| Summary: | The influence of submarine canyons on currents is studied using the Rossby adjustment method
for an inviscid fluid on an /-plane. Two geometric models are used: (1) a flat
bottom, uniform width, vertical edged and infinitely long canyon which cuts through a flat
infinite ocean (F canyon model), and (2) a sloping bottom, uniform width, vertical edged
and finite long canyon which extends from the shelf break into a semi-infinitely long strait
(S canyon model).
The waves which exist around an F canyon are composed of both superinertial
waves (Poincare waves) and subinertial waves ("canyon waves"). The canyon waves are
more important than Poincare waves in the determination of the steady state. The dispersion
relation of the canyon waves is obtained. The canyon waves are dispersive and propagate
in both directions along the canyon.
While both the geostrophic and the transient solutions of Rossby adjustment over
the F and the S canyons are studied, the emphasis of this thesis is to study the geostrophic
state. For a homogeneous fluid in the northern hemisphere: (1) when a shelf flow approaches
an F canyon, a net transport along the canyon is generated to the left (looking
downstream) of the approaching shelf flow; (2) when a shelf flow approaches an S canyon,
if the flow is left-bound (with the coast to its left looking downstream), a net in-canyon
flux is generated, while if the flow is right-bound (with the coast to its right looking
downstream), a net out-canyon flux is generated. For a two-layer stratified fluid (regardless
of the shear) in the northern hemisphere: (3) over an F canyon in which the interface is above the shelf, the lower layer adjusts over the canyon in a similar way as in a homogeneous
fluid but over the length scale of the baroclinic Rossby radius, while the upper layer
adjusts in a way to accommodate the changes at the interface; (4) over an S canyon in
which the interface is below the shelf, a left/right-bound shelf flow leads to an in/outcanyon
flow throughout the water column.
The time scale for adjustment is 1/f for both a homogeneous and a stratified fluid.
A parameter, σ ε {0, 1}, which is denoted as the Canyon Number, is found to
control the geostrophic state over a canyon. The Canyon Number, which is calculated from
the geometric parameters of the shelf-canyon system, determines the interactive strength of
one canyon edge on the circulation induced by the other edge. The parameter cr can be
used to unify theories over canyons, steps, ridges and straits.
The research has demonstrated that a canyon can have an important influence on
cross-shelf circulation and has gone beyond earlier work in explaining the details of flow
patterns around canyons.
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