Pair Correlation Function of Vorticity in a Coherent Vortex

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Abstract

We study the correlations of vorticity fluctuations inside a coherent vortex resulting from the inverse energy cascade in two-dimensional turbulence. The presence of a coherent flow, which is a differential rotation, suppresses small-scale fluctuations of the flow, which are created by an external force, and lead to the fact that these fluctuations can be considered as non-interacting and, therefore, examined in a linear approximation. We calculate the pair correlation function of vorticity and demonstrate that it has a power-law behavior both in space and in time. The obtained results allow us to start a systematic study of the effects associated with the nonlinear interaction of fluctuations, which play an essential role on the periphery of a coherent vortex. Our results are also applicable to the statistics of a passive scalar in a strong shear flow.

About the authors

I. V Kolokolov

Landau Institute for Theoretical Physics, Russian Academy of Sciences; National Research University Higher School of Economics

Email: igor.kolokolov@gmail.com
142432, Chernogolovka, Moscow region, Russia; 101000, Moscow, Russia

V. V Lebedev

Landau Institute for Theoretical Physics, Russian Academy of Sciences; National Research University Higher School of Economics

Email: igor.kolokolov@gmail.com
142432, Chernogolovka, Moscow region, Russia; 190008, St. Petersburg, Russia

M. M Tumakova

Landau Institute for Theoretical Physics, Russian Academy of Sciences; National Research University Higher School of Economics

Author for correspondence.
Email: igor.kolokolov@gmail.com
142432, Chernogolovka, Moscow region, Russia; 101000, Moscow, Russia

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