Anomalous Diffusion of Sand Tracer Particles Under Waves

Abstract

A model is presented for the horizontal and vertical diffusion of sand tracer particles by waves and is verified using a reanalysis of the experiments of Miller and Komar (1979, https://doi.org/10.1086/628455). In the model, sand particles take random jumps at a rate associated with the wave period but also can bury one another resulting in intermittent long rest times between jumps. The particle jump length between burials is modeled by considering a vortex entrainment and advection mechanism, resulting in a probability distribution as a function of wave orbital excursion amplitude and particle settling velocity. The model is formalized using the theory of continuous time random walks to obtain closed‐form expressions for the horizontal particle spreading rate, and plume shape, without tunable parameters. Importantly, the model predicts subdiffusive particle spreading, a previously unconsidered phenomenon that is apparent in the experimental data. The plume horizontal extent versus time is also well predicted compared to experimental data.