The estimation of vertical eddy diffusivities below the thermocline in lakes

Abstract

Mathematical models of the spatial and temporal variation of passive substances in lakes and oceans require a quantitative formulation of vertical turbulent transport. Methods of estimating vertical eddy diffusivity coefficients in lakes for such substances as temperature, inorganic ions, or biologically active materials are briefly reviewed. One widely used method, the McEwen method, is discussed, and it is shown how this method can lead to erroneous results. Another method, the flux gradient method, is examined and compared with the McEwen method in specific case studies of thermal energy transfers. Lack of agreement between values obtained by the McEwen method and the flux gradient method has led some investigators to postulate‐a flux of thermal energy into the deep layers of a lake by density currents. An alternative explanation of the discrepancy is offered by noting that deepwater turbulent mixing may result from a microstructure of layers and sheets caused by, for example, a Kelvin‐Helmholtz shear instability in the flows or other instability mechanisms.