UBC Theses and Dissertations
Linear stability analysis of a oceanic frontal system over a Submarine ridge De︠ry, Francis
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  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 . In the second case, a slope is introduced beneath the front to simulate a shelf-break analogous to Flagg and Beardsley's  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.
Item Citations and Data