Submaximal exchange between a convectively forced basin and a large reservoir

Abstract

If a sill-enclosed basin, connected to a large reservoir, is suddenly subjected to a de-stabilizing surface buoyancy flux, it will first mix vertically by turbulent convection before the resulting lateral buoyancy gradient generates a horizontal exchange flow across the sill. We present a study which examines the unsteady adjustment of such a basin under continued steady forcing. It is shown, through theoretical development and laboratory experimentation, that two consecutive unsteady regimes characterized by different dynamic balances are traversed as the flow approaches a steady state.Once established the exchange flow is controlled at the sill crest where it is hydraulically critical. In the absence of a lateral contraction, the single control at the sill crest allows a range of submaximal exchange states with the flow at the sill being dependent not only on the forcing and geometrical parameters but also on mixing conditions within the basin which are, in turn, dependent on the sill exchange. The sill–basin system is therefore strongly coupled although it remains isolated from the external reservoir conditions by a region of internally supercritical flow. Results from the laboratory experiments are used to demonstrate the link between the forcing and the exchange flow at the sill. Steady-state measurements of the interior mean velocity and buoyancy fields are also compared with previous analytical models.