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Energy cascades in rapidly rotating and stratified turbulence within elongated domains

Published online by Cambridge University Press:  20 December 2021

Adrian van Kan Open the ORCID record for Adrian van Kan [Opens in a new window]  and
Alexandros Alexakis Open the ORCID record for Alexandros Alexakis [Opens in a new window]
Adrian van Kan*
Affiliation:
Laboratoire de Physique de l'Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France Department of Physics, University of California, Berkeley, CA 94720, USA
Alexandros Alexakis
Affiliation:
Laboratoire de Physique de l'Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France
*
†Email address for correspondence: avankan@ens.fr
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Abstract

We study forced, rapidly rotating and stably stratified turbulence in an elongated domain using an asymptotic expansion at simultaneously low Rossby number $\mathit {Ro}\ll 1$ and large domain height compared with the energy injection scale, $h=H/\ell _{in}\gg 1$. The resulting equations depend on the parameter $\lambda =(h \mathit {Ro} )^{-1}$ and the Froude number $\mathit {Fr}$. An extensive set of direct numerical simulations (DNS) is performed to explore the parameter space $(\lambda,\mathit {Fr})$. We show that a forward energy cascade occurs in one region of this space, and a split energy cascade outside it. At weak stratification (large $\mathit {Fr}$), an inverse cascade is observed for sufficiently large $\lambda$. At strong stratification (small $\mathit {Fr}$) the flow becomes approximately hydrostatic and an inverse cascade is always observed. For both weak and strong stratification, we present theoretical arguments supporting the observed energy cascade phenomenology. Our results shed light on an asymptotic region in the phase diagram of rotating and stratified turbulence, which is difficult to attain by brute-force DNS.

JFM classification

Turbulent Flows: Turbulent transition Turbulent Flows: Stratified turbulence Turbulent Flows: Rotating turbulence

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JFM Papers
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Journal of Fluid Mechanics , Volume 933 , 25 February 2022 , A11
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© The Author(s), 2021. Published by Cambridge University Press

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References

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