Transition from inertial wave turbulence to geostrophic turbulence in rotating fluids - an experimental study

Thomas Le_Reun
Aix-Marseille Université, CNRS, Centrale Marseille, IRPHE UMR 7342, Marseille

We present an experimental investigation of the turbulent saturation of the flow driven by parametric resonance of inertial waves in a rotating fluid. In our setup, a half-meter wide ellipsoid filled with water is brought to solid body rotation, and then undergoes sustained harmonic modulation of its rotation rate. This triggers the exponential growth of a pair of inertial waves via a mechanism called the libration-driven elliptical instability. Once the saturation of this instability is reached, we observe a turbulent state for which energy is supplied through the resonant inertial waves only. Depending on the amplitude of the rotation rate modulation, two different saturation states are observed. At large forcing amplitudes, the saturation flow main feature is a steady, geostrophic anticyclone. Its amplitude vanishes as the forcing amplitude is decreased while remaining above the threshold of the elliptical instability. Below this secondary transition, the saturation flow is a superposition of inertial waves which are in weakly non-linear resonant interaction, a state that could asymptotically lead to inertial wave turbulence. In addition to being a first experimental observation of a wave-dominated saturation in unstable rotating flows, the present study is also an experimental confirmation of the model of Le Reun et al, PRL 2017 who introduced the possibility of these two turbulent regimes. The transition between these two regimes and there relevance to geophysical applications are finally discussed.