Flow over finite isolated topography
Citable URI
https://hdl.handle.net/1912/5459DOI
10.1575/1912/5459Abstract
One and two layer models are used to study flow over axisymmetric isolated
topography. Inviscid or nearly inviscid flow in which nonlinear effects have order
one importance is considered, and both the effects of β and finite topography are
included.
A onelayer quasigeostrophic model is used to find the shape of Taylor columns
on both the fplane and the βplane in the inviscid limit of the frictional problem.
In this limit, the boundary of the Taylor column is a streamline, and the velocity
in both directions vanishes on the boundary. The fluid within the Taylor column is
stagnant, corresponding to the solution that Ingersoll (1969) found for flow over a
right circular cylinder on the fplane. In this case, the Taylor column is circular. An
iterative boundary integral technique is used to find the solutions for flow over a cone
on the fplane. In this case the Taylor column has a tear drop shape. Solutions are
also found for flow on the βplane over a cylinder, and the Taylor column is approximately
elliptical for westward flow with the major axis in the x direction, while it is
slightly elongated in the y direction for eastward flow. The stagnation point of the
Taylor column is located on the edge of the topography for all the solutions found.
It was not possible to find solutions for smooth topographic shapes.
Steady solutions for flow over a right circular cylinder of finite height are
studied when the quasigeostrophic approximation no longer applies. The solution
consists of two parts, one which is similar to the quasigeostrophic solution and is
driven by the potential vorticity anomaly over the topography and the other which
is similar to the solution of potential flow around an cylinder and is driven by the
matching conditions on the edge of the topography. When the effect of β is large, the
transport over the topography is enhanced as the streamlines follow lines of constant
background potential vorticity. For eastward flow, the Rossby wave drag can be much
larger than predicted from quasigeostrophic theory. A twolayer model over finite topography using the quasigeostrophic approximation
is developed. The topography is a right circular cylinder which goes all of
the way through the lower layer and an order Rossby number amount into the upper
layer, so that the quasigeostrophic approximation can be applied consistently. This
geometry allows description of flow in which an isopycnal intersects the topography.
The model is valid for a different regime than existing models of steady flow over
finite topography in a continuously stratified fluid in which the bottom boundary is
an isopycnal surface. The solutions contain the two components that are found in the
the barotropic model of flow over finite topography. The model breaks down when
the interface goes above the topography which occurs more easily when the stratification
is weak. Closed streamlines occur more readily over the topography when
the stratification is weak, whereas in traditional quasigeostrophic theory they occur
more readily when the stratification is strong. Near the topography, the interface is
depressed to the right and raised to the left (looking downstream).
A hierarchy of timedependent models is used to examine the initial value
problem of flow initiation over topography on the fplane. A modified contour dynamics
method is developed that extends the range of problems to which contour
dynamics can be applied. The method allows boundary and matching conditions to
be applied on a circular boundary. A onelayer quasigeostrophic model is used to
show that more fluid that originates over the topography remains there when the flow
is turned on slowly than when it is turned on quickly. Flow over finite topography
in a onelayer model shows a variety of different behaviors depending on the topographic
height. When the topography has moderate height, two cyclonic eddies are
created; when the topography fills up most of the water column, the fluid oscillates on
and off the topography as it moves around the topography in a clockwise direction,
and none of the fluid is shed downstream. Two quasigeostrophic stratified models
are considered, one in which the topography is small, and the other in which it is
finite. In the small topography model, an eddy is shed which is cyclonic, warmcore,
and bottomtrapped. In contrast, the shed eddy is cyclonic, coldcore, and surfaceintensified
in the finite depth model using the geometry described above.
Description
Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution November 1990
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