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.
