Dispersion in a stratified benthic boundary layer

Abstract

A dispersion model for the stratified benthic boundary layer is formulated. It is based on “small-scale” vertical dispersion and a “large-scale” horizontal flow field. A modified Langevin equation governs the stochastic vertical migration of an ensemble of marked fluid elements. These elements are spread out by the horizontal flow, determined by a one-dimensional model, which includes a two-equation (k - ε) turbulence scheme. The later yields statistical information necessary for the stochastic process. Statistical properties of the dispersion process are then calculated from the evolution of the ensemble of elements. A rather idealized case with a linearly stratified fluid subject to a suddenly imposed barotropic pressure gradient is considered. A quasi-geostrophic interior flow is formed with a benthic boundary layer at the bottom. Marked fluid elements are released at the bottom and then followed for several pendulum days. It is found that the dispersion process is well characterized by K = Cu_*l (where u_* and l are the friction velocity at the bottom and the layer thickness, respectively), and where C≈15. A similar relation but based on external parameters only, becomes: