Experimental study of the non-linear saturation of the elliptical instability: inertial wave turbulence versus geostrophic turbulence

Abstract

In this paper, 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 set-up, 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 injected into 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 mainly consists of 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 their relevance to geophysical applications are finally discussed.

arXiv commentPublished in Journal of Fluid Mechanics, 30 pages, 19 pages

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• Mean zonal flows induced by weak mechanical forcings in rotating spheroids
• Onset of three-dimensionality in rapidly rotating turbulent flows
• Three-dimensionality of the triadic resonance instability of a plane inertial wave
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• Internal gravity waves in stratified flows with and without vortical modes
• Precession-driven flows in stress-free ellipsoids
• The interactions of the elliptical instability and convection
• Kinematic dynamos in triaxial ellipsoids
• Breaking of internal waves parametrically excited by ageostrophic anticyclonic instability
• Geophysical flows over topography, a playground for laboratory experiments
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