Any statistically steady state admits small perturbations, and the dynamics and the statistical structure of the perturbations can be interesting both in itself and as a characteristic of the state. Here we consider the case of a coherent two-dimensional flow, when the perturbations are large-scale and have relatively slow dynamics, so they should be considered as a small variations of the coherent flow. In order to have slow dynamics, the perturbations should be almost homogeneous along the streamlines of the coherent flow. We show that such kind of perturbations can be considered as waves with some dispersion law. We find the dispersion law and propagation length of the waves as a function of the radial position inside a vortex flow.