Stochastic diffusion by progressive waves in turbulence

Pollutants that are chemically inert flow with the carrier fluid passively while diffuse at the same time. In this study, the diffusion behavior of passive pollutant in a progressive wave field with strong turbulence is examined with analytical means. The focus is on the nonlinear interactions between the stochastic diffusion and the deterministic wave-induced oscillatory advection. We limit our scope to cases whereby a small parameter, ɛ, exists between the advective and diffusive displacements, which then allows a perturbation analysis to be performed. With the sinusoidal progressive wave, the results show that the oscillating wave motion can either increase or decrease the stochastic diffusion depending on the wave characteristics. Longer wave lengths and shorter wave periods tend to promote diffusion, while shorter wave lengths and longer wave periods act in the opposite manner. The reinforcing effect is however much stronger than the diminishing effect.