Mixing and stratification in lakes of varying horizontal length scales: Scaling arguments and energy partitioning

Abstract

This work analyzes the effects that changes in the surface area of stratified lakes have on the partitioning of energy among different pools, and, ultimately, on the strength of thermal stratification. Proposed restoration plans for the Salton Sea (USA), the surface area of which could be reduced by 80%, provided the original motivation of this work. Scaling arguments, based on a one‐dimensional model of lake stratification and three‐dimensional simulations, are consistent in predicting weaker mixing for smaller lakes. It is demonstrated that energy partitioning is affected by geometry for lakes that have a quarter internal wave period (Ti/4) that is shorter than the duration of wind forcing events, ∆tw. In these cases, it is demonstrated that mixing is, in general, stronger in larger basins due to greater mechanical energy fluxes across the free surface; larger shear production of turbulent kinetic energy Etk; and a larger fraction of Etk becoming background potential energy through diapycnal mixing. All these variables scale with the length of the basin. In lakes where Ti/4 > ∆tw, the rates of exchange among the different energy pools and the magnitudes of these pools are not sensitive to changes in lake size. Our results suggest that stratification in the reduced Salton Sea will be stronger than in the lake as it exists today, mainly in late summer. It is during that time when, due to high insolation values, stratification becomes strong and Ti/4 in the reduced sea will likely become small in comparison with the diurnal winds.