On the dynamics of the near-surface currents in the Arctic Ocean

Abstract

Starting from the Navier–Stokes equation (in rotating, spherical coordinates), and the equation of state coupled with the first law of thermodynamics for the atmosphere, a general description of the near-surface flow in the Arctic Ocean, and the atmosphere above it, is developed. This includes a suitable stress boundary condition at the air–ice–water interface. Invoking only the thin-shell approximation, for both the atmosphere and the ocean, an appropriate asymptotic reduction is developed; this approach ensures that all the physical attributes are retained at leading order. The wind is described via the properties of the Prandtl layer and the atmospheric boundary layer, with some observations about the geostrophic flow higher in the troposphere. The corresponding equations for the ocean, with a suitable surface wind, are used to model the two dominant features of the arctic surface-current field: the rotating Beaufort Gyre and, using a transformation of the spherical coordinates that removes the polar singularities in geographical coordinates, the Transpolar Drift. In addition, we show that the stress conditions at the ice–water interface ensure that the sea-ice necessarily moves faster than the ocean on which it floats, and in a direction between that of the surface wind and that of the ocean surface current.