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Accelerating Dense-Water Flow down a Slope

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  • 1 Proudman Oceanographic Laboratory, Liverpool, United Kingdom
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Abstract

Where water is denser on a shallow shelf than in the adjacent deep ocean, it tends to flow down the slope from shelf to ocean. The flow can be in a steady bottom boundary layer for moderate combinations of upslope density gradient −ρx and bottom slope (angle θ to horizontal):
i1520-0485-39-6-1495-eq1
Here g is acceleration due to gravity, ρ0 is a mean density, and f is twice the component of the earth’s rotation normal to the sloping bottom. For stronger combinations of the horizontal density gradient and bottom slope, the flow accelerates. Analysis of an idealized initial value problem shows that, when b ≥ 1, there is a bottom boundary layer with downslope flow, intensifying exponentially at a rate fb2(1 + b)−1/2/2, and slower-growing flow higher up. For stronger stratification b > 21/2, that is, a relatively weak Coriolis constraint, the idealized problem posed here may not be the most apposite but suggests that the whole water column accelerates, at a rate [ρ0−1|ρx|g sinθ]1/2 if f is negligible.

Corresponding author address: John M. Huthnance, Proudman Oceanographic Laboratory, 6 Brownlow St., Liverpool L3 5DA, United Kingdom. Email: jmh@pol.ac.uk

Abstract

Where water is denser on a shallow shelf than in the adjacent deep ocean, it tends to flow down the slope from shelf to ocean. The flow can be in a steady bottom boundary layer for moderate combinations of upslope density gradient −ρx and bottom slope (angle θ to horizontal):
i1520-0485-39-6-1495-eq1
Here g is acceleration due to gravity, ρ0 is a mean density, and f is twice the component of the earth’s rotation normal to the sloping bottom. For stronger combinations of the horizontal density gradient and bottom slope, the flow accelerates. Analysis of an idealized initial value problem shows that, when b ≥ 1, there is a bottom boundary layer with downslope flow, intensifying exponentially at a rate fb2(1 + b)−1/2/2, and slower-growing flow higher up. For stronger stratification b > 21/2, that is, a relatively weak Coriolis constraint, the idealized problem posed here may not be the most apposite but suggests that the whole water column accelerates, at a rate [ρ0−1|ρx|g sinθ]1/2 if f is negligible.

Corresponding author address: John M. Huthnance, Proudman Oceanographic Laboratory, 6 Brownlow St., Liverpool L3 5DA, United Kingdom. Email: jmh@pol.ac.uk

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