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Experimental study of the nonlinear saturation of the elliptical instability: inertial wave turbulence versus geostrophic turbulence

Published online by Cambridge University Press:  27 September 2019

Thomas Le Reun Open the ORCID record for Thomas Le Reun [Opens in a new window] ,
Benjamin Favier Open the ORCID record for Benjamin Favier [Opens in a new window]  and
Michael Le Bars
Thomas Le Reun*
Affiliation:
Aix Marseille Univ, CNRS, Centrale Marseille, IRPHE UMR 7342, Marseille, France
Benjamin Favier
Affiliation:
Aix Marseille Univ, CNRS, Centrale Marseille, IRPHE UMR 7342, Marseille, France
Michael Le Bars
Affiliation:
Aix Marseille Univ, CNRS, Centrale Marseille, IRPHE UMR 7342, Marseille, France
*
†Email address for correspondence: [email protected]
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Abstract

In this paper, we present an experimental investigation of the turbulent saturation of the flow driven by the parametric resonance of inertial waves in a rotating fluid. In our set-up, a half-metre 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 nonlinear 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. (Phys. Rev. Lett., vol. 119 (3), 2017, 034502) who introduced the possibility of these two turbulent regimes. The transition between these two regimes and their relevance to geophysical applications are finally discussed.

JFM classification

Geophysical and Geological Flows: Waves in rotating fluids Instability: Parametric instability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 879 , 25 November 2019 , pp. 296 - 326
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Copyright
© 2019 Cambridge University Press 

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