Modelling bottom stress in depthaveraged flows
Citable URI
https://hdl.handle.net/1912/5384DOI
10.1575/1912/5384Keyword
Ocean circulationAbstract
The relationship between depthaveraged velocity and bottom stress for winddriven flow in
unstratified coastal waters is examined here. The adequacy of traditional linear and quadratic
drag laws is addressed by comparison with a 2 1/2D model. A 2 1/2D model is one in which a
simplified 1D depthresolving model (DRM) is used to provide an estimate of the relationship
between the flow and bottom stress at each grid point of a depthaveraged model (DAM).
Bottom stress information is passed from the DRM to the DAM in the form of drag tensor
with two components: one which scales the flow and one which rotates it. This eliminates
the problem of traditional drag laws requiring the flow and bottom stress to be collinear. In
addition , the drag tensor field is updated periodically so that the relationship between the
velocity and bottom stress can be timedependent. However, simplifications in the 2 1/2D model
that render it computationally efficient also impose restrictions on the timescale of resolvable
processes. Basically, they must be much longer than the vertical diffusion time scale.
Four progressively more complicated scenarios are investigated. The important factors
governing the importance of bottom friction in each are found to be 1) nondimensional surface
Ekman depth, u.5/fh where u.s is the surface shear velocity, f is the Coriolis parameter and
h is the water depth 2) the nondimensional bottom roughness, zo/h where zo is the roughness
length and 3) the angle between the wind stress and the shoreline. Each has significant influence
on the drag law. The drag tensor magnitude, r, and the drag sensor angle, θ are functions of
all three, while a drag tensor which scales with the square of the depthaveraged velocity has a
magnitude, Cd, that only depends on zo/h.
The choice of drag Jaw is found to significantly affect the response of a domain. Spin
up times and phase relationships vary between models. In general, the 2 1/2D model responds
more quickly than either a constant r or constant Cd model. Steadystate responses are also
affected. The two most significant results are that failure to account for θ in the drag law
sometimes leads to substantial errors in estimating the sea surface height and to extremely
poor resolution of crossshore bottom stress. The latter implies that crossshore nearbottom
transport is essentially neglected by traditional DAMs.
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 May 1989
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