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The response of a continuously stratified fluid to an oscillating flow past an obstacle

Published online by Cambridge University Press:  14 June 2013

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: [email protected]
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Abstract

An oscillating continuously stratified flow past an isolated obstacle is investigated using scaling arguments and two-dimensional non-hydrostatic numerical experiments. A new dynamic scaling is introduced that incorporates the blocking of fluid with insufficient energy to overcome the background stratification and crest the obstacle. This clarifies the distinction between linear and nonlinear flow regimes near the crest of the obstacle. The flow is decomposed into propagating and non-propagating components. In the linear limit, the non-propagating component is related to the unstratified potential flow past the obstacle and the radiating component exhibits narrow wave beams that are tangent to the obstacle at critical points. When the flow is nonlinear, the near crest flow oscillates between states that include asymmetric, crest-controlled flows. Thin, fast, supercritical layers plunge in the lee, separate from the obstacle and undergo shear instability in the fluid interior. These flow features are localized to the neighbourhood of the crest where the flow transitions from subcriticality to supercriticality and are non-propagating. The nonlinear excitation of energetic non-propagating components reduces the efficiency of topographic radiation in comparison with linear dynamics.

JFM classification

Geophysical and Geological Flows: Hydraulic control Geophysical and Geological Flows: Internal waves Geophysical and Geological Flows: Topographic effects
Type
Papers
Information
Journal of Fluid Mechanics , Volume 727 , 25 July 2013 , pp. 83 - 118
Copyright
©2013 Cambridge University Press 

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