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Onset of three-dimensionality in rapidly rotating turbulent flows

Published online by Cambridge University Press:  28 August 2020

Kannabiran Seshasayanan Open the ORCID record for Kannabiran Seshasayanan [Opens in a new window]  and
Basile Gallet Open the ORCID record for Basile Gallet [Opens in a new window]
Kannabiran Seshasayanan*
Affiliation:
Service de Physique de l’État Condensé, CEA, CNRS UMR 3680, Université Paris-Saclay, CEA Saclay, 91191Gif-sur-Yvette, France
Basile Gallet
Affiliation:
Service de Physique de l’État Condensé, CEA, CNRS UMR 3680, Université Paris-Saclay, CEA Saclay, 91191Gif-sur-Yvette, France
*
†Email address for correspondence: [email protected]
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Abstract

Turbulent flows driven by a vertically invariant body force were proven to become exactly two-dimensional (2-D) above a critical rotation rate, using upper bound theory. This transition in dimensionality of a turbulent flow has key consequences for the energy dissipation rate. However, its location in parameter space is not provided by the bounding procedure. To determine this precise threshold between exactly two-dimensional and partially three-dimensional (3-D) flows, we perform a linear stability analysis over a fully turbulent 2-D base state. This requires integrating numerically a quasi-2-D set of equations over thousands of turnover times, to accurately average the growth rate of the 3-D perturbations over the statistics of the turbulent 2-D base flow. We leverage the capabilities of modern graphics processing units to achieve this task, which allows us to investigate the parameter space up to $Re=10^5$. At the Reynolds numbers typical of 3-D direct numerical simulations and laboratory experiments, $Re\in [10^2, 5\times 10^3]$, the turbulent 2-D flow becomes unstable to 3-D motion through a centrifugal-type instability. However, at even higher Reynolds numbers, another instability takes over. A candidate mechanism for the latter instability is the parametric excitation of inertial waves by the modulated 2-D flow, a phenomenon that we illustrate with an oscillatory 2-D Kolmogorov flow.

JFM classification

Turbulent Flows: Rotating turbulence Geophysical and Geological Flows: Geostrophic turbulence
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 901 , 25 October 2020 , R5
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

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