Modelling of turbulent mixing at the shelf edge

Abstract

A two-dimensional cross-sectional model of the shelf slope, initially in the form of a single point model on the slope is used to investigate the sensitivity of the bottom boundary layer thickness, and along and across slope flows to the parameterization of vertical mixing and the magnitude of bottom friction. A range of formulations for determining bottom mixing, from simple, in terms of a Richardson-number-dependent mixing, through both one and two equation turbulence energy models are considered. Calculations using both upwelling and downwelling favourable along slope flows together with the cascading of dense water down the shelf slope, show that the solution in the downwelling case is significantly influenced by convective mixing rather than turbulent mixing and consequently is not particularly sensitive to the form of the turbulence energy closure model. In the upwelling case convective mixing does not occur and the solution is more sensitive to the methods used to parameterize vertical mixing. In the case of cascading where there is a significant density gradient above a well mixed bottom boundary layer the solution is particularly sensitive to the parameterization of mixing, and bottom friction. This suggests that measurements of boundary layer thickness, associated flow fields and bed stresses under upwelling or cascading conditions together with turbulence energy dissipation rates would yield a suitable data set for a rigorous validation of turbulence energy models, and hence improved parameterizations of mixing in shelf slope regions. Calculations using the model in cross shelf form show that in a more physically realistic situation, the assumption made in the single-point model that the flow above the bottom boundary layer is not influenced by changes in this layer is only correct on a short time scale (of order a few days). In the cross shelf calculation differences in shelf edge slope influence the thickness of the boundary layer, which varies from point to point. These changes in shelf slope and boundary layer thickness produce a circulation above the bottom boundary layer after a few days which invalidates the concept of this flow being independent of the boundary layer.