Flow Properties in Rotating, Stratified Hydraulics

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Abstract
This paper discusses three distinct features of rotating, stratified hydraulics, using a reduced-gravity configuration. First, a new upstream condition is derived corresponding to a wide, almost motionless basin, and this is applied to flow across a rectangular sill and compared with the case of a zero potential vorticity upstream condition. For this geometry, it is shown that unidirectional flow permits more water to pass through the sill than bidirectional flow. Second, the general problem is considered of flow from any upstream configuration that passes through sills that vary slowly in depth cross sill (and so are effectively many deformation radii wide). Only two flow configurations permit any realistic amount of flux across the sill: either the fluid occupies a narrow region within the sill, with a small flux, or the fluid occupies a wide region, with sluggish geostrophic flow except for at boundary layers at each side. In the latter case, hydraulic control is not likely to occur. The zero potential vorticity limit, suitably modified, gives an upper bound to the net flux across the sill. Both configurations require bidirectional flow for all upstream conditions, so that unidirectional flow can be expected to occur only in relatively narrow sills. The relevance of providing upstream conditions for hydraulic flow is thus called into question. Third, the flux through four oceanic sills is recomputed, modeling the sills as parabolic or V-shaped. It is noted that general circulation models will not give a good representation of the flux in such cases.

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