Ocean circulations driven by meridional density gradients

Abstract

State-of-the-art ocean models spinning up from realistic density fields rapidly develop deep western boundary currents and meridional overturning circulations (MOCs). Wajsowicz and Gill [Wajsowicz, R. and Gill, A.E., Adjustment of the ocean under buoyancy forces, Part I: the role of Kelvin waves. J. Phys. Oceanogr. 1986, 16, 2097–2114] found that the initial spin-up of a flat-bottomed ocean model from a meridionally varying density field is well described by the shallow water equations for a two-layer fluid and that the initial evolution on a β-plane could be understood in terms of f-plane dynamics: Kelvin waves propagate rapidly round the ocean boundaries establishing eastern and western boundary currents. The time-mean baroclinic motion of a two-layer fluid in a closed basin on an f-plane which spins up from an initial state of rest with a meridionally sloping interface is derived here and compared with Gill's [Gill, A.E., Adjustment under gravity in a rotating channel, J. Fluid Mech. 1976, 77, 603–621] steady-state solution for an open channel. These solutions are used to illustrate the constraints imposed by the no normal flow inviscid boundary conditions which also apply to solutions on a sphere or β-plane. Miles’ [Miles, J.W., Kelvin waves on oceanic boundaries. J. Fluid Mech. 1972, 55, 113–127] solution for Kelvin waves on a sphere is used to analyse the initial spin-up on a β-plane. Motivated by the slow speed of the geostrophic adjustment by the planetary waves at mid- to high-latitudes and the influence of the inviscid boundary conditions, simple, analytical steady-state solutions driven by relaxation of the internal interface towards a meridionally varying reference field and closed by dissipative boundary layers are derived using the planetary geostrophic equations for the baroclinic motion in a two-layer fluid. The solutions can be applied to basins which span the equator and derived using the full nonlinear continuity equation for any shape of basin. The depth of the internal interface is constant along the eastern boundaries and the equator but its east–west variations can be a large fraction of the pole to equator difference at high latitudes. The solutions support significant MOCs and, when periodic east–west boundary conditions are imposed at the southern boundary, can be shown to have a significant cross-equatorial baroclinic flow in the western boundary layer with greater southward flow in the lower layer than the surface layer.