Simulating vertical turbulent dispersal with finite volumes and binned random walks

Early life stages in fish are often modeled by individual-based models. The transport of individuals with ocean currents is addressed through particle-tracking techniques, which typically simulate vertical turbulent dispersal with random walk schemes. These schemes, however, perform poorly when the eddy diffusivity displays steep gradients, as in stratified water columns, and near the surface and sea floor.

In the present paper, we advocate the use of a binned random walk, which keeps track, not of the exact vertical position of a tracer particle, but only of the layer in which the particle resides. The binned random walk is derived by discretizing the Eulerian equations governing the vertical dispersal with the finite-volume method.

The scheme is easily implemented, even when layers are non-uniform and turbulence statistics originate from a circulation model, and, by construction, always satisfies the well-mixed criterion. We demonstrate the scheme and discuss its applicability.