Diffusive Transport by Breaking Waves

Abstract

Abstract A simple conceptual model of the relationship between advective transport by breaking waves and diffusive transport is derived. line model postulates that the displacement of fluid parcels by a breaking wave is analogous to molecular diffusion (in a manner similar to conventional mixing length theory). Unlike molecular diffusion, in which the fluctuations of nearby particles are independent, in fluid flow the motion of nearby parcels can be coherent. The effectively random phase of wavebreaking events with respect to an individual particle, however, results in a macroscopic “random walk” of the parcel with a step size related to the width of the breaking wave and a timescale related to the frequency of wave breaking events. As in the case of molecular diffusion, the motion of individual molecules or fluid parcels is unpredictable (chaotic, in fact), but averaging over a large ensemble of parcels results in an ensemble variance that increases linearly with time, formally equivalent to molecular di...