Skip to main content Accesibility Help
×
×
Home

Resolving the horizontal direction of internal tide generation

  • Friederike Pollmann (a1), Jonas Nycander (a2), Carsten Eden (a1) and Dirk Olbers (a3) (a4)
Abstract

The mixing induced by breaking internal gravity waves is an important contributor to the ocean’s energy budget, shaping, inter alia, nutrient supply, water mass transformation and the large-scale overturning circulation. Much of the energy input into the internal wave field is supplied by the conversion of barotropic tides at rough bottom topography, which hence needs to be described realistically in internal gravity wave models and mixing parametrisations based thereon. A new semi-analytical method to describe this internal wave forcing, calculating not only the total conversion but also the direction of this energy flux, is presented. It is based on linear theory for variable stratification and finite depth, that is, it computes the energy flux into the different vertical modes for two-dimensional, subcritical, small-amplitude topography and small tidal excursion. A practical advantage over earlier semi-analytical approaches is that the new one gives a positive definite conversion field. Sensitivity studies using both idealised and realistic topography allow the identification of suitable numerical parameter settings and corroborate the accuracy of the method. This motivates the application to the global ocean in order to better account for the geographical distribution of diapycnal mixing induced by low-mode internal gravity waves, which can propagate over large distances before breaking. The first results highlight the significant differences of energy flux magnitudes with direction, confirming the relevance of this more detailed approach for energetically consistent mixing parametrisations in ocean models. The method used here should be applicable to any physical system that is described by the standard wave equation with a very wide field of sources.

Copyright
Corresponding author
Email address for correspondence: friederike.pollmann@uni-hamburg.de
References
Hide All
Arbic, B. K., Wallcraft, A. J. & Metzger, E. J. 2010 Concurrent simulation of the eddying general circulation and tides in a global ocean model. Ocean Model. 32 (3–4), 175187.
Baddour, N. 2009 Operational and convolution properties of two-dimensional Fourier transforms in polar coordinates. J. Opt. Soc. Am. A 26 (8), 17671777.
Balmforth, N. J. & Peacock, T. 2009 Tidal conversion by supercritical topography. J. Phys. Oceanogr. 39 (8), 19651974.
Becker, J. J., Sandwell, D. T., Smith, W. H. F., Braud, J., Binder, B., Depner, J., Fabre, D., Factor, J., Ingalls, S., Kim, S.-H., Ladner, R., Marks, K., Nelson, S., Pharaoh, A., Trimmer, R., Von Rosenberg, J., Wallace, G. & Weatherall, P. 2009 Global bathymetry and elevation data at 30 arc seconds resolution: SRTM30_PLUS. Marine Geodesy 32 (4), 355371.
Bell, T. H. 1975a Lee waves in stratified flows with simple harmonic time dependence. J. Fluid Mech. 67 (04), 705722.
Bell, T. H. 1975b Topographically generated internal waves in the open ocean. J. Geophys. Res. 80 (3), 320327.
Carter, G. S., Merrifield, M. A., Becker, J. M., Katsumata, K., Gregg, M. C., Luther, D. S., Levine, M. D., Boyd, T. J. & Firing, Y. L. 2008 Energetics of M2 barotropic-to-baroclinic tidal conversion at the hawaiian islands. J. Phys. Oceanogr. 38 (10), 22052223.
Chelton, D. B., Deszoeke, R. A., Schlax, M. G., El Naggar, K. & Siwertz, N. 1998 Geographical variability of the first baroclinic Rossby radius of deformation. J. Phys. Oceanogr. 28 (3), 433460.
Egbert, G. D. & Ray, R. D. 2001 Estimates of M2 tidal energy dissipation from TOPEX/Poseidon altimeter data. J. Geophys. Res.-Oceans 106 (C10), 2247522502.
Egbert, G. D., Ray, R. D. & Bills, B. G. 2004 Numerical modeling of the global semidiurnal tide in the present day and in the last glacial maximum. J. Geophys. Res.-Oceans 109 (C3), C03003.
Falahat, S., Nycander, J., Roquet, F., Thurnherr, A. M. & Hibiya, T. 2014a Comparison of calculated energy flux of internal tides with microstructure measurements. Tellus A 66.
Falahat, S., Nycander, J., Roquet, F. & Zarroug, M. 2014b Global calculation of tidal energy conversion into vertical normal modes. J. Phys. Oceanogr. 44 (12), 32253244.
Garrett, C. & Kunze, E. 2007 Internal tide generation in the deep ocean. Annu. Rev. Fluid Mech. 39, 5787.
Goff, J. A. & Arbic, B. K. 2010 Global prediction of abyssal hill roughness statistics for use in ocean models from digital maps of paleo-spreading rate, paleo-ridge orientation, and sediment thickness. Ocean Model. 32 (1–2), 3643.
Goff, J. A. & Jordan, T. H. 1988 Stochastic modeling of seafloor morphology: inversion of sea beam data for second-order statistics. J. Geophys. Res.-Solid Earth 93 (B11), 1358913608.
Green, J. A. M. & Nycander, J. 2013 A comparison of tidal conversion parameterizations for tidal models. J. Phys. Oceanogr. 43 (1), 104119.
Guo, Y. & Holmes-Cerfon, M. 2016 Internal wave attractors over random, small-amplitude topography. J. Fluid Mech. 787, 148174.
Holloway, P. E. & Merrifield, M. A. 1999 Internal tide generation by seamounts, ridges, and islands. J. Geophys. Res.-Oceans 104 (C11), 2593725951.
Karimpour, F., Zareei, A., Tchoufag, J. & Alam, M.-R. 2017 Sensitivity of internal wave energy distribution over seabed corrugations to adjacent seabed features. J. Fluid Mech. 824, 7496.
Kelly, S. M. & Nash, J. D. 2010 Internal-tide generation and destruction by shoaling internal tides. Geophys. Res. Lett. 37 (23).
Khatiwala, S. 2003 Generation of internal tides in an ocean of finite depth: analytical and numerical calculations. Deep-Sea Res. I 50 (1), 321.
Klymak, J. M., Legg, S. & Pinkel, R. 2010 A simple parameterization of turbulent tidal mixing near supercritical topography. J. Phys. Oceanogr. 40 (9), 20592074.
Koltermann, K. P., Gouretski, V. & Jancke, K. 2011 Hydrographic Atlas of the World Ocean Circulation Experiment (WOCE): Volume 3: Atlantic Ocean. National Oceanography Centre.
Kurapov, A. L., Egbert, G. D., Allen, J. S., Miller, R. N., Erofeeva, S. Y. & Kosro, P. M. 2003 The M 2 internal tide off Oregon: inferences from data assimilation. J. Phys. Oceanogr. 33 (8), 17331757.
Li, Y. & Mei, C. C. 2014 Scattering of internal tides by irregular bathymetry of large extent. J. Fluid Mech. 747, 481505.
Llewellyn Smith, S. G. & Young, W. R. 2002 Conversion of the barotropic tide. J. Phys. Oceanogr. 32 (5), 15541566.
Melet, A., Nikurashin, M., Muller, C., Falahat, S., Nycander, J., Timko, P. G., Arbic, B. K. & Goff, J. A. 2013 Internal tide generation by abyssal hills using analytical theory. J. Geophys. Res.-Oceans 118 (11), 63036318.
Müller, M., Cherniawsky, J. Y., Foreman, M. G. G. & von Storch, J.-S. 2012 Global M 2 internal tide and its seasonal variability from high resolution ocean circulation and tide modeling. Geophys. Res. Lett. 39 (19).
Müller, P. & Natarov, A. 2003 The internal wave action model (IWAM). In Near-Boundary Processes and Their Parameterization: Proc.‘Aha Huliko’a Winter Workshop, School of Ocean and Earth Science and Technology, Special Publication, Honolulu, HI, University of Hawaii at Manoa, pp. 95105.
Munk, W. & Wunsch, C. 1998 Abyssal recipes II: energetics of tidal and wind mixing. Deep-Sea Res. I 45 (12), 19772010.
Niwa, Y. & Hibiya, T. 2004 Three-dimensional numerical simulation of M2 internal tides in the East China Sea. J. Geophys. Res.-Oceans 109 (C4).
Nycander, J. 2005 Generation of internal waves in the deep ocean by tides. J. Geophys. Res.-Oceans 110 (C10).
Nycander, J. 2006 Tidal generation of internal waves from a periodic array of steep ridges. J. Fluid Mech. 567, 415432.
Olbers, D. 1983 Models of the oceanic internal wave field. Rev. Geophys. 21 (7), 15671606.
Olbers, D. & Eden, C. 2013 A global model for the diapycnal diffusivity induced by internal gravity waves. J. Phys. Oceanogr. 43 (8), 17591779.
Pétrélis, F., Llewellyn Smith, S. G. & Young, W. R. 2006 Tidal conversion at a submarine ridge. J. Phys. Oceanogr. 36 (6), 10531071.
Samelson, R. M. 1998 Large-scale circulation with locally enhanced vertical mixing. J. Phys. Oceanogr. 28 (4), 712726.
St Laurent, L. & Garrett, C. 2002 The role of internal tides in mixing the deep ocean. J. Phys. Oceanogr. 32 (10), 28822899.
Talley, L. D. 2013 Closure of the global overturning circulation through the Indian, Pacific, and Southern Oceans: schematics and transports. Oceanography 26 (1), 8097.
Vic, C., Naveira Garabato, A. C., Green, J. A. M., Spingys, C., Forryan, A., Zhao, Z. & Sharples, J. 2018 The lifecycle of semidiurnal internal tides over the northern mid-atlantic ridge. J. Phys. Oceanogr. 48 (1), 6180.
Wunsch, C. & Ferrari, R. 2004 Vertical mixing, energy, and the general circulation of the oceans. Annu. Rev. Fluid Mech. 36, 281314.
Zarroug, M., Nycander, J. & Döös, K. 2010 Energetics of tidally generated internal waves for nonuniform stratification. Tellus A 62 (1), 7179.
Zhang, J., Schmitt, R. W. & Huang, R. X. 1999 The relative influence of diapycnal mixing and hydrologic forcing on the stability of the thermohaline circulation. J. Phys. Oceanogr. 29 (6), 10961108.
Zhang, L., Buijsman, M. C., Comino, E. & Swinney, H. L. 2017 Internal wave generation by tidal flow over periodically and randomly distributed seamounts. J. Geophys. Res.-Oceans 122, 50635074.
Zilberman, N. V., Becker, J. M., Merrifield, M. A. & Carter, G. S. 2009 Model estimates of M2 internal tide generation over Mid-Atlantic Ridge topography. J. Phys. Oceanogr. 39 (10), 26352651.
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

JFM classification

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed