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Tidally generated internal-wave attractors between double ridges

Published online by Cambridge University Press:  11 January 2011

P. ECHEVERRI ,
T. YOKOSSI ,
N. J. BALMFORTH  and
T. PEACOCK
P. ECHEVERRI*
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
T. YOKOSSI
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
N. J. BALMFORTH
Affiliation:
Departments of Mathematics and Earth and Ocean Science, The University of British Columbia, Vancouver, BC V6T 1Z4, Canada
T. PEACOCK
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
*
†Email address for correspondence: paulae@alum.mit.edu
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Abstract

A study is presented of the generation of internal tides by barotropic tidal flow over topography in the shape of a double ridge. An iterative map is constructed to expedite the search for the closed ray paths that form wave attractors in this geometry. The map connects the positions along a ray path of consecutive reflections from the surface, which is double-valued owing to the presence of both left- and right-going waves, but which can be made into a genuine one-dimensional map using a checkerboarding algorithm. Calculations are then presented for the steady-state scattering of internal tides from the barotropic tide above the double ridges. The calculations exploit a Green function technique that distributes sources along the topography to generate the scattering, and discretizes in space to calculate the source density via a standard matrix inversion. When attractors are present, the numerical procedure appears to fail, displaying no convergence with the number of grid points used in the spatial discretizations, indicating a failure of the Green function solution. With the addition of dissipation into the problem, these difficulties are avoided, leading to convergent numerical solutions. The paper concludes with a comparison between theory and a laboratory experiment.

JFM classification

Geophysical and Geological Flows: Internal waves Geophysical and Geological Flows: Stratified flows Geophysical and Geological Flows: Topographic effects
Type
Papers
Information
Journal of Fluid Mechanics , Volume 669 , 25 February 2011 , pp. 354 - 374
Copyright
Copyright © Cambridge University Press 2011

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References

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