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Internal Tide Energy Conversion

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Internal tide energy conversion refers to the energy conversion from barotropic to baroclinic modes as surface tides flow over steep and rough topography in the deep ocean generating internal tides. The "lost" barotropic tidal energy is often accounted for through a linear friction term in large-scale numerical models that are barotropic or not fine-scaled enough to resolve the energy conversion. It is implemented in ADCIRC through a spatially varying nodal attribute called internal_tide_friction, in the fort.13 file.

Background and Theory

The basic theory for generation of internal tides in the deep ocean was established several decades ago.[1] However, it was not thought to be incredibly important to the global energy balance of the surface tides until the modern satellite era when it was discovered that internal tides are responsible for approximately 30% of the global barotropic tidal dissipation.[2][3][4]

Following this revelation, the past two decades have been subject to a number of theoretical [5] [6] [7] [8] and numerical [9] [10] [11] investigations into internal tide generation and their effects on the surface tides through parameterization of the energy conversion in large-scale numerical tidal models. [12] [13] [14] [15] [16] [17] [18]

Attribute Summary

In a computational domain covering a large portion of the deep ocean, the effect of internal tide energy conversion may be needed to obtain more accurate tidal solutions. The user should only elect to use the internal_tide_friction nodal attribute when tides are included in the simulation through tidal boundary conditions and tidal potential functions. The attribute may not be important for domains that are small in size and/or do not cover a significant portion of the "deep ocean" (the portion of the ocean excluding the continental shelf).

ADCIRC reads the internal_tide_friction attribute in as the IT_Fric variable, which can have 1 (scalar) or 3 (tensor) dimensions. The attribute has dimensions of [1/time], meaning that it is a linear friction term which is multiplied by the velocity in the governing equations, and is normalized by the ocean depth prior to simulation. Hence, it ignores the water surface elevation portion of the total water depth, which is reasonable since the term and theory it is based on is only applicable to deep ocean. Typically, it is only applied to ocean depths greater than 100-500 m.[14][16]

Specifying IT_Fric Values

IT_Fric values are determined through analytical formulations based on Bell's linear theory[1], valid in what is called sub-critical topography.[2]

Recent publications using ADCIRC[14][15] provide relevant formulation and implementation details.


  1. 1.0 1.1 T.H. Bell, Topographically generated internal waves in the open ocean, J. Geophys. Res. 80 (1975) 320–327. doi:10.1029/JC080i003p00320.
  2. 2.0 2.1 C. Garrett, E. Kunze, Internal Tide Generation in the Deep Ocean, Annu. Rev. Fluid Mech. 39 (2007) 57–87. doi:10.1146/annurev.fluid.39.050905.110227.
  3. G.D. Egbert, R.D. Ray, Significant dissipation of tidal energy in the deep ocean inferred from satellite altimeter data, Nature. 405 (2000) 775–778. doi:10.1038/35015531
  4. G.D. Egbert, R.D. Ray, Estimates of M2 tidal energy dissipation from TOPEX/Poseidon altimeter data, J. Geophys. Res. Ocean. 106 (2001) 22475–22502. doi:10.1029/2000JC000699.
  5. A. Melet, M. Nikurashin, C. Muller, S. Falahat, J. Nycander, P.G. Timko, B.K. Arbic, J.A. Goff, Internal tide generation by abyssal hills using analytical theory, J. Geophys. Res. Ocean. 118 (2013) 6303–6318. doi:10.1002/2013JC009212.
  6. F. Pétrélis, S.L. Smith, W.R. Young, F. Pétrélis, S.L. Smith, W.R. Young, Tidal Conversion at a Submarine Ridge, J. Phys. Oceanogr. 36 (2006) 1053–1071. doi:10.1175/JPO2879.1.
  7. L. St. Laurent, C. Garrett, The Role of Internal Tides in Mixing the Deep Ocean, J. Phys. Oceanogr. 32 (2002) 2882–2899. doi:10.1175/1520-0485(2002)032<2882:TROITI>2.0.CO;2.
  8. L. St. Laurent, S. Stringer, C. Garrett, D. Perrault-Joncas, The generation of internal tides at abrupt topography, Deep Sea Res. Part I Oceanogr. Res. Pap. 50 (2003) 987–1003. doi:10.1016/S0967-0637(03)00096-7.
  9. J. Nycander, Generation of internal waves in the deep ocean by tides, J. Geophys. Res. 110 (2005) C10028. doi:10.1029/2004JC002487.
  10. A. Lefauve, C. Muller, A. Melet, A three-dimensional map of tidal dissipation over abyssal hills, J. Geophys. Res. C Ocean. 120 (2015) 4760–4777. doi:10.1002/2014JC010598.
  11. M.H. Alford, T. Peacock, J. a MacKinnon, J.D. Nash, M.C. Buijsman, L.R. Centuroni, S.-Y. Chao, M.-H. Chang, D.M. Farmer, O.B. Fringer, K.-H. Fu, P.C. Gallacher, H.C. Graber, K.R. Helfrich, S.M. Jachec, C.R. Jackson, J.M. Klymak, D.S. Ko, S. Jan, T.M.S. Johnston, S. Legg, I.-H. Lee, R.-C. Lien, M.J. Mercier, J.N. Moum, R. Musgrave, J.-H. Park, A.I. Pickering, R. Pinkel, L. Rainville, S.R. Ramp, D.L. Rudnick, S. Sarkar, A. Scotti, H.L. Simmons, L.C. St Laurent, S.K. Venayagamoorthy, Y.-H. Wang, J. Wang, Y.J. Yang, T. Paluszkiewicz, T.-Y.D. Tang, The formation and fate of internal waves in the South China Sea., Nature. 521 (2015) 65–9. doi:10.1038/nature14399.
  12. S.R. Jayne, L.C. St. Laurent, Parameterizing tidal dissipation over rough topography, Geophys. Res. Lett. 28 (2001) 811–814. doi:10.1029/2000GL012044.
  13. M.C. Buijsman, B.K. Arbic, J.A.M. Green, R.W. Helber, J.G. Richman, J.F. Shriver, P.G. Timko, A. Wallcraft, Optimizing internal wave drag in a forward barotropic model with semidiurnal tides, Ocean Model. 85 (2015) 42–55. doi:10.1016/j.ocemod.2014.11.003.
  14. 14.0 14.1 14.2 W.J. Pringle, D. Wirasaet, A. Suhardjo, J. Meixner, J.J. Westerink, A.B. Kennedy, S. Nong, Finite-Element Barotropic Model for the Indian and Western Pacific Oceans: Tidal Model-Data Comparisons and Sensitivities, Ocean Model. 129 (2018) 13–38. doi:10.1016/j.ocemod.2018.07.003.
  15. 15.0 15.1 W.J. Pringle, D. Wirasaet, J.J. Westerink, Modifications to Internal Tide Conversion Parameterizations and Implementation into Barotropic Ocean Models, EarthArXiv. (2018) 9. doi:10.31223/osf.io/84w53.
  16. 16.0 16.1 B.K. Arbic, A.J. Wallcraft, E.J. Metzger, Concurrent simulation of the eddying general circulation and tides in a global ocean model, Ocean Model. 32 (2010) 175–187. doi:10.1016/j.ocemod.2010.01.007.
  17. A. Schmittner, G.D. Egbert, An improved parameterization of tidal mixing for ocean models, Geosci. Model Dev. 7 (2014) 211–224. doi:10.5194/gmd-7-211-2014.
  18. J.A.M. Green, J. Nycander, A Comparison of Tidal Conversion Parameterizations for Tidal Models, J. Phys. Oceanogr. 43 (2013) 104–119. doi:10.1175/JPO-D-12-023.1.