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Internal wave generation by tidal flow over a two-dimensional ridge: energy flux asymmetries induced by a steady surface trapped current

Published online by Cambridge University Press:  11 December 2017

Kevin G. Lamb Open the ORCID record for Kevin G. Lamb [Opens in a new window]  and
M. Dunphy
Kevin G. Lamb*
Affiliation:
Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
M. Dunphy
Affiliation:
Institute of Ocean Sciences, Fisheries and Oceans Canada, Sidney, British Columbia, Canada V8L 4B2
*
†Email address for correspondence: [email protected]
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Abstract

The effects of a surface trapped steady background current on internal waves generated by tidal currents oscillating over a small symmetric ridge are investigated using a two-dimensional primitive equation model. A rigid lid is used with a linearly stratified fluid and the effects of rotation are not considered. We consider uni-directional background currents $\bar{U}(z)\geqslant 0$ confined to a surface layer lying well above the ridge. The current introduces asymmetries in the generated wave field. For sufficiently narrow ridges the upstream energy flux is larger than the downstream flux while the opposite is the case for sufficiently wide ridges. The total energy flux radiating away from the ridge is not significantly affected by the current. Mean second-order currents and pressure fields are shown to make important contributions to the total energy flux. A first-order linear theory, valid for a general stratification and surface current, which accurately predicts the wave field is also developed.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Geophysical and Geological Flows: Internal waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 836 , 10 February 2018 , pp. 192 - 221
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Copyright
© 2017 Cambridge University Press 

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References

Aiki, H., Matthews, J. P. & Lamb, K. G. 2011 Modeling and energetics of tidally generated wave trains in the Lombok Strait: impact of the Indonesian throughflow. J. Geophys. Res. 116, C03023.Google Scholar
Bell, J. B., Colella, P. & Glaz, H. M. 1989 A second-order projection method for the incompressible Navier–Stokes equations. J. Comput. Phys. 85, 257–283.Google Scholar
Bell, T. H. 1975a Lee waves in stratified flow with simple harmonic time dependence. J. Fluid Mech. 67, 705–722.Google Scholar
Bell, T. H. 1975b Topographically generated internal waves in the open ocean. J. Geophys. Res. 80, 320–327.Google Scholar
Broutman, D., Rottman, J. W. & Eckermann, S. D. 2004 Ray methods for internal waves in the atmosphere and ocean. Annu. Rev. Fluid Mech. 36, 233–253.Google Scholar
Buijsman, M. C., Ansong, J. K., Arbic, B. K., Richman, J. G., Shriver, J. F., Timko, P. G., Wallcraft, A. J., Whalen, C. B. & Zhao, Z.-X. 2016 Impact of parameterized internal wave drag on the semidiurnal energy balance in a global ocean circulation model. J. Phys. Oceanogr. 46, 1399–1419.Google Scholar
Egbert, G. D. & Ray, R. D. 2001 Estimates of M 2 tidal energy dissipation from TOPEX/Poseidon altimeter data. J. Geophys. Oceanogr. 106, 24 821–24 852.Google Scholar
Falahat, S., Nycander, J., Roquet, F., Thurnherr, A. M. & Hibiya, T. 2014 Comparison of calculated energy flux of internal tides with microstructure measurements. Tellus A 66, 23240.Google Scholar
Ferrari, R., Mashayek, A., McDougall, T. J., Nikurashin, M. & Campin, J.-M. 2016 Turning ocean mixing upside down. J. Phys. Oceanogr. 46, 2239–2261.Google Scholar
Garrett, C. & Kunze, E. 2007 Internal tide generation in the deep ocean. Annu. Rev. Fluid Mech. 39, 57–87.Google Scholar
Holliday, D. & McIntyre, M. E. 1981 On potential energy density in an incompressible, stratified fluid. J. Fluid Mech. 107, 221–225.Google Scholar
Kelly, S. M., Nash, J. D. & Kunze, E. 2010 Internal-tide energy over topography. J. Geophys. Res. 115, C06014.Google Scholar
Khatiwala, S. 2003 Generation of internal tides in an ocean of finite depth: analytical and numerical calculations. Deep-Sea Res. I 50, 3–21.Google Scholar
Lamb, K. G. 1994 Numerical experiments of internal wave generation by strong tidal flow across a finite amplitude bank edge. J. Geophys. Res. 99, 843–864.CrossRefGoogle Scholar
Lamb, K. G. 2007 Energy and pseudoenergy flux in the internal wave field generated by tidal flow over topography. Cont. Shelf Res. 27, 1208–1232.Google Scholar
Lamb, K. G. 2008 On the calculation of the available potential energy of an isolated perturbation in a density-stratified fluid. J. Fluid Mech. 597, 415–427.Google Scholar
Lamb, K. G. 2010 Energetics of internal solitary waves in a background sheared current. Nonlinear Process. Geophys. 17, 553–568.Google Scholar
Lamb, K. G. & Nguyen, V. T. 2009 Calculating energy flux in internal solitary waves with an application to reflectance. J. Phys. Oceanogr. 39, 559–580.Google Scholar
Lefauve, A., Muller, C. & Melet, A. 2015 A three-dimensional map of tidal dissipation over abyssal hills. J. Geophys. Res. Oceans 120, 4760–4777.Google Scholar
Llewellyn Smith, S. G. & Young, W. R. 2002 Conversion of the barotropic tide. J. Phys. Oceanogr. 32, 1544–1566.Google Scholar
Lyard, F., Lefevre, F., Letellier, T. & Francis, O. 2006 Modelling the global ocean tides: modern insights from FES20042004. Ocean Dyn. 56, 394–415.Google Scholar
Mathur, M., Carter, G. S. & Peacock, T. 2016 Internal tide generation using Green function analysis: to WKB or not to WKB. J. Phys. Oceanogr. 46, 2157–2168.Google Scholar
Matthews, J. P., Aiki, H., Masuda, S., Awaji, T. & Ishikawa, Y. 2011 Monsoon regulation of Lombok Strait internal waves. J. Geophys. Res. 116, C05007.Google Scholar
Mercier, M. J., Mathur, M., Gostiaux, L., Gerkema, T., Magalhães, J. M., Da Silva, J. C. B. & Dauxois, T. 2012 Soliton generation by internal tidal beams impinging on a pycnocline: laboratory experiments. J. Fluid Mech. 704, 37–60.Google Scholar
Munk, W. & Wunsch, C. 1998 Abyssal recipes. Part II. Energetics of tidal and wind mixing. Deep-Sea Res. 45, 1977–2010.Google Scholar
Nash, J. D., Alford, M. H. & Kunze, E. 2005 Estimating internal wave energy fluxes in the ocean. J. Atmos. Ocean. Technol. 22, 1551–1570.CrossRefGoogle Scholar
Nikurashin, M. & Ferrari, R. 2013 Overturning circulation driven by breaking internal waves in the deep ocean. Geophys. Res. Lett. 40, 3133–3137.Google Scholar
Pickering, A., Alford, M., Nash, J., Rainville, L., Buijsman, M., Ko, D. S. & Lim, B. 2015 Structure and variability of internal tides in Luzon Strait. J. Phys. Oceanogr. 45, 1574–1594.Google Scholar
Polzin, K. L., Toole, J. M., Ledwell, J. R. & Schmitt, R. W. 1997 Spatial variability of turbulent mixing in the abyssal ocean. Science 276, 93–96.Google Scholar
Scott, R. B., Goff, J. A., Naveira Garabato, A. C. & Nurser, A. J. G. 2011 Global rate and spectral characteristics of internal gravity wave generation by geostrophic flow over topography. J. Geophys. Res. 116, C09029.Google Scholar
Scotti, A., Beardsley, R. & Butman, B. 2006 On the interpretation of energy and energy fluxes of nonlinear internal waves: an example from Massachusetts Bay. J. Fluid Mech. 561, 103–112.Google Scholar
Shepherd, T. G. 1993 A unified theory of available potential energy. Atmos.-Ocean 31, 1–26.CrossRefGoogle Scholar
da Silva, J. C. B., New, A. I. & Magalhaes, J. M. 2011 On the structure and propagation of internal solitary waves generated at the Mascarene plateau in the Indian ocean. Deep-Sea Res. I 58, 229–240.Google Scholar
Waterhouse, A. F., MacKinnon, J. A., Nash, J. D., Alford, M. H., Kunze, E., Simmons, H. L., Polzin, K. L., St. Laurent, L. C., Sun, O. M., Pinkel, R. et al. 2014 Global patterns of diapycnal mixing from measurements of the turbulent dissipation rate. J. Phys. Oceanogr. 44, 1854–1872.Google Scholar
Wunsch, C. & Ferrari, R. 2004 Vertical mixing, energy, and the general circulation of the oceans. Annu. Rev. Fluid Mech. 36, 281–314.Google Scholar