Skip to main content
×
Home
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 16
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Wang, Jinhu Chen, Xu Wang, Wei and Li, Qiang 2015. Laboratory experiments on the resonance of internal waves on a finite height subcritical topography. Ocean Dynamics, Vol. 65, Issue. 9-10, p. 1269.


    Jouve, Laurène and Ogilvie, Gordon I. 2014. Direct numerical simulations of an inertial wave attractor in linear and nonlinear regimes. Journal of Fluid Mechanics, Vol. 745, p. 223.


    Bajars, Janis Frank, Jason and Maas, Leo R. M. 2013. On the appearance of internal wave attractors due to an initial or parametrically excited disturbance. Journal of Fluid Mechanics, Vol. 714, p. 283.


    Li, Qiang 2014. Numerical assessment of factors affecting nonlinear internal waves in the South China Sea. Progress in Oceanography, Vol. 121, p. 24.


    Warn-Varnas, Alex Ko, Dong S. and Gangopadhyay, Avijit 2015. Signatures of tidal interference patterns in the South China Sea. Journal of Oceanography, Vol. 71, Issue. 3, p. 251.


    Guo, C. and Chen, X. 2014. A review of internal solitary wave dynamics in the northern South China Sea. Progress in Oceanography, Vol. 121, p. 7.


    Brouzet, C. Ermanyuk, E. V. Joubaud, S. Sibgatullin, I. and Dauxois, T. 2016. Energy cascade in internal-wave attractors. EPL (Europhysics Letters), Vol. 113, Issue. 4, p. 44001.


    Scolan, Hélène Ermanyuk, Eugeny and Dauxois, Thierry 2013. Nonlinear Fate of Internal Wave Attractors. Physical Review Letters, Vol. 110, Issue. 23,


    Kelly, Samuel M. Nash, Jonathan D. Martini, Kim I. Alford, Matthew H. and Kunze, Eric 2012. The Cascade of Tidal Energy from Low to High Modes on a Continental Slope. Journal of Physical Oceanography, Vol. 42, Issue. 7, p. 1217.


    Zhang, Likun and Swinney, Harry L. 2014. Virtual Seafloor Reduces Internal Wave Generation by Tidal Flow. Physical Review Letters, Vol. 112, Issue. 10,


    Buijsman, Maarten C. Legg, Sonya and Klymak, Jody 2012. Double-Ridge Internal Tide Interference and Its Effect on Dissipation in Luzon Strait. Journal of Physical Oceanography, Vol. 42, Issue. 8, p. 1337.


    Kelly, Samuel M. Jones, Nicole L. and Nash, Jonathan D. 2013. A Coupled Model for Laplace's Tidal Equations in a Fluid with One Horizontal Dimension and Variable Depth. Journal of Physical Oceanography, Vol. 43, Issue. 8, p. 1780.


    Wang, Gang Zheng, Quanan Lin, Min Dai, Dejun and Qiao, Fangli 2015. Three dimensional simulation of internal wave attractors in the Luzon Strait. Acta Oceanologica Sinica, Vol. 34, Issue. 11, p. 14.


    Rainville, Luc Lee, Craig M. Rudnick, Daniel L. and Yang, Kai-Chieh 2013. Propagation of internal tides generated near Luzon Strait: Observations from autonomous gliders. Journal of Geophysical Research: Oceans, Vol. 118, Issue. 9, p. 4125.


    Klymak, Jody M. Buijsman, Maarten Legg, Sonya and Pinkel, Robert 2013. Parameterizing Surface and Internal Tide Scattering and Breaking on Supercritical Topography: The One- and Two-Ridge Cases. Journal of Physical Oceanography, Vol. 43, Issue. 7, p. 1380.


    Li, Qiang Wang, Bing Chen, Xu Chen, Xueen and Park, Jae-Hun 2016. Variability of nonlinear internal waves in the South China Sea affected by the Kuroshio and mesoscale eddies. Journal of Geophysical Research: Oceans, Vol. 121, Issue. 4, p. 2098.


    ×
  • Journal of Fluid Mechanics, Volume 669
  • February 2011, pp. 354-374

Tidally generated internal-wave attractors between double ridges

  • P. ECHEVERRI (a1), T. YOKOSSI (a1), N. J. BALMFORTH (a2) and T. PEACOCK (a1)
  • DOI: http://dx.doi.org/10.1017/S0022112010005069
  • Published online: 11 January 2011
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.

Copyright
Corresponding author
Email address for correspondence: paulae@alum.mit.edu
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

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.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Keywords: