The momentum balance of steady flow past an island

The momentum balance of steady flow past an island R C Musgrave and T Peacock Massachusetts Institute of Technology rmusg@mit.edu Abstract The interaction of large-scale ocean currents with tall topography generates phenom- ena from turbulence at the smallest scales, to lee waves and quasi-geostrophic eddies at the largest. We investigate the role of such processes in setting the momentum balance downstream of an island in an idealized, three-dimensional numerical simulation. Our parameter regime is inspired by conditions close to Palau in the western Pacific, where the North Equatorial Current is incident on the meridionally oriented island and Mariana Ridge. In our highly idealized setup, a strong, shallow, meridionally tilted thermocline supporting a zonal geostrophic surface flow encounters a tall, meridionally elongated is- land. Pressure gradients are setup around the ridge which drive both ageostrophic and geostrophic processes, extracting and redistributing momentum from the background flow. Introduction The classical problem of unstratified flow past a bluff body is associated with a range of processes, including boundary layer formation, flow separation, vortex shedding and form drag (Kundu et al., 2012). In the ocean, flow past islands gives rise to qualitatively sim- ilar processes, but it is modified by planetary rotation, stratification, non-uniform flows and irregular bathymetry. Island wakes in the lee of a cylindrical island were considered in a comprehensive study by Dong et al. (2007), who found that flows are sensitive to three nondimensional parameters: the Reynolds number (Re), Rossby number (Ro) and the Burger number (Bu). As for homogeneous flows, wake eddies are attached for low Reynolds numbers, and form a von K´arm´an vortex street for high Reynolds numbers. However, stratification and rotation cause the evolution of the wake to differ from the ho- mogeneous case, with the appearance of centrifugal, barotropic and baroclinic instabilities downstream. The influence of topography on the large scale circulation is mediated by such pro- cesses, which redistribute the momentum of the overlying flow. In addition to triggering wake eddies, islands in the ocean have submerged flanks which can generate lee waves. In the atmosphere, lee waves alter the mean flow by transporting momentum away from topography and depositing it where they dissipate (Bretherton, 1969). In this idealized numerical study, we begin to relate the effects of islands to the larger scale wind driven circulation of the subtropical gyres by examining their influence on momentum pathways. The subtropical gyres are commonly assumed to be in Sverdrup balance, which means that the momentum input by the wind is balanced by lateral viscos- ity at strong western boundary currents. This linear theory assumes a flat ocean bottom, and though it appears to explain the largest scale flows, evidence of this balance in the real ocean has not been established (Wunsch and Roemmich, 1985). In contrast to the gyres, the Antarctic Circumpolar Current is thought to be in a different balance, with the momentum input by the windstress balanced by bottom pressure against topography. We are interested in the importance of both form drag and nonlinear processes arising VIII th Int. Symp. on Stratified Flows, San Diego, USA, Aug. 29 - Sept. 1, 2016