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Tidally generated internal-wave attractors between double ridges

  • P. ECHEVERRI (a1), T. YOKOSSI (a1), N. J. BALMFORTH (a2) and T. PEACOCK (a1)
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.

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Email address for correspondence: paulae@alum.mit.edu
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N. J. Balmforth , G. R. Ierley & W. R. Young 2002 Tidal conversion by subcritical topography. J. Phys. Oceanogr. 32, 29002914.

N. J. Balmforth & T. Peacock 2009 Tidal conversion by supercritical topography. J. Phys. Oceanogr. 39, 19651974.

N. J. Balmforth , E. A. Spiegel & C. Tresser 1995 Checkerboard maps. Chaos 5 (1), 216226.


C. Garrett & E. Kunze 2007 Internal tide generation in the deep ocean. Annu. Rev. Fluid Mech. 39, 5787.

D. G. Hurley & G. Keady 1997 The generation of internal waves by vibrating elliptic cylinders. Part 2. Approximate viscous solution. J. Fluid Mech. 351, 119138.

S. Jan , R. C. Lien & C. H. Ting 2008 Numerical study of baroclinic tides in Luzon Strait. J. Oceanogr. 64, 789802.

F. P. A. Lam & L. R. M. Maas 2008 Internal wave focusing revisited; a reanalysis and new theoretical links. Fluid Dyn. Res. 40, 95122.


L. R. M. Maas 2005 Wave attractors – linear yet nonlinear. Intl J. Bifurcation Chaos 15, 27572782.

L. R. M. Maas , D. Benielli , J. Sommeria & F. P. A. Lam 1997 Observation of an internal wave attractor in a confined stably-stratified fluid. Nature 388, 557561.


A. M. M. Manders , L. R. M. Maas & T. Gerkema 2004 Observations of internal tides in the Mozambique Channel. J. Geophys. Res. 109, C12034.



G. I. Ogilvie & D. N. C. Lin 2004 Tidal dissipation in rotating giant planets. Astrophys. J. 610 (1), 477509.

T. Peacock , P. Echeverri & N. J. Balmforth 2008 An experimental investigation of internal tide generation by two-dimensional topography. J. Phys. Oceanogr. 38, 235242.

F. Pétrélis , Smith, S. G. Llewellyn & W. R. Young 2006 Tidal conversion at a submarine ridge. J. Phys. Oceanogr. 36, 10531071.

R. D. Pingree & A. L. New 1989 Downward propagation of internal tide energy into the Bay of Biscay. Deep Sea Res. A 36, 735758.


M. Rieutord & L. Valdettaro 1997 Inertial waves in a rotating spherical shell. J. Fluid Mech. 341, 7799.

D. L. Rudnick , T. J. Boyd , R. E. Brainard , G. S. Carter , G. D. Egbert , M. C. Gregg , P. E. Holloway , J. M. Klymak , E. Kunze , C. M. Lee , M. D. Levine , D. S. Luther , J. P. Martin , M. A. Merrifield , J. N. Moum , J. D. Nash , R. Pinkel , L. Rainville & T. B. Sanford 2003 From tides to mixing along the Hawaiian Ridge. Science 301, 355357.

L. C. St Laurent & C. Garrett 2002 The role of internal tides in mixing the deep ocean. J. Phys. Oceanogr. 32, 28822899.

L. C. St Laurent , S. Stringer , C. Garrett & D. Perrault-Joncas 2003 The generation of internal tides at abrupt topography. Deep Sea Res. I 50, 9871003.

W. Tang & T. Peacock 2010 Lagrangian coherent structures and internal wave attractors. Chaos 20, 017508.


Z. Zhao , V. Klemas , Q. Zheng & X. H. Yan 2004 Remote sensing evidence for baroclinic tide origin of internal solitary waves in the northeastern South China Sea. Geophys. Res. Lett. 31, L06302.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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