Oceanography The Official Magazine of
The Oceanography Society
Volume 25 Issue 02

View Issue TOC
Volume 25, No. 2
Pages 150 - 159


The Direct Breaking of Internal Waves at Steep Topography

By Jody M. Klymak , Sonya Legg, Matthew H. Alford, Maarten Buijsman , Robert Pinkel, and Jonathan D. Nash 
Jump to
Article Abstract Citation References Copyright & Usage
Article Abstract

Internal waves are often observed to break close to the seafloor topography that generates them, or from which they scatter. This breaking is often spectacular, with turbulent structures observed hundreds of meters above the seafloor, and driving turbulence dissipations and mixing up to 10,000 times open-ocean levels. This article provides an overview of efforts to observe and understand this turbulence, and to parameterize it near steep “supercritical” topography (i.e., topography that is steeper than internal wave energy characteristics). Using numerical models, we demonstrate that arrested lee waves are an important turbulence-producing phenomenon. Analogous to hydraulic jumps in water flowing over an obstacle in a stream, these waves are formed and then break during each tidal cycle. Similar lee waves are also observed in the atmosphere and in shallow fjords, but in those cases, their wavelengths are of similar scale to the topography, whereas in the ocean, they are small compared to the water depth and obstacle size. The simulations indicate that these nonlinear lee waves propagate against the generating flow (usually the tide) and are arrested because they have the same phase speed as the oncoming flow. This characteristic allows estimation of their size a priori and, using a linear model of internal tide generation, computation of how much energy they trap and turn into turbulence. This approach yields an accurate parameterization of mixing in numerical models, and these models are being used to guide a new generation of observations.


Klymak, J.M., S. Legg, M.H. Alford, M. Buijsman, R. Pinkel, and J.D. Nash. 2012. The direct breaking of internal waves at steep topography. Oceanography 25(2):150–159, https://doi.org/10.5670/oceanog.2012.50.


Alford, M.H. 2003. Redistribution of energy available for ocean mixing by long-range propagation of internal waves. Nature 423:159–162, https://doi.org/10.1038/nature01628.

Alford, M.H., J.A. MacKinnon, Z. Zhao, R. Pinkel, J. Klymak, and T. Peacock. 2007. Internal waves across the Pacific. Geophysical Research Letters 34, L24601, https://doi.org/10.1029/2007GL031566.

Alford, M.H., J.A. MacKinnon, J.D. Nash, H. Simmons, A. Pickering, J.M. Klymak, R. Pinkel, O. Sun, L. Rainville, R. Musgrave, and others. 2011. Energy flux and dissipation in Luzon Strait: Two tales of two ridges. Journal of Physical Oceanography 41:2,211–2,222, https://doi.org/10.1175/JPO-D-11-073.1.

Arbic, B.K., J.G. Richman, J.F. Shriver, P.G. Timko, E.J. Metzger, and A.J. Wallcraft. 2012. Global modeling of internal tides within an eddying ocean general circulation model. Oceanography 25(2):20–29, https://doi.org/10.5670/oceanog.2012.38.

Aucan, J., M.A. Merrifield, D.S. Luther, and P. Flament. 2006. Tidal mixing events on the deep flanks of Kaena Ridge, Hawaii. Journal of Physical Oceanography 36:1,202–1,219, https://doi.org/10.1175/JPO2888.1.

Baines, P.G. 1995. Topographic Effects in Stratified Flows. Cambridge University Press, 500 pp.

Balmforth, N., G. Ierley, and W. Young. 2002. Tidal conversion by subcritical topography. Journal of Physical Oceanography 32:2,900–2,914, https://doi.org/10.1175/1520-0485(2002)032<2900:TCBST>2.0.CO;2.

Bell, T.H. 1975. Lee waves in stratified flows with simple harmonic time dependence. Journal of Fluid Mechanics 67:705–722, https://doi.org/10.1017/S0022112075000560.

Buijsman, M., S. Legg, and J.M. Klymak. In press. Double ridge internal tide interference and its effect on dissipation in Luzon Strait. Journal of Physical Oceanography.

Carter, G.S., and M.C. Gregg. 2006. Persistent near-diurnal internal waves observed above a site of M2 barotropic-to-baroclinic conversion. Journal of Physical Oceanography 36:1,136–1,147, https://doi.org/10.1175/JPO2884.1.

D’Asaro, E.A. 1995. Upper-ocean inertial currents forced by a strong storm. Part II: Modeling. Journal of Physical Oceanography 25:2,937–2,952, https://doi.org/10.1175/1520-0485(1995)025<2937:UOICFB>2.0.CO;2.

Echeverri, P., T. Yokossi, N. Balmforth, and T. Peacock. 2011. Tidally generated internal-wave attractors between double ridges. Journal of Fluid Mechanics 669:354–374, https://doi.org/10.1017/S0022112010005069.

Eriksen, C.C. 1982. Observations of internal wave reflection off sloping bottoms. Journal of Geophysical Research 87(C1):525–538, https://doi.org/10.1029/JC087iC01p00525.

Farmer, D.M., and L. Armi. 1999. Stratified flow over topography: The role of small-scale entrainment and mixing in flow establishment. Proceedings of the Royal Society of London A 455:3,221–3,258, https://doi.org/10.1098/rspa.1999.0448.

Garrett, C., and E. Kunze. 2007. Internal tide generation in the deep ocean. Annual Review of Fluid Mechanics 39:57–87, https://doi.org/10.1146/annurev.fluid.39.050905.110227.

Henyey, F.S., J. Wright, and S.M. Flatté. 1986. Energy and action flow through the internal wave field. Journal of Geophysical Research 91:8,487–8,495, https://doi.org/10.1029/JC091iC07p08487.

Jan, S., C. Chern, J. Wang, and S. Chao. 2007. Generation of diurnal K1 internal tide in the Luzon Strait and its influence on surface tide in the South China Sea. Journal of Geophysical Research 112, C06019, https://doi.org/10.1029/2006JC004003.

Johnston, T.M.S., and M.A. Merrifield. 2003. Internal tide scattering at seamounts, ridges, and islands. Journal of Geophysical Research 108, 3180, https://doi.org/10.1029/2002JC001528.

Kelly, S., and J. Nash. 2010. Internal-tide generation and destruction by shoaling internal tides. Geophysical Research Letters 37, L23611, https://doi.org/10.1029/2010GL045598.

Klymak, J.M., M.H. Alford, R. Pinkel, R.C. Lien, Y.J. Yang, and T.Y. Tang. 2011. The breaking and scattering of the internal tide on a continental slope. Journal of Physical Oceanography 41:926–945, https://doi.org/10.1175/2010JPO4500.1.

Klymak, J.M., and M.C. Gregg. 2004. Tidally generated turbulence over the Knight Inlet sill. Journal of Physical Oceanography 34:1,135–1,151, https://doi.org/10.1175/1520-0485(2004)034<1135:TGTOTK>2.0.CO;2.

Klymak, J.M., and S.M. Legg. 2010. A simple mixing scheme for models that resolve breaking internal waves. Ocean Modelling 33:224–234, https://doi.org/10.1016/j.ocemod.2010.02.005.

Klymak, J.M., S. Legg, and R. Pinkel. 2010a. High-mode stationary waves in stratified flow over large obstacles. Journal of Fluid Mechanics 644:312–336, https://doi.org/10.1017/S0022112009992503.

Klymak, J.M., S. Legg, and R. Pinkel. 2010b. A simple parameterization of turbulent tidal mixing near supercritical topography. Journal of Physical Oceanography 40:2,059–2,074, https://doi.org/10.1175/2010JPO4396.1.

Klymak, J.M., J.N. Moum, J.D. Nash, E. Kunze, J.B. Girton, G.S. Carter, C.M. Lee, T.B. Sanford, and M.C. Gregg. 2006. An estimate of tidal energy lost to turbulence at the Hawaiian Ridge. Journal of Physical Oceanography 36:1,148–1,164, https://doi.org/10.1175/JPO2885.1.

Klymak, J.M., R. Pinkel, and L. Rainville. 2008. Direct breaking of the internal tide near topography: Kaena Ridge, Hawaii. Journal of Physical Oceanography 38:380–399, https://doi.org/10.1175/2007JPO3728.1.

Legg, S., and J.M. Klymak. 2008. Internal hydraulic jumps and overturning generated by tidal flow over a tall steep ridge. Journal of Physical Oceanography 38:1,949–1,964, https://doi.org/10.1175/2008JPO3777.1.

Levine, M.D., and T.J. Boyd. 2006. Tidally-forced internal waves and overturns observed on a slope: Results from the HOME survey component. Journal of Physical Oceanography 36:1,184–1,201, https://doi.org/10.1175/JPO2887.1.

Llewellyn Smith, S.G., and W.R. Young. 2003. Tidal conversion at a very steep ridge. Journal of Fluid Mechanics 495:175–191, https://doi.org/10.1017/S0022112003006098.

MacKinnon, J.A., and K.B. Winters. 2005. Subtropical catastrophe: Significant loss of low-mode tidal energy at 28.9°N. Geophysical Research Letters 32, 15605, https://doi.org/10.1029/2005GL023376.

Martini, K.I., M.H. Alford, E. Kunze, S.M. Kelly, and J.D. Nash. 2011. Observations of internal tides on the Oregon continental slope. Journal of Physical Oceanography 41:1,772–1,794, https://doi.org/10.1175/2011JPO4581.1.

McPhee, E.E., and E. Kunze. 2002. Boundary layer intrusions from a sloping bottom: A mechanism for generating intermediate nepheloid layers. Journal of Geophysical Research 107, 3050, https://doi.org/10.1029/2001JC000801.

Munk, W., and C. Wunsch. 1998. Abyssal recipes II: Energetics of tidal and wind mixing. Deep Sea Research Part I 45:1,977–2,010, https://doi.org/10.1016/S0967-0637(98)00070-3.

Nash, J.D., M.H. Alford, E. Kunze, K. Martini, and S. Kelley. 2007. Hotspots of deep ocean mixing on the Oregon continental slope. Geophysical Research Letters 34, L01605, https://doi.org/10.1029/2006GL028170.

Nash, J.D., E. Kunze, J.M. Toole, and R.W. Schmitt. 2004. Internal tide reflection and turbulent mixing on the continental slope. Journal of Physical Oceanography 34(5):1,117–1,134, https://doi.org/10.1175/1520-0485(2004)034<1117:ITRATM>2.0.CO;2.

Nash, J.D., E.L. Shroyer, S.M. Kelly, M.E. Inall, T.F. Duda, M.D. Levine, N.L. Jones, and R.C. Musgrave. 2012. Are any coastal internal tides predictable? Oceanography 25(2):80–95, https://doi.org/10.5670/oceanog.2012.44.

Nikurashin, M., and S. Legg. 2011. A mechanism for local dissipation of internal tides generated at rough topography. Journal of Physical Oceanography 41:378–395, https://doi.org/10.1175/2010JPO4522.1.

Polzin, K.L. 2009. An abyssal recipe. Ocean Modelling 30(4):298–309, https://doi.org/10.1016/j.ocemod.2009.07.006.

Polzin, K.L., J.M. Toole, J.R. Ledwell, and R.W. Schmitt. 1997. Spatial variability of turbulent mixing in the abyssal ocean. Science 276:93–96, https://doi.org/10.1126/science.276.5309.93.

Rainville, L., and R. Pinkel. 2006. Baroclinic energy flux at the Hawaiian Ridge: Observations from the R/P FLIP. Journal of Physical Oceanography 36:1,104–1,122, https://doi.org/10.1175/JPO2882.1.

Scinocca, J.F., and W.R. Peltier. 1989. Pulsating downslope windstorms. Journal of the Atmospheric Sciences 46:2,885–2,914, https://doi.org/10.1175/1520-0469(1989)046<2885:PDW>2.0.CO;2.

Simmons, H.L. 2008. Spectral modification and geographic redistribution of the semi-diurnal internal tide. Ocean Modelling 21:126–138, https://doi.org/10.1016/j.ocemod.2008.01.002.

Simmons, H.L., R.W. Hallberg, and B.K. Arbic. 2004. Internal wave generation in a global baroclinic tide model. Deep Sea Research Part II 51:3,069–3,101, https://doi.org/10.1016/j.dsr2.2004.09.015.

St. Laurent, L.C., H.L. Simmons, and S.R. Jayne. 2002. Estimating tidally driven mixing in the deep ocean. Geophysical Research Letters 29(23), 2106, https://doi.org/10.1029/2002GL015633.

St. Laurent, L.C., J.M. Toole, and R.W. Schmitt. 2001. Buoyancy forcing by turbulence above rough topography in the abyssal Brazil Basin. Journal of Physical Oceanography 31:3,476–3,495, https://doi.org/10.1175/1520-0485(2001)031<3476:BFBTAR>2.0.CO;2.

St. Laurent, L.C., and J.D. Nash. 2004. An examination of the radiative and dissipative properties of deep ocean internal tides. Deep Sea Research Part II 51:3,029–3,042, https://doi.org/10.1016/j.dsr2.2004.09.008.

St. Laurent, L.C., S. Stringer, C. Garrett, and D. Perrault-Joncas. 2003. The generation of internal tides at abrupt topography. Deep Sea Research Part I 50:987–1,003, https://doi.org/10.1016/S0967-0637(03)00096-7.

Thorpe, S.A. 1977. Turbulence and mixing in a Scottish loch. Philosophical Transactions of the Royal Society of London A 286:125–181, https://doi.org/10.1098/rsta.1977.0112.

Copyright & Usage

This is an open access article made available under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution, and reproduction in any medium or format as long as users cite the materials appropriately, provide a link to the Creative Commons license, and indicate the changes that were made to the original content. Images, animations, videos, or other third-party material used in articles are included in the Creative Commons license unless indicated otherwise in a credit line to the material. If the material is not included in the article’s Creative Commons license, users will need to obtain permission directly from the license holder to reproduce the material.