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

G. Pillet, E. V. Ermanyuk, L. R.M. Maas, I. N. Sibgatullin, T. Dauxois

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)203-225
Number of pages23
JournalJournal of Fluid Mechanics
Volume845
DOIs
Publication statusPublished - 25 Jun 2018

Keywords

  • geophysical and geological flows
  • internal waves
  • stratified flows
  • ENERGY
  • INSTABILITY
  • OCEAN
  • RECTANGULAR BASIN
  • ONE SLOPING BOUNDARY
  • EMPIRICAL MODE DECOMPOSITION
  • FLUID
  • SPECTRUM
  • PROPAGATION
  • INERTIAL WAVES

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