Deterministic Diffusion, Effective Shear and Patchiness in Shallow Tidal Flows

Abstract

In order to better understand the observed variability of dispersion processes in the sea, we study the passive advection of particles by non-random, tidal (i.e. oscillatory) flows with spatial inhomogeneities due to the bottom topography of the basin. The model velocity field we use is two-dimensional, incompressible and periodic in space (Zimmerman 1976 and 1978). A very broad spectrum of possibilities is uncovered. Four basic mechanisms can be defined:

• 1. Non-dispersive and semi-diffusive patches;

• 2. Chaotic trajectories with properties similar to those of a random walk;

• 3. Position dependence of the drift velocity leading to shear stretching;

• 4. Trapping of chaotic trajectories by regular (≡non-chaotic) ones leads to anomalous diffusion and anomalous stretching.

The importance of each mechanism for the dispersion process varies with the values of the parameters characterizing the velocity field.

When the effects of turbulent diffusion are included, all the above mentioned phenomena become (long-lived) transients.

Numerical calculations done with more realistic velocity fields in the Wadden Sea and Western Scheldt estuary confirm the presence of chaotic trajectories.

This simple model is capable of predicting essentially all the surprising properties of dispersion in shallow seas.