Publication Date:
2022-05-25
Description:
Submitted in partial fulfillment of the
requirements for the degree of
Doctor of Philosophy
at the Massachusetts Institute of Technology
and the Woods Hole Oceanographic Institution
April, 1976
Description:
Two numerical applications of two-level quasigeostrophic theory
are used to investigate the interrelationships of the mean and mesoscale
eddy fields in a closed-basin ocean model. The resulting techniques
provide a more accurate description of the local dynamics, origins, and
parametric dependences of the eddies than that available in previous
modelling studies.
First, we propose a novel and highly efficient quasigeostrophic
closed-domain model which has among its advantages a heightened resolution
in the boundary layer regions. The pseudospectral method,
employing an orthogonal expansion in Fourier and Chebyshev functions,
relies upon a discrete Green's function technique capable of satisfying
to spectral accuracy rather arbitrary boundary conditions on the
eastern and western (continental) walls. Using this formulation, a
series of four primary numerical experiments tests the sensitivity of
wind-driven single and double-gyred eddying circulations to a transition
from free-slip to no-slip boundary conditions. These comparisons
indicate that, in the absence of topography, no-slip boundaries act
primarily to diffuse vorticity more efficiently. The interior transport
fields are thus reduced by as much as 50%, but left qualitatively unchanged.
In effect, once having separated from the western wall, the
internal jet has no know1edge, apart from its characteristic flow
speed, of the details of the boundary layer structure.
Next, we develop a linearized stability theory to analyze the
local dynamic processes responsible for the eddy fields observed in
these idealized models. Given two-dimensional (x, z) velocity profiles
of arbitrary horizontal orientation, the resulting eigenfunction
problems are solved to predict a variety of eddy properties: growth
rate, length and time scales, spatial distribution, and energy fluxes.
This simple methodology accurately reproduces many of the eddy
statistics of the fully nonlinear fields; for instance, growth rates
of 10-100 days predicted for the growing waves by the stability
analysis are consistent with observed model behavior and have been
confirmed independently by a perturbation growth test. Local energetic
considerations indicate that the eddy motions arise in distinct and
recognizable regions of barotropic and baroclinic activity. The baroclinic
instabilities deîend sensitively on the vertical shear which
must exceed 0(5 cm sec-1) across the thermocline to induce eddy growth.
As little as a 10% reduction in |uz|, however, severely suppresses the
cascade of mean potential energy to the eddy field. In comparison,
the barotropic energy conversion process scales with the horizontal
velocity shear, |uy|, whose threshold values for instability,
a (2 x 10-6 sec-1), is undoubtedly geophysically realizable. A simple
scatter diagram of |uy| versus |uz| for all the unstable modes studied
shows a clear separation between the regions of barotropic and baroclinic
instability. While the existence of baroclinic modes can be
deduced from either time mean or instantaneous flow profiles, barotropic
modes cannot be predicted from mean circulation profiles (in
which the averaging process reduces the effective horizontal shears).
Finally, we conduct a separate set of stability experiments on
analytically generated jet profiles. The resulting unstable modes
align with the upper level velocity maxima and, although highly sensitive
to local shear amplitude, depend much less strongly on jet
separation and width. Thus, the spatial and temporal variability of
the mesoscale statistics monitored in the nonlinear eddy simulations
can be attributed almost entirely to time-dependent variations in local
shear strength. While these results have been obtained in the absence
of topography and in an idealized system, they yet have strong implications
for the importance of the mid-ocean and boundary layer regions as
possible eddy generation sites.
Description:
This research has been made possible by National Science Foundation grant
OCE74-03001 A03, formerly DES73-00528, and the National Science
Foundation funded National Center for Atmospheric Research.
Keywords:
Ocean currents
;
Ocean waves
Repository Name:
Woods Hole Open Access Server
Type:
Thesis
Format:
6161797 bytes
Format:
application/pdf
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