  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.
