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Mean flow generation by three-dimensional nonlinear internal wave beams

Published online by Cambridge University Press:  07 February 2019

F. Beckebanze Open the ORCID record for F. Beckebanze [Opens in a new window] ,
K. J. Raja  and
L. R. M. Maas Open the ORCID record for L. R. M. Maas [Opens in a new window]
F. Beckebanze*
Affiliation:
Mathematical Institute, Utrecht University, P.O. Box 80010, 3508 TA Utrecht, The Netherlands
K. J. Raja
Affiliation:
Laboratoire des Écoulements Géophysiques et Industriels, Université Grenoble Alpes, Grenoble, CS 40700, France
L. R. M. Maas
Affiliation:
Institute for Marine and Atmospheric Research Utrecht (IMAU), Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands
*
†Email address for correspondence: [email protected]
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Abstract

We study the generation of resonantly growing mean flow by weakly nonlinear internal wave beams. With a perturbational expansion, we construct analytic solutions for three-dimensional internal wave beams, exact up to first-order accuracy in the viscosity parameter. We specifically focus on the subtleties of wave beam generation by oscillating boundaries, such as wave makers in laboratory set-ups. The exact solutions to the linearized equations allow us to derive an analytic expression for the mean vertical vorticity production term, which induces a horizontal mean flow. Whereas mean flow generation associated with viscous beam attenuation – known as streaming – has been described before, we are the first to also include a peculiar inviscid mean flow generation in the vicinity of the oscillating wall, resulting from line vortices at the lateral edges of the oscillating boundary. Our theoretical expression for the mean vertical vorticity production is in good agreement with earlier laboratory experiments, for which the previously unrecognized inviscid mean flow generation mechanism turns out to be significant.

JFM classification

Geophysical and Geological Flows: Internal waves Vortex Flows: Vortex interactions
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 864 , 10 April 2019 , pp. 303 - 326
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Copyright
© 2019 Cambridge University Press 

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