Title:
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Gravity Currents on Earth and Mars.
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In this thesis we ~nvestigate three problems in the earth sciences where
gravity currents play an important role.
In the first part we consider two types of terrestrial gravity current: kata- .
batic winds and submarine turbidity currents. We derive and solve the
classical Prandtl model for katabatic wind flow in which the vertical wind
profile is resolved. We show that this model breaks down when the slope
becomes small, and pose a~ improved model which removes this singularity.
Solutions of the improved model are compared with observations and
output from a numerical model.
We then investigate two layer-averaged models that are used to describe
the flow of submarine turbidity currents. We find that both models predict
that in some circumstances 'ignition' can occur, in which the current velocity
becomes unbounded. We show that the only way this phenomenon
can be prevented is by a decrease in the underlying slope.
In the second part, we consider the unusual morphology of the Martian
north polar ice cap. We use a model for the sublimation kinetics at the
ice-atmosphere interface and include an explicit description of dust, both
suspended in the atmosphere and frozen within the ice cap. Thansport of
dust and ice are then included, and the model is investigated analytically
and numerically. We find that this model can have multiple steady states,
and that troughs may form during a transition between steady states. In
this model, such a transition may be caused by obliquity-induced climate
change.
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