The vertical structure of the wind-driven circulation

Abstract

This thesis consists of three loosely related theoretical studies. In chapters 1 - 3 the physical mechanisms which determine the three dimensional structure of the currents in the Sverdrup interior of a wind-driven gyre are discussed. A variety of simple analytic models suggest that the subsurface geostrophic contours in a wind gyre are closed and so the flow in these regions is not determined by lateral boundary conditions. Instead a turbulent, quasigeostrophic extension of the Batchelor-Prandtl theorem suggests that the potential vorticity is uniform inside these laterally isolated regions. The requirement that the potential vorticity be uniform leads simply and directly to predictions of the shape and extent of the wind gyre and the vertical structure of the currents within it. In chapter 4 the propogation of Rossby wave trains through slowly varying forced mean flows is examined by solving the linearized potential vorticity equation using the WKB method. If the mean flow is forced the action defined by Bretherton and Garrett (1968) is not conserved. Surprisingly, there is another quadratic wave property which is conserved, the wave enstrophy. In chapter 5 shear dispersion in an oscillatory velocity field, similar to that of an inertial oscillation, is discussed. The goal of this section is to develop intuition about the role of internal waves in horizontal ocean mixing. The problem is examined using a variety of models and techniques. The most important result is (23.2) which is an expression for the effective horizontal diffusivity produced by the interaction of vertical diffusivity and oscillatory vertical shear. Given an empirical velocity shear spectrum and an estimate of the vertical diffusivity this result could be used to calculate a horizontal eddy diffusivity which parameterizes the horizontal mixing due to the internal wave field.