Abstract:
This thesis is made of two separate, but interrelated parts.
In Part I the instability of a baroclinic Rossby wave
in a two-layer ocean of inviscid fluid without topography,
is investigated and its results are applied in the ocean.
The velocity field of the basic state (the wave) is characterized
by significant horizontal and vertical shears, non-zonal
currents, and unsteadiness due to its westward propagation.
This configuration is more relevant to the ocean
than are the steady, zonal 'meteorological' flows, which
dominate the literature of baroclinic instability. Truncated
Fourier series are used in perturbation analyses.
The wave is found to be unstable for a wide range of
the wavelength; growing perturbations draw their energy from
kinetic or potential energy of the wave depending upon
whether the wavelength, 2πL, is much smaller or larger than
2πLρ, respectively, where Lρ is the internal radius of deformation. When the shears are comparable dynamically,
L~Lρ , the balance between the two energy transfer processes is very sensitive to the ratios L/Lρ and U/C as well,
where U is a typical current speed, and C a typical phase
speed of the wave. For L = Lρ they are augmenting if
U < C, yet they detract from each other if U > C.
The beta-effect tends to stabilize the flow, but perturbations
dominated by a zonal velocity can grow irrespective
of the beta-effect.
It is necessary that growing perturbations are comprised
of both barotropic and baroclinic modes vertically.
The scale of the fastest growing perturbation is significantly
larger than L for barotropically controlled flows
(L < Lρ ), reduces to the wave scale L for a mixed kind
(L ~ Lρ ) and is fixed slightly larger than Lρ for baroclinically controlled flows (L > Lρ ).
Increasing supply of potential energy causes the normalized
growth rate, αL/U, to increase monotonically as
L → Lρ from below. As L increases beyond Lρ,
the growth rate αLρ /U shows a slight increase, but soon
approaches an asymptotic value.
In a geophysical eddy field like the ocean this model
shows possible pumping of energy into the radius of deformation
(~ 40 km rational scale, or 250 km wavelength) from
both smaller and larger scales through nonlinear interactions,
which occur without interference from the beta-effect.
The e-folding time scale is about 24 days if
U = 5 cm/sec and L = 90 km. Also it is strongly suggested
that, given the observed distribution of energy versus
length scale, eddy-eddy interactions are more vigorous than
eddy-mean interaction, away from intènse currents like the
Gulf Stream. The flux of energy toward the deformation
scale, and the interaction of barotropic and baroclinic
modes, occur also in fully turbulent 'computer' oceans, and
these calculations provide a theoretical basis for source of
these experimental cascades.
In Part II an available potential energy (APE) is defined
in terms appropriate to a limited area synoptic density
map (e.g., the 'MODE-I' data) and then in terms appropriate
to time-series of hydrographic station at a single geographic location (e. g., the 'Panulirus' data).
Instantaneously the APE shows highly variable spatial
structure, horizontally as well as vertically, but the vertical
profile of the average APE from 19 stations resembles
the profile of vertical gradient of the reference stratification.
The eddy APE takes values very similar to those of
the average kinetic energy density at 500 m, 1500 m and
3000 m depth in the MODE area.
In and above the thermocline the APE has roughly the
same level in the MODE area (centered at 28°N, 69° 40'W) as
at the Panulirus station (32° 10'N, 64° 30'W), yet in the
deep water there is significantly more APE at the Panulirus
station. This may in part indicate an island effect near
Bermuda.