On the occurrence of chaotic advection in a simple model of a tidal flow perturbed by sand waves

Abstract

The study of passive particle transportation by fluid flow forms an important topic of research, since it can be used to predict trajectories of small particles such as sediment, nutrients and microplastics. What makes this topic even more interesting is that it has been shown by (Aref 1984), (Ottino 1990), (Ridderinkhof and Zimmerman 1992), (Beerens et al. 1994) a.o. that two-dimensional non-integrable Hamilton systems may induce highly irregular trajectories of passive particles. This behaviour is known as stirring by chaotic advection. In this study we use a simple model derived by (Besio et al. 2004) to find an analytical approximation of the flow field of a system with a tidal flow, perturbed by sand waves (shallow tidal area). So far, behaviour of particle trajectories in this system has been studied in two horizontal dimensions by e.g. (Beerens et al. 1994). This study will focus on the system in a vertical plane, in order to assess the influence of particle depth. We use the flow field to numerically calculate the trajectory of passive particles using the symplectic integration method St¨ormer-Verlet. Through varying the system parameters we find that stirring by chaotic advection occurs in this system for realistic environmental settings. Particles near the surface do not travel significant distances, while particles near the bottom can end up anywhere in the flow. This indicates that tidal currents play a significant role in the transport of particles in shallow tidal areas.