  We examine fluctuations of vorticity excited by an external random force in
two-dimensional fluid in the presence of a strong external shear flow. The
problem is motivated by the analysis of big coherent vortices appearing as a
consequence of the inverse energy cascade in a finite box at large Reynolds
numbers. We develop the perturbation theory for calculating nonlinear
corrections to correlation functions of the flow fluctuations assuming that the
external force is short correlated in time. We analyze corrections to the pair
correlation function of vorticity and some moments. The analysis enables one to
establish validity of the perturbation theory for laboratory experiments and
numerical simulations.
