Near-surface mixing in a freshwater lake

Abstract

Mixing rates in the upper 10 m of a freshwater lake during the spring heating season are examined by means of fine-structure temperature profiles. Dissipation rate, eddy diffusivity, and vertical heat flux are estimated from 'Thorpe reordering' of measured temperature profiles, a technique that allows these parameters to be obtained from the energy-containing scales of the turbulence rather than from the much smaller scales at which kinetic energy dissipation and scalar diffusion actually occur. The estimated vertical heat fluxes agree reasonably well with the seasonal variability of the lake's total heat content and with the observed short-term variability in mixed-layer temperature. These results suggest that satisfactory estimates of turbulent vertical diffusivities in the surface mixing layer can be obtained from Thorpe reordering. This technique can be applied to data that are considerably simpler and cheaper to obtain than are the measurements of microscale shear required for the more usual 'dissipation' method. Concurrent measurements of vertically averaged shear from a nearby surface mooring are used to study the use of Richardson numbers as a parameter in diffusion models. It is shown that considerable mixing can occur even when the Richardson number based on vertical and temporal averages of shear and density gradient is much larger than the assumed critical value of O(1). Therefore, in regions where the shear and strain variances evaluated over a fixed vertical scale cannot be related either observationally or by means of modelled spectra to the unresolved high wave-number variances, the use of diffusivity parametrizations based on measured, averaged Richardson numbers cannot be justified.