The Salinity, Heat, and Buoyancy Budgets of a Coastal Current in a Marginal Sea

The Atlantic overturning circulation has conventionally been pictured in the meridional-vertical plane, but a significant densification of the water masses involved also occurs as the surface branch of the circulation flows in boundary currents around the subpolar gyre and northern marginal seas. Here an analytical model of the heat and salt budget for an idealized coastal boundary current in a marginal sea is presented. The boundary current exchanges heat and freshwater with the atmosphere as well as with the interior of the basin through eddy and Ekman transports. Its along-coast volume transport is assumed to be constant and independent of buoyancy; it is set, for example, by the wind forcing. Because the atmospheric fluxes of heat and freshwater are different, the temperature and salinity of the boundary current adjust on different length scales. The size of these length scales compared with the circumference of the basin determines the properties of the water that flows over the sill. Furthermore, the relative size of the two length scales determines the evolution of the density as the current moves around the basin. If temperature and salinity adjust on the same length scale (or if the density forcing is represented by a single component), then the density will increase or decrease monotonically from the inflow to the outflow. However, when the adjustment length scale for temperature is shorter than that for salinity, a warm and salty inflow can cool significantly before it freshens. As a result, the density first increases to a local maximum before decreasing again. Therefore, when salinity as well as temperature is included in the buoyancy forcing, the outflow from the basin can be significantly denser than for the equivalent single-component density forcing and can be more sensitive to the forcing parameters. The relevance and implications for the Nordic seas are discussed.