Publication Date:
2022-05-26
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
June, 1982
Description:
Oceanic fluctuations are dependent on geographical location. Near
intense currents, the eddy field is highly energetic and has broad meridional
extent. It is likely that the energy arises from instabilities of
the intense current. However, the meridional extent of the linearly most
unstable modes of such intense jets is much narrower than the observed
region of energetic fluctuations. It is proposed here that weaker instabilities,
in the linear sense, which are very weakly trapped to the current,
may be the dominant waves in the far field.
As a preliminary problem, the (barotropic) instability of parallel
shear flow on the beta plane is discussed. An infinite zonal flow with
a continuous cross-stream velocity gradient is approximated with segments
of uniform flow, joined together by segments of uniform potential vorticity.
This simplification allows an exact dispersion relation to be found.
There are two classes of linearly unstable solutions. One type is trapped
to the source of energy and has large growth rates. The second type
are weaker instabilities of the shear flow which excite Rossby waves in
the far field: the influence of these weaker instabilities extends far
beyond that of the most unstable waves.
The central focus of the thesis i: the linear stability of thin, twolayer,
zonal jets on the beta plane, with both horizontal and vertical
shear. The method used for the parallel shear flow is extended to the
two-layer flow. Each layer of the jet has uniform velocity in the center,
bordered by shear zones with zero potential vorticity gradient. The
velocity in each layer outside the jet is constant in latitude. Separate
linearly unstable modes arise from horizontal and vertical shear. The
energy source for the vertical shear modes is nearly all potential while
the source for the horizontal shear modes is both kinetic and potential.
The most unstable waves are tightly trapped to the jet, within two or
three deformation radii for small but nonzero beta. Rossby waves and
baroclinically unstable waves (in the presence of vertical shear) exist
outside the jet because of a nonzero potential vorticity gradient there.
Weakly growing jet instabilities can force these waves when their phase
speeds and wavelengths match. In particular, westward jets and any jets
with vertical shear exterior to the jet can radiate in this sense. The
radiating modes influence a large region, their decay scales inversely
proportional to the growth rate. Two types of radiating instability are
found: (1) a subset of the main unstable modes near marginal stability
and (2) modes which appear to be destabilized neutral modes. Westward
jets have more vigorously unstable radiating modes.
Applications of the model are made to the eddy field south of the Gulf
Stream, using data from the POLYMODE settings along 55°W and farther into
the gyre at MODE. The energy decay scale and the variation of vertical
structure with latitude in different frequency bands can be roughly explained
by the model. The lower frequency disturbances decay more slowly
and become more surface intensified in the far field. These disturbances
are identified with the weak, radiating instabilities of the model. The
higher frequency disturbances are more trapped and retain their vertical
structure as they decay, and are identified with the trapped, strongly
unstable modes of the jet.
Description:
This work was supported by a grant from the National Science Foundation,
Office of Atmospheric Science.
Keywords:
Baroclinicity
;
Eddy flux
;
Ocean currents
;
Ocean circulation
Repository Name:
Woods Hole Open Access Server
Type:
Thesis
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