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The effect of a strong density step on blocked stratified flow over topography

Published online by Cambridge University Press:  24 February 2020

Arjun Jagannathan Open the ORCID record for Arjun Jagannathan [Opens in a new window] ,
Kraig B. Winters  and
Laurence Armi
Arjun Jagannathan*
Affiliation:
Scripps Institution of Oceanography, University of California San Diego, La Jolla, CA 92093, USA
Kraig B. Winters
Affiliation:
Scripps Institution of Oceanography, University of California San Diego, La Jolla, CA 92093, USA
Laurence Armi
Affiliation:
Scripps Institution of Oceanography, University of California San Diego, La Jolla, CA 92093, USA
*
†Email address for correspondence: [email protected]
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Abstract

The dynamical connection between topographic control and wave excitation aloft is investigated theoretically and numerically in the idealized setting of two-dimensional stratified flow over an isolated ridge. We consider a constant far upstream inflow with uniform stratification except for a sharp density step located above the height of the ridge crest. Below this step, the stratification is sufficiently strong that the low level flow is blocked upstream and a hydraulically controlled flow spills over the crest. Above the density step, the flow supports upward radiating waves. In the inviscid limit, a bifurcating isopycnal separates the hydraulically controlled overflow from the wave field aloft. We show that, depending on the height of the density step, the sharp interface can either remain approximately flat, above the controlled downslope flow, or plunge in the lee of the obstacle as part of the controlled overflow itself. Whether the interface plunges or not is a direct consequence of hydraulic control at the crest. The flow above the crest responds to the top of the sharp density step as if it were a virtual topography. We find that a plunging interface can excite a wave field aloft that is approximately six times as energetic, with 15 % higher pressure drag, than that in a comparable flow in which the interface remains approximately flat.

JFM classification

Geophysical and Geological Flows: Hydraulic control Geophysical and Geological Flows: Topographic effects Geophysical and Geological Flows: Stratified flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 889 , 25 April 2020 , A23
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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