Modulation of stochastic diffusion by wave motion

Pollutants that are chemically inert flow with the carrier fluid passively while diffuse at the same time. In this study, the stochastic diffusion behavior of the passive pollutant in a progressive or standing wave field is examined with analytical means. Our focus is on the nonlinear interactions between the stochastic diffusion and the deterministic wave motions, and we limit the scope to cases whereby a small parameter, ε, exists between the advective and diffusive displacements, which then allows a perturbation analysis to be performed. With a sinusoidal progressive wave, the results show that the deterministic wave motion can either increase or decrease the embedded stochastic diffusion depending on the wave characteristics. Longer wave lengths and shorter wave periods tend to promote diffusion significantly, while shorter wave lengths and longer wave periods act in the opposite manner but with a much smaller effect. An analysis of the standing wave motion, represented by a combination of left and right moving progressive waves, shows that the effects due to two opposing waves to the stochastic diffusion can be superimposed.