Waves and circulation driven by oscillatory winds in an idealized ocean basin

We examine, via direct numerical integration, the transient and rectified response of a flat-bottomed barotropic ocean to a spatially localized oscillatory wind-stress pattern. These experiments exemplify in many respects the dynamics which drive the deep motion in recent eddy-resolving ocean circulation studies [e.g., Holland and Rhines (1980)], and may be contrasted with the results of Pedlosky (1965) and Veronis (1966) for spatially broad, time-dependent forcing. By considering doubly re-entrant (periodic) and closed basin geometries, the structure and magnitude of the induced circulation is shown to depend most critically on the form of the mean quasi-geostrophic contours (which are closed and blocked, respectively, in the periodic and basin geometries). In both situations, however, the forced primary wave field may be usefully understood by appeal to the radiation pattern of a time-periodic Green's function, and (in a basin) its image in the western boundary. The dynamics of the prograde and retrograde rectified circulation is seen to relate most directly to the mean eddy potential vorticity flux v′ q′ (and not to the Reynolds stress u′ v′). In particular: Eulerian vorticity budgets indicate the dominance of the turbulent Sverdrup balance [βv ∼—▿ · v′q′] in nearly all parts of the flow; Lagrangian (particle-wise) balances clearly emphasize the regions of counter-gradient q fluxes in providing the propulsion necessary for fluid particles to cross the mean quasigeostrophic contours. Although these flows do not strictly comply with the assumptions of recent q-transport theories, nonetheless all the qualitative (and some of the quantitative) features predicted by these theories are confirmed in the simulations.