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Damping of quasi-two-dimensional internal wave attractors by rigid-wall friction

Published online by Cambridge University Press:  26 February 2018

F. Beckebanze Open the ORCID record for F. Beckebanze [Opens in a new window] ,
C. Brouzet Open the ORCID record for C. Brouzet [Opens in a new window] ,
I. N. Sibgatullin  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
C. Brouzet
Affiliation:
Univ Lyon, ENS de Lyon, Univ Claude Bernard, CNRS, Laboratoire de Physique, F-69342 Lyon, France
I. N. Sibgatullin
Affiliation:
Department of Mechanics and Mathematics, Moscow State University, Moscow 119191, Russia Institute for System Progamming, Moscow 109004, Russia Shirshov Institute of Oceanology, Moscow 117997, Russia
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

The reflection of internal gravity waves at sloping boundaries leads to focusing or defocusing. In closed domains, focusing typically dominates and projects the wave energy onto ‘wave attractors’. For small-amplitude internal waves, the projection of energy onto higher wavenumbers by geometric focusing can be balanced by viscous dissipation at high wavenumbers. Contrary to what was previously suggested, viscous dissipation in interior shear layers may not be sufficient to explain the experiments on wave attractors in the classical quasi-two-dimensional trapezoidal laboratory set-ups. Applying standard boundary layer theory, we provide an elaborate description of the viscous dissipation in the interior shear layer, as well as at the rigid boundaries. Our analysis shows that even if the thin lateral Stokes boundary layers consist of no more than 1 % of the wall-to-wall distance, dissipation by lateral walls dominates at intermediate wave numbers. Our extended model for the spectrum of three-dimensional wave attractors in equilibrium closes the gap between observations and theory by Hazewinkel et al. (J. Fluid Mech., vol. 598, 2008, pp. 373–382).

JFM classification

Boundary Layers: Boundary layer structure Geophysical and Geological Flows: Geophysical and Geological Flows Geophysical and Geological Flows: Internal waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 841 , 25 April 2018 , pp. 614 - 635
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Copyright
© 2018 Cambridge University Press 

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