Wave turbulent diffusion due to the Doppler shift

Turbulent diffusion of a passive tracer caused by a random wavefield is believed to be quadratic with respect to the energy spectrum epsilon(k) of the velocity field (i.e. proportional to epsilon(4), where epsilon is the order of the wave amplitudes). So, the wave turbulent diffusion (say, on the ocean surface or in the air) is often believed to be dominated by the turbulent diffusion due to the incompressible flow. In this paper, we show that the wave turbulent diffusion can be associated with the Doppler shift and find that the wave turbulent diffusion can be more significant than previously thought. This mechanism works if the velocity field is compressible and statistically anisotropic, with the result that the wave system has a significant Stokes drift. The contribution of this mechanism has a lower order in epsilon. We confirm our results with numerical simulations. To derive these results, we develop the statistical near-identity transformation.