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Spontaneous suppression of inverse energy cascade in instability-driven 2-D turbulence

Published online by Cambridge University Press:  01 December 2022

Adrian van Kan Open the ORCID record for Adrian van Kan [Opens in a new window] ,
Benjamin Favier Open the ORCID record for Benjamin Favier [Opens in a new window] ,
Keith Julien  and
Edgar Knobloch
Adrian van Kan*
Affiliation:
Department of Physics, University of California at Berkeley, Berkeley, CA 94720, USA
Benjamin Favier
Affiliation:
IRPHE, Aix Marseille Univ., CNRS, Centrale Marseille, 13384 Marseille, France
Keith Julien
Affiliation:
Department of Applied Mathematics, University of Colorado, Boulder, CO 80309, USA
Edgar Knobloch
Affiliation:
Department of Physics, University of California at Berkeley, Berkeley, CA 94720, USA
*
†Email address for correspondence: [email protected]
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Abstract

Instabilities of fluid flows often generate turbulence. Using extensive direct numerical simulations, we study two-dimensional turbulence driven by a wavenumber-localised instability superposed on stochastic forcing, in contrast to previous studies of state-independent forcing. As the contribution of the instability forcing, measured by a parameter $\gamma$, increases, the system undergoes two transitions. For $\gamma$ below a first threshold, a regular large-scale vortex condensate forms. Above this threshold, shielded vortices (SVs) emerge within the condensate. At a second, larger value of $\gamma$, the condensate breaks down, and a gas of weakly interacting vortices with broken symmetry spontaneously emerges, characterised by preponderance of vortices of one sign only and suppressed inverse energy cascade. The latter transition is shown to depend on the damping mechanism. The number density of SVs in the broken symmetry state slowly increases via a random nucleation process. Bistability is observed between the condensate and mixed SV-condensate states. Our findings provide new evidence for a strong dependence of two-dimensional turbulence phenomenology on the forcing.

JFM classification

Vortex Flows: Vortex dynamics
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 952 , 10 December 2022 , R4
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

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