Abstract
The effect of a small-scale topography on large-scale, small-amplitude oceanic motion
is analysed using a two-dimensional quasi-geostrophic model that includes free-surface and β effects, Ekman friction and viscous (or turbulent) dissipation. The
topography is two-dimensional and periodic; its slope is assumed to be much larger
than the ratio of the ocean depth to the Earth's radius. An averaged equation of
motion is derived for flows with spatial scales that are much larger than the scale
of the topography and either (i) much larger than or (ii) comparable to the radius
of deformation. Compared to the standard quasi-geostrophic equation, this averaged
equation contains an additional dissipative term that results from the interaction
between topography and dissipation. In case (i) this term simply represents an
additional Ekman friction, whereas in case (ii) it is given by an integral over the
history of the large-scale flow. The properties of the additional term are studied in
detail. For case (i) in particular, numerical calculations are employed to analyse the
dependence of the additional Ekman friction on the structure of the topography and
on the strength of the original dissipation mechanisms.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Cited by
19 articles.
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