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Pair Correlation Function of Vorticity in a Coherent Vortex
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, sup-
presses 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.