The seasonal thermal structure of deep temperate lakes

A theoretical description is given of the seasonal variation of the thermal structure of deep, temperate lakes. The influence of the unsteady and nonlinear interaction between the wind-induced turbulence and the stable buoyancy gradients due to surface heating on the thermal eddy diffusivities is assumed to be given by a product of the eddy diffusivities under conditions of neutral stability and an appropriate function of a stratification parameter, which, in this case, is taken to be the gradient Richardson number. An implicit account is taken of the interaction between the current and thermal structures within the lake, and free convection is also included implicitly during the cooling portion of the annual cycle. The basic equation, which is integrated by finite difference means, is an unsteady, nonlinear diffusion equation describing the vertical temperature structure. The boundary condition on the heat exchange at the lake surface is formulated in terms of the concept of an equilibrium temperature. The seasonal stratification cycle of a lake is determined as the response of the lake to certain imposed “external parameters” which specify the exchange of mechanical and thermal energies between the lake and the environment. The results of calculations of the vertical thermal structure using this model agree with the observed qualitative features of the stratification cycle. For the one case in which quantitative comparisons are made, good agreement with observations is obtained. A brief discussion comparing the features of the present theory with those of other existing theories is also given.