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 quantify 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 exchange flow over the sill. The numerical experiments were formulated at laboratory scales and conducted using a boundary-fitting, clustered grid to resolve the entrainment and mixing processes within the flow and to facilitate quantitative 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 through the surface is balanced by dissipation within the basin and advection of potential energy over the sill and into the reservoir. The analyses focus primarily on this latter quantity because it is closely related to the outflow density and volume transport in two-layered exchange flows. Scaling laws relating the energetics of the flow to the surface buoyancy flux and the geometrical scales of the basin–sill system are derived and validated using the numerical results. A second set of experiments was conducted to quantify the transient energetics in response to a sudden change in the surface forcing. These results, combined with a linear impulse–response analysis, were used to derive a general expression describing the advection of potential energy across the sill for periodically forced systems. The analytical predictions are shown to compare favorably with directly simulated flows and to be reasonably consistent with limited field observations of the seasonal variability through the Strait of Bab al Mandab.