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.

A velocity-variation-based formulation for bedload particle hops in rivers

“…The random variable of hop distance (or step length) with its probability density function (p.d.f.) has since been extensively studied for probabilistic formulations of bedload sediment transport (Paintal 1971;Hassan, Church & Schick 1991;Parker, Paola & Leclair 2000;Ancey et al 2008;Ancey 2010;Bradley & Tucker 2012;Hassan et al 2013;Yager, Kenworthy & Monsalve 2015;Wilson 2018). For example, focusing on the exchange of bedload particles between those in motion and those staying in the riverbed, the streamwise transport of tracer particles has been intensively explored recently, with the aim of understanding the problem of anomalous diffusion.…”

Testing magnetic tracers as indicators of sediment transport in a wave flume experiment

“…The technique relies upon the injection of natural or artificial particle tracers into a studied area and their subsequent recovery and analysis in the laboratory or, alternatively, their in situ determination. In coastal environments, the use of sediment tracers has proved to be a reliable technique for the study of sediment transport, both in terms of a Eulerian approach determining net transport rates, and a Lagrangian approach tracking sediment particles (Silva et al ., 2007; Bosnic et al ., 2017; Wilson, 2018; Pearson et al ., 2021). Over the past three decades, various alternative methodologies for measuring sediment transport have emerged.…”