Random flows in rotating fluid layers are studied in two spatial dimensions. The Eulerian and Lagrangian correlation functions for such flows are analysed by approximating the actual two-dimensional flow by an autonomous system consisting of many overlapping and mutually convecting vortices. Analytical expressions for the full space–time-varying Eulerian velocity correlation are derived solely in terms of flow parameters. An extension of the arguments giving these results also allows the derivation of analytical expressions for the Lagrangian velocity correlation function. The analytical results are supported by a numerical simulation.