_i$
and $\Omega_o$ is the inner and outer sphere rotation rate. A finite number of
particular inertial modes has previously been found. By scanning the Rossby
number from $-2.5 < Ro = (\Omega_{i}-\Omega_{o})/\Omega_{o} < 0$ at two fixed
$\Omega_{o}$, we report the existence of similar inertial modes. However, the
behavior of the flow described here differs much from previous spherical
Couette experiments. We show that the kinetic energy of the dominant inertial
mode dramatically increases with decreasing Rossby number that 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 as0
$E^{1/5}$. 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.
