Response characteristics of a buoyancy-driven sea

The authors consider the flow in a semienclosed sea, or basin, subjected to a destabilizing surface buoyancy flux and separated from a large adjoining reservoir by a sill. A series of numerical experiments were conducted to q uantify the energetics of the flow within the basin, that is, the amount of kinetic and potential energy stored within the basin and the rate at which these quantities are transported to and from the reservoir via the exchang e flow over the sill. The numerical experiments were formulated at laborato ry scales and conducted using a boundary-fitting, clustered grid to resolve the entrainment and mixing processes within the flow and to facilitate qua ntitative comparison with previous laboratory experiments. Volume and boundary integrated energetics were computed for both steady and time-varying flows. In the steady-state limit, the rate of energy flux thr ough the surface is balanced by dissipation within the basin and advection of potential energy over the sill and into the reservoir. The analyses focu s primarily on this latter quantity because it is closely related to the ou tflow density and volume transport in two-layered exchange flows. Scaling l aws relating the energetics of the flow to the surface buoyancy flux and th e geometrical scales of the basin-sill system are derived and validated usi ng the numerical results. A second set of experiments was conducted to quantify the transient energet ics in response to a sudden change in the surface forcing. These results, c ombined with a linear impulse-response analysis, were used to derive a gene ral expression describing the advection of potential energy across the sill for periodically forced systems, The analytical predictions are shown to c ompare favorably with directly simulated flows and to be reasonably consist ent with limited field observations of the seasonal variability through the Strait of Bab al Mandab.