Exchange between a freshwater embayment and a large lake through a long, shallow channel

Abstract

We analyze the exchange between a weakly forced lacustrine embayment and a large lake through a long, shallow channel. Exchange in the channel is the result of a multiple and subtle balance in which spatial thermal variations (baroclinic forcing), oscillations in the water level (barotropic forcing), bottom friction, diffusion, wind forcing, and the effects of unsteadiness are all important. Temperature gradients across the channel result from differences in thermal inertia of the embayment and lake at seasonal time scales and differences in the wind-driven internal dynamics of the lake and the embayment at diurnal to synoptic time scales. These gradients are, in general, weak and barotropic forcing dominates the channel momentum balance; however, episodic upwelling in the lake can shift the balance in favor of baroclinic dominance. A combination of scaling, analysis of observational data, and threedimensional simulations are used to demonstrate that bed stress, vertical turbulent diffusion, wind stress, and unsteadiness effect exchange relative to the predictions of internal hydraulic theoryߞthe quasisteady inviscid theory that describes the motion resulting from a purely barotropic/baroclinic force balance.