Wind-forced seasonal exchange between marginal seas and the open ocean

The circulation within marginal seas subject to periodic winds, and their exchange with the open ocean, are explored using idealized numerical models and theory. This is motivated by the strong seasonal cycle in winds over the Nordic Seas and the exchange with the subpolar North Atlantic Ocean through the Denmark Strait and Faroe Bank Channel, although the analysis is general in nature and relevant to other marginal seas. Two distinct regimes are identified: an interior with closed 𝑓 /ℎ contours and a shallow shelf region that connects to the open ocean. The interior develops a strong oscillating along-topography circulation with weaker ageostrophic radial flows. The relative importance of the bottom Ekman layer and interior ageostrophic flows depends only on 𝜔ℎ/𝐶_d , where 𝜔 is the forcing frequency, ℎ is the bottom depth, and 𝐶_d is a linear bottom drag coefficient. The dynamics on the shelf are controlled by the frictional decay of coastal waves over an along-shelf scale 𝐿 = 𝑓₀ 𝐿_s 𝐻_s /𝐶_d , where 𝑓₀ is the Coriolis parameter, and 𝐿_s and 𝐻_s are the shelf width and depth. For 𝐿 much less than the perimeter of the basin, the surface Ekman transport is provided primarily by overturning within the marginal sea and there is little exchange with the open ocean. For 𝐿 on the order of the basin perimeter or larger, most of the Ekman transport is provided from outside the marginal sea. There is also an opposite exchange through the deep part of the strait, as required to conserve mass within the marginal sea. This demonstrates a direct connection between the dynamics of coastal waves on the shelf and the exchange of deep waters through the strait, some of which is derived from below sill depth.