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Hydraulic control of continuously stratified flow over an obstacle

Published online by Cambridge University Press:  18 April 2012

Kraig B. Winters  and
Laurence Armi
Kraig B. Winters*
Affiliation:
Scripps Institution of Oceanography and Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, CA 92093, USA
Laurence Armi
Affiliation:
Scripps Institution of Oceanography and Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, CA 92093, USA
*
†Email address for correspondence: kraig@coast.ucsd.edu
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Abstract

Motivated by the laboratory experiments of Browand & Winant (Geophys. Fluid Dyn., vol. 4, 1972, pp. 29–53), a series of two-dimensional numerical simulations of flow past a cylinder of diameter are run for different values of the approach Froude number between and at . The observed flow is characterized by blocking and upstream influence in front of the cylinder and by relatively thin, fast jets over the top and bottom of the cylinder. This continuously stratified flow can be understood in terms of an inviscid non-diffusive integral inertia–buoyancy balance reminiscent of reduced-gravity single-layer hydraulics, but one where the reduced gravity is coupled to the thickness of the jets. The proposed theoretical framework describes the flow upstream of the obstacle and at its crest. The most important elements of the theory are the inclusion of upstream influence in the form of blocked flow within an energetically constrained depth range and the recognition that the flow well above and well below the active, accelerated layers is dynamically uncoupled. These constraints determine, through continuity, the transport in the accelerated layers. Combining these results with the observation that the flow is asymmetric around the cylinder, i.e. hydraulically controlled, allows us to determine the active layer thicknesses, the effective reduced gravity and thus all of the integral flow properties of the fast layers in good agreement with the numerically computed flows.

JFM classification

Geophysical and Geological Flows: Hydraulic control Geophysical and Geological Flows: Stratified flows Geophysical and Geological Flows: Topographic effects
Type
Papers
Information
Journal of Fluid Mechanics , Volume 700 , 10 June 2012 , pp. 502 - 513
Copyright
Copyright © Cambridge University Press 2012

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