Thermohaline circulation in a two-layer model with sloping boundaries and a mid-ocean ridge

A model ocean basin has continental slopes at the west and north and a mid-ocean ridge running north–south. The first problem treated here is Stommelʹs (Deep-Sea Res. 5 (1958) 80) abyssal flow of a homogeneous fluid in the presence of topography with a source of fluid at the northwest corner. The flow is driven by uniform upwelling everywhere except over the non-flat topography where the fluid is not driven and inviscid. The solution over the topography is determined by conservation of potential vorticity with the flow being driven by matching to the known solution over the flat bottom. A second problem is the two-layer case for which we use an analysis by Salmon (J. Mar. Res. 50 (1992) 341) in which he obtained expressions for the potential vorticity distribution for inviscid, non-forced flow over topography. We produce analytical solutions for the two-layer case. Conservation of potential vorticity over the slopes leads to flows that make large north–south excursions as the fluid crosses the topographic regions over the western slope and the mid-ocean ridge. We justify our procedure by showing a similarity between a wind-driven double gyre solution of Salmonʹs that shows a cyclonic circulation on the onshore (Gulf Stream) side of the anticyclonic wind gyre and an observed cyclonic gyre in the Slope Sea inshore of the Gulf Stream. For the two-layer case we obtain flow over the midocean ridge in the lower layer that compares favorably with the excursion of particles over the mid-Atlantic Ridge as reported by Defant (Deutsche Atlantische Expedition ‘Meteor’ 1925–1927, 6, 1941, pp. 191–260; Physical Oceanography, Vol. I, Pergamon Press, New York, Oxford, London, Paris, 1961). Our inviscid solutions contain sharp discontinuities which will have to be smoothed by friction when viscosity is added, but it is possible that friction will take the flow far from the one that we have derived. A numerical solution of the problem is planned to test this possibility.