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The structure of low-Froude-number lee waves over an isolated obstacle

Published online by Cambridge University Press:  08 November 2011

Stuart B. Dalziel ,
Michael D. Patterson ,
C. P. Caulfield  and
Stéphane Le Brun
Stuart B. Dalziel*
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
Michael D. Patterson
Affiliation:
Department of Architecture and Civil Engineering, University of Bath, Bath BA2 7AY, UK
C. P. Caulfield
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK BP Institute, University of Cambridge, Madingley Road, Cambridge CB3 0EZ, UK
Stéphane Le Brun
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK École Polytechnique, Route de Saclay, 91120 Palaiseau, France
*
†Email address for correspondence: [email protected]
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Abstract

We present new insight into the classical problem of a uniform flow, linearly stratified in density, past an isolated three-dimensional obstacle. We demonstrate how, for a low-Froude-number obstacle, simple linear theory with a linearized boundary condition is capable of providing excellent quantitative agreement with laboratory measurements of the perturbation to the density field. It has long been known that such a flow may be divided into two regions, an essentially horizontal flow around the base of the obstacle and a wave-generating flow over the top of the obstacle, but until now the experimental diagnostics have not been available to test quantitatively the predicted features. We show that recognition of a small slope that develops across the obstacle in the surface separating these two regions is vital to rationalize experimental measurements with theoretical predictions. Utilizing the principle of stationary phase and causality arguments to modify the relationship between wavenumbers in the lee waves, linearized theory provides a detailed match in both the wave amplitude and structure to our experimental observations. Our results demonstrate that the structure of the lee waves is extremely sensitive to departures from horizontal flow, a detail that is likely to be important for a broad range of geophysical manifestations of these waves.

JFM classification

Geophysical and Geological Flows: Internal waves Geophysical and Geological Flows: Topographic effects
Type
Papers
Information
Journal of Fluid Mechanics , Volume 689 , 25 December 2011 , pp. 3 - 31
Copyright
Copyright © Cambridge University Press 2011

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