  The growth rate of small-scale density inhomogeneities (the entropy
production rate) is given by the sum of the Lyapunov exponents in a random
flow. We derive an analytic formula for the rate in a flow of weakly
interacting waves and show that in most cases it is zero up to the fourth order
in the wave amplitude. We then derive an analytic formula for the rate in a
flow of potential waves and solenoidal currents. Estimates of the rate and the
fractal dimension of the density distribution show that the interplay between
waves and currents is a realistic mechanism for providing patchiness of
pollutant distribution on the ocean surface.
