Renormalized transport of inertial particles in surface flows

Surface transport of inertial particles is investigated by means of the perturbative approach, introduced by Maxey (1987 J. Fluid Mech. 174 441), which is valid when the deflections induced on the particle trajectories by the fluid flow can be considered small. We consider a class of compressible random velocity fields, mimicking the chaotic behaviour of nonlinearly interacting surface standing waves. The effect of recirculations is modelled by an oscillatory component in the Eulerian time-correlation profile. The main issue we address here is whether fluid velocity fluctuations, in particular the effect of recirculation, may produce nontrivial corrections to the streaming particle velocity. Our result is that a small (large) degree of recirculation is associated with a decrease (increase) of streaming with respect to a quiescent fluid. The presence of this effect is confirmed numerically, away from the perturbative limit. Our approach also allows us to calculate the explicit expression for the eddy diffusivity, and to compare both the efficiency of diffusive and ballistic transport and the different anisotropic character of dispersion induced by compressibility