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Growing condensate in two-dimensional turbulence

M. Chertkov·C. Connaughton·I. Kolokolov·V. Lebedev
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Abstract

We report a numerical study, supplemented by phenomenological explanations, of ``energy condensation'' in forced 2D turbulence in a biperiodic box. Condensation is a finite size effect which occurs after the standard inverse cascade reaches the size of the system. It leads to emergence of a coherent vortex dipole. We show that the time growth of the dipole is self-similar, and it contains most of the injected energy, thus resulting in an energy spectrum which is markedly steeper than the standard $k^{-5/3}$ one. Once the coherent component is subtracted, however, the remaining fluctuations have a spectrum close to $k^{-1}$. The fluctuations decay slowly as the coherent part grows.

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M. Chertkov, C. Connaughton, I. Kolokolov, V. Lebedev. 2007-02-28. Growing condensate in two-dimensional turbulence. https://doi.org/10.1103/physrevlett.99.084501

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