The influence of topography on steady currents and internal waves

Abstract

Observations of the ocean in the vicinity of Bermuda on two different occasions show systematic distortions of the isotherms close to the island and an area of intensive mixing on the northern coast. Two mechanisms are investigated and each produces some agreement with data from different flow regimes. Firstly, the island is modeled as a circularly symmetric obstacle with steep sides and a small aspect ratio. A steady, rotating, and stratified flow which, far from the island, is uniform in the horizontal and a linear function of the vertical coordinate is taken to be flowing past the island. Neglecting circulation effects, the problem is solved to first order in a small parameter, α, which measures the steepness of the island and a small Rossby number, ε. This allows a calculation of the depth contours of isotherms to 0(ε2,εα). For one set of data the flow is such that the slope effect of 0(εα) predominates while for another period of observation both slope and Rossby number influences are of the same magnitude. In both cases qualitative agreement between fact and theory is remarkably good. In addition, it is shown that the north slope (for a west-east current) is the most favored area for mixing as there the Richardson number is a minimum and the flow is most likely to separate from the boundary. A second means of producing isotherm distortion and mixing areas close to the island concerns the nonlinear effects of shoaling internal gravity waves. For normal incidence on a two-dimensional beach the Reynolds stresses produced by the fundamental wave motion are shown to force a mean Eulerian current which is equal hut opposite in sense to the Stokes drift. This causes the mean Lagrangian current to vanish so that the physical constraint that there be no net motion of fluid particles along isopycnals into the beach is satisfied. In addition, isotherms are distorted in a fashion analogous to the surface set-down produced by shoaling surface waves. The mean isopycnal shift can be as much as 10m where the theory has some validity. Distortions of the predicted form are observed in the data from a period when the mean currents were small. Consideration of the oblique incidence problem shows that this generalization has little effect on the expected magnitude of the shifts but that a significant longshore current can be forced by the breaking of the waves.