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Coexistence of two equilibrium configurations in two-dimensional turbulence

Wesley Agoua

Xi-Yuan Yin

Tong Wu

Wouter J. T. Bos*

  • *Contact author: wouter.bos@ec-lyon.fr
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Phys. Rev. Fluids 10, 034604 – Published 11 March, 2025

DOI: https://doi.org/10.1103/PhysRevFluids.10.034604

Abstract

In the past, two families of statistical mechanics approaches have been applied to the two-dimensional Euler equations. The first one is formulated in Fourier space and considers the Galerkin-truncated dynamics. The other one is formulated in physical space and considers either point vortices or coarse-grained vorticity. We show that in a Galerkin-truncated system, both methods describe a part of the flow. A condensate can be identified, assuming that it can be characterized by an unspecified functional relation between the vorticity and the stream function. It is shown, a posteriori, that this function is a hyperbolic sine relation, as predicted by point-vortex statistical mechanics. The energy spectrum associated with the condensate is well described by an exponential function and the tails of the probability density function of the vorticity follow a power law. Analytical arguments to explain these observations are proposed. After removing the condensate, the remaining field can be described by Fourier-statistical mechanics.

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Phys. Rev. Fluids 10, 034604– Published 11 March, 2025
  • Received 9 October 2024
  • Accepted 3 February 2025
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