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Internal wave attractors in three-dimensional geometries: trapping by oblique reflection

Published online by Cambridge University Press:  20 April 2018

G. Pillet ,
E. V. Ermanyuk ,
L. R. M. Maas ,
I. N. Sibgatullin  and
T. Dauxois Open the ORCID record for T. Dauxois [Opens in a new window]
G. Pillet
Affiliation:
Université de Lyon, ENS de Lyon, UCBL, CNRS, Laboratoire de Physique, 69342 Lyon, France
E. V. Ermanyuk
Affiliation:
Lavrentyev Institute of Hydrodynamics, av. Lavrentyev 15, Novosibirsk 630090, Russia Novosibirsk State University, Pirogova str. 2, Novosibirsk 630090, Russia
L. R. M. Maas
Affiliation:
Institute for Marine and Atmospheric Research, Utrecht University, 3584 CC Utrecht, The Netherlands
I. N. Sibgatullin
Affiliation:
Lomonosov Moscow State University, Moscow 119991, Russia
T. Dauxois*
Affiliation:
Université de Lyon, ENS de Lyon, UCBL, CNRS, Laboratoire de Physique, 69342 Lyon, France
*
†Email address for correspondence: Thierry.Dauxois@ens-lyon.fr
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Abstract

We study experimentally the propagation of internal waves in two different three-dimensional (3D) geometries, with a special emphasis on the refractive focusing due to the 3D reflection of obliquely incident internal waves on a slope. Both studies are initiated by ray tracing calculations to determine the appropriate experimental parameters. First, we consider a 3D geometry, the classical set-up to get simple, two-dimensional (2D) parallelogram-shaped attractors in which waves are forced in a direction perpendicular to a sloping bottom. Here, however, the forcing is of reduced extent in the along-slope, transverse direction. We show how the refractive focusing mechanism explains the formation of attractors over the whole width of the tank, even away from the forcing region. Direct numerical simulations confirm the dynamics, emphasize the role of boundary conditions and reveal the phase shifting in the transverse direction. Second, we consider a long and narrow tank having an inclined bottom, to simply reproduce a canal. In this case, the energy is injected in a direction parallel to the slope. Interestingly, the wave energy ends up forming 2D internal wave attractors in planes that are transverse to the initial propagation direction. This focusing mechanism prevents indefinite transmission of most of the internal wave energy along the canal.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Geophysical and Geological Flows: Internal waves Geophysical and Geological Flows: Stratified flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 845 , 25 June 2018 , pp. 203 - 225
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Copyright
© 2018 Cambridge University Press 

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