Circulation and exchange in choked marginal seas

Abstract

A theory for the exchange between a rotating, buoyancy-forced marginal sea and an ocean is developed and tested numerically. Cooling over the marginal sea leads to sinking and sets up a two-layer exchange flow, with a warm surface layer entering from the ocean and a cool layer exiting at depth. The connecting strait is sufficiently narrow and shallow to cause the exchange flow to be hydraulically controlled. The incoming surface layer forms a baroclinically unstable boundary current that circles the marginal sea in a cyclonic sense and feeds heat to the interior by way of eddies. Consistent with the overall heat and volume balances for the marginal sea, there is a continuous family of hydraulically controlled states with critical flow at the most constricted section of the strait. Included in this family is a limiting “maximal-exchange” solution with two sections of hydraulic control in the strait and with fixed layer depths at the most constricted section. The state of exchange for a given forcing is predicted using a theory that assumes energy conservation over a certain path connecting the strait to the marginal sea or, in some cases, the ocean. Depending on the configuration of the exchange, long-wave information may be blocked from entering the strait from the marginal sea, from the open ocean, or both. The scenario that holds determines what is predicted and what needs to be input. Numerical tests of the prediction for the temperature difference and the state of exchange are carried out for straits with a pure contraction in width and for a constant width strait with a topographic sill. The comparison is reasonable in most cases, though the numerical model is not able to reproduce cases of multiple states predicted by the theory for certain forcing values. The analytical model is an alternative to the Price and Yang and Siddall et al. models of a marginal sea outflow.