Tidally generated internal-wave attractors between double ridges
Author(s)Echeverri, Paula; Yokossi, Tite; Peacock, Thomas; Balmforth, Neil J.
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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.
DepartmentMassachusetts Institute of Technology. Department of Economics; Massachusetts Institute of Technology. Department of Mechanical Engineering
Journal of Fluid Mechanics
Cambridge University Press
ECHEVERRI, P., T. YOKOSSI, N. J. BALMFORTH, and T. PEACOCK. Tidally Generated Internal-wave Attractors Between Double Ridges. Journal of Fluid Mechanics 669 (February 11, 2011): 354-374. Copyright © Cambridge University Press 2011
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