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Bistability of the large-scale dynamics in quasi-two-dimensional turbulence

Published online by Cambridge University Press:  24 March 2022

Xander M. de Wit Open the ORCID record for Xander M. de Wit [Opens in a new window] ,
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]
Xander M. de Wit
Affiliation:
Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité, Paris, France Fluids and Flows Group, Department of Applied Physics, and J. M. Burgers Centre for Fluid Dynamics, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
Adrian van Kan
Affiliation:
Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité, 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 Paris-Diderot, Sorbonne Paris Cité, Paris, France
*
†Email address for correspondence: alexandros.alexakis@phys.ens.fr
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Abstract

In many geophysical and astrophysical flows, suppression of fluctuations along one direction of the flow drives a quasi-two-dimensional upscale flux of kinetic energy, leading to the formation of strong vortex condensates at the largest scales. Recent studies have shown that the transition towards this condensate state is hysteretic, giving rise to a limited bistable range in which both the condensate state as well as the regular three-dimensional state can exist at the same parameter values. In this work, we use direct numerical simulations of thin-layer flow to investigate whether this bistable range survives as the domain size and turbulence intensity are increased. By studying the time scales at which rare transitions occur from one state into the other, we find that the bistable range grows as the box size and/or Reynolds number $Re$ are increased, showing that the bistability is neither a finite-size nor a finite-$Re$ effect. We furthermore predict a cross-over from a bimodal regime at low box size, low $Re$ to a regime of pure hysteresis at high box size, high $Re$, in which any transition from one state to the other is prohibited at any finite time scale.

JFM classification

Turbulent Flows: Turbulence simulation Turbulent Flows: Turbulent transition
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 939 , 25 May 2022 , R2
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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