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The characteristics of billows generated by internal solitary waves

Published online by Cambridge University Press:  05 January 2017

Magda Carr ,
James Franklin ,
Stuart E. King ,
Peter A. Davies ,
John Grue  and
David G. Dritschel
Magda Carr*
Affiliation:
School of Mathematics and Statistics, University of St Andrews, KY16 9SS, UK
James Franklin
Affiliation:
Department of Civil Engineering, University of Dundee, DD1 4HN, UK
Stuart E. King
Affiliation:
School of Mathematics and Statistics, University of St Andrews, KY16 9SS, UK
Peter A. Davies
Affiliation:
Department of Civil Engineering, University of Dundee, DD1 4HN, UK
John Grue
Affiliation:
Department of Mathematics, University of Oslo, 0316 Oslo, Norway
David G. Dritschel
Affiliation:
School of Mathematics and Statistics, University of St Andrews, KY16 9SS, UK
*
†Email address for correspondence: magda.carr@st-andrews.ac.uk
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Abstract

The spatial and temporal development of shear-induced overturning billows associated with breaking internal solitary waves is studied by means of a combined laboratory and numerical investigation. The waves are generated in the laboratory by a lock exchange mechanism and they are simulated numerically via a contour-advective semi-Lagrangian method. The properties of individual billows (maximum height attained, time of collapse, growth rate, speed, wavelength, Thorpe scale) are determined in each case, and the billow interaction processes are studied and classified. For broad flat waves, similar characteristics are seen to those in parallel shear flow, but, for waves not at the conjugate flow limit, billow characteristics are affected by the spatially varying wave-induced shear flow. Wave steepness and wave amplitude are shown to have a crucial influence on determining the type of interaction that occurs between billows and whether billow overturning can be arrested. Examples are given in which billows (i) evolve independently of one another, (ii) pair with one another, (iii) engulf/entrain one another and (iv) fail to completely overturn. It is shown that the vertical extent a billow can attain (and the associated Thorpe scale of the billow) is dependent on wave amplitude but that its value saturates once a given amplitude is reached. It is interesting to note that this amplitude is less than the conjugate flow limit amplitude. The number of billows that form on a wave is shown to be dependent on wavelength; shorter waves support fewer but larger billows than their long-wave counterparts for a given stratification.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Geophysical and Geological Flows: Internal waves
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Papers
Information
Journal of Fluid Mechanics , Volume 812 , 10 February 2017 , pp. 541 - 577
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© 2017 Cambridge University Press 

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Footnotes

‡

Present address: School of Mathematics, University of Edinburgh, EH9 3FD, UK.

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