Theoretical Model of the Thermocline in a Freshwater Basin

Abstract

Two striking empirical facts represent a starting point of the discussion: (i) vertical temperature profile in a thermocline, a region of supercritical stability adjoining a mixed layer, proves to be self-similar in a series of laboratory experiments and, though with much less accuracy, in natural water reservoirs; (ii) comparison of the experimental data on kinematic heat flux Q and vertical temperature gradient ?T/?z shows that the effective heat conductivity K ≡ ?Q/(?T/?z) is much higher than the molecular one, and, rather unexpectedly, increases with the increase of |?T/?z|, in contrast with the well-known inverse dependence of K on |?T/?z|, which takes place in weakly stable shear flows. A theoretical model of a regime under consideration is proposed based on the hypothesis on governing parameters of intermittent turbulence generated on the background of strongly stable stratification by breaking of internal waves and turbulence/wave interactions, the heat transfer equation and the balance equation for turbulent kinetic energy. The solution of the problem of a propagating-wave type coincides with the empirical approximation of a dimensionless, self-similar temperature profile only in the special case of pronounced deepening of the mixed layer. This explains the fact of much better accuracy of similarity representation of the temperature profile in laboratory thermoclines. Indeed, all known experiments just dealt with development of a thermocline under the condition of a deepening mixed layer. The model contains two dimensionless constants whose values are found by means of comparison of the solution with the results of laboratory experiments on penetrative conviction. Using these constants, a numerical simulation of the thermocline in laboratory experiments by Deardorff and Willis on shear currents in an annulus appears to be quite realistic. This result confirms applicability of the model to different types of laboratory thermoclines.