A note on the diffusion in fluids with wave-induced random motion. Applications to the barotropic Rossby waves

An asymptotic theory, describing turbulent diffusion due to wave-induced random motion in incompressible or compressible fluids, is constructed. It is shown that even weakly nonlinear waves cause irreversible stretching of material lines. The results obtained are applied to the Rossby-wave-induced motion in the atmosphere or ocean. An expression for the effective coefficient of diffusivity is calculated, which indicates that the diffusion due to Rossby waves can be strongly anisotropic even for an isotropic wave spectrum.