Wind-driven fluctuating western boundary currents

In this paper a linear theory for the barotropic large-scale current fluctu ations at midlatitudes driven by fluctuating winds is presented. It is base d on both numerical and analytical arguments and provides an extention of t he steady Munk's theory of the wind-driven circulation to the case of a tim e-dependent wind forcing. The numerical resolution of a circulation model f orced by an idealized oscillatory wind in a box leads to two distinct range s for the oceanic fluctuating response. The first one is Rossby wavelike an d westward intensified, with a width of the western boundary layer decreasi ng with increasing eddy viscosity A(H). For sufficiently high values of the latter, a second range arises in which the wavelike character disappears a nd the boundary layer width increases with A(H). To explain this behavior a n analytical expression is proposed for the first (linear inertial-viscous) range in terms of an appropriate superposition of damped forced Rossby wav es. Such expression provides also a length scale for the oscillating wester n boundary layer, which is inversely proportional to viscosity and proporti onal to the fourth power of the forcing frequency omega. The second (purely viscous) range corresponds to oscillating Munk's western boundary layer an d Sverdrup flow in the oceanic interior. A nondimensional number, Gamma = A (H)beta(2)/omega(3), is determined (beta is the variation of the Coriolis p arameter with latitude), which controls the transition between the two rang es. In the inertial-visicous range Gamma < 1, whereas in the purely viscous range Gamma > 1. The theory is validated by means of several numerical experiments for diffe rent values of A(H) and omega and is then applied to an idealized North Atl antic. The inertial-viscous range is found to be effective for forcing peri ods longer than 20-40 days and shorter than 60-130 days depending on the la teral eddy viscosity, whereas the time-dependent Munk layer and Sverdrup ba lance are expected for longer periods. The relevance of the present theory in connection with fluctuations of the width of western boundary currents a nd with GCM results is discussed. The experimental evidence of wind-driven fluctuations in large-scale oceanic currents is analyzed in relation to the se theoretical results.