The stability of frontally-trapped baroclinic waves along the crest of an oceanic ridge
on an f-plane is examined to determine under which conditions two neighboring, inviscid
water layers, each of uniform density and momentum, can coexist without mixing by eddies
associated with instabilities. A linear stability analysis for a weak disturbance is performed
over a steady laminar state. The study follows that of Gawarkiewicz [1991] for a frontal
system over a shelf-break, but deviates by building an implicit dispersion relation to solve,
by finite difference, a fourth-order ordinary differential equation. The implicit dispersion
relation for a submarine ridge, with straight slopes that extend to infinity, depends on four
parameters that characterize the physical system. They are the nondimensional wave
number, the nondimensionalized ridge slopes, and a quantity, analogous to the Richardson
number, that characterizes the shearing force against the buoyancy at the pycnocline. For a
model with finite straight slopes, the positions at which the slopes meet the flat bottom have
to be taken into account in t he boundary conditions.
The model is applied to various cases. First, both slopes are set to zero for a flat topography
case and for comparison with Orlanski [1968]. In the second case, a slope is
introduced beneath the front to simulate a shelf-break analogous to Flagg and Beardsley's
[1978] model with a seaward false bottom condition. Stable branches of backward-propagating
waves occur with phase velocity faster than the layers' speed. Unstable features
occur for waves with phase velocity less or equal to the layers' speed.
In further cases, the false bottom condition is replaced by shifting the foot of the ridge
away from the shelf break, into a near or far location. The main findings are that a ridgefoot
displacement does not change most unstable features, but it increases the number of stable
branches.
Finally, the shelfbreak model is modified for a symmetric ridge model by introducing
another finite straight slope of the same value and length. In these cases, the main unstable
features are not different from the shelfbreak model. It creates forward-propagating waves
with phase velocity faster than the layers' speed.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:BVAU.2429/5936 |
| Date | 05 1900 |
| Creators | De︠ry, Francis |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Relation | UBC Retrospective Theses Digitization Project [http://www.library.ubc.ca/archives/retro_theses/] |
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