Wind-induced chaotic advection in shallow flow geometries. Part I: Circular basins

A numerical study is presented of horizontal wind-induced mixing in shallow water basins. The shallow water equations are solved on a dynamically adaptive quadtree grid using a Godunov-type finite volume scheme to predict the wind-induced flow field. Passive tracer dynamics are then simulated by time-integration of the advection equations using a Runge-Kutta Cash-Karp algorithm, with the flow velocities interpolated from the grid-based flow field. In a circular basin suggested by Kranenburg U Hydraul Res 30 (1992) 29], numerical predictions of particle motions and mixing processes are in close qualitative agreement with Kranenburg's analytical solutions for the case of a wind of constant intensity abruptly changing direction between north-west and north-east. New results are presented for the case of wind changing direction between west and east. Further investigations are carried out for circular basins with conical and more complicated bed topographies. It is observed that the particle motions invariably alter from regular to chaotic as the storm duration increases, in agreement with Kranenburg's findings. The effect of basin plan-form shape on mixing is considered in the companion paper.