A diffusion model for the development of a boundary layer in lakes

Abstract

The development of a boundary layer characterised by very low gradients in temperature and salinity near the bottom boundary of a lake does not necessarily imply an increase in diapycnal mixing within the boundary layer. The results of a quasi three-dimensional diffusion model for a basin with sloping boundaries demonstrate that in lakes a boundary layer also develops when the diapycnal diffusivity is chosen to be constant.

In the model mixing is assumed to be anisotropic and is described as an isopycnal and diapycnal turbulent diffusion process. Advective transport is not considered. Therefore, the model is restricted to the description of the purely diffusive response of a lake. It should be regarded as a contribution to the discussion of boundary mixing and not as a complete mixing model for a specific lake. The isopycnal and diapycnal turbulent diffusion coefficients are presumed to be constant in space and time. The direction of isopycnal and diapycnal density flux changes with time since mixing of the density distribution influences the orientations of the isopycnals. This interaction between mixing process and density distribution is accounted for by the model.

According to the model the density distribution, and therefore the development of a boundary layer, only depends on diapycnal mixing while the distribution of a passive tracer depends on both, isopycnal and diapycnal mixing. The application of the model to the subalpine Lake Alpnach demonstrates that a simple diffusion model is sufficient to predict the development of a boundary layer. Considering that the model does not include advective processes and that diffusivities have been assumed to be constant in space and time, the structure of the boundary layer predicted agrees surprisingly well with experimental data.