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

View Issue TOC
Volume 25, No. 2
Pages 132 - 139

OpenAccess

Examining Breaking Internal Waves on a Shelf Slope Using Numerical Simulations

By Subhas K. Venayagamoorthy  and Oliver B. Fringer  
Jump to
Article Abstract Citation References Copyright & Usage
Article Abstract

The subject of internal waves interacting with bottom topographic features in the ocean has received much attention in the past few decades. This heightened interest is mainly due to a conjecture that breaking internal waves at boundaries can be a significant source of turbulence, leading to mixing and transport in the ocean. In this paper, we present results from high-resolution three-dimensional numerical simulations of an internal wave interacting with a shelf break in a linearly stratified fluid in order to highlight the instabilities that contribute to wave breaking over topography. The results show the development of a nonlinear internal bolus (a vortex core of dense fluid) that moves upslope as a result of the interaction and subsequent breaking of the internal wave. We present details of the different stages of the interaction process that lead to wave breakdown and formation of internal boluses and their subsequent evolution toward smaller scales of motion and turbulence as they propagate onshore.

Citation

Venayagamoorthy, S.K., and O.B. Fringer. 2012. Examining breaking internal waves on a shelf slope using numerical simulations. Oceanography 25(2):132–139, https://doi.org/10.5670/oceanog.2012.48.

References

Abarbanel, H., D. Holm, J. Marsden, and T. Ratiu. 1984. Richardson number criterion for the nonlinear stability of three-dimensional stratified flow. Physical Review Letters 52:2,352–2,355, https://doi.org/10.1103/PhysRevLett.52.2352.

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.

Apel, J.R., J.R. Holbrock, A.K. Liu, and J.J. Tsai. 1985. The Sulu Sea internal soliton experiment. Journal of Physical Oceanography 15:1,625–1,651, https://doi.org/10.1175/1520-0485(1985)015<1625:TSSISE>2.0.CO;2.

Armi, L. 1978. Some evidence for boundary mixing in the deep ocean. Journal of Geophysical Research 83:1,971–1,979, https://doi.org/10.1029/JC083iC04p01971.

Barad, M.F., and O.B. Fringer. 2010. Simulations of shear instabilities in interfacial gravity waves. Journal of Fluid Mechanics 644:61–95, https://doi.org/10.1017/S0022112009992035.

Carter, G.S., M.C. Gregg, and R.-C. Lien. 2005. Internal waves, solitary waves, and mixing on the Monterey Bay shelf. Continental Shelf Research 25:1,499–1,520, https://doi.org/10.1016/j.csr.2005.04.011.

Dauxois, T., A. Didier, and E. Falcon. 2004. Observation of near-critical reflection of internal waves in a stably stratified fluid. Physics of Fluids 16:1,936–1,941, https://doi.org/10.1063/1.1711814.

Drazin, P.G. 1977. On the instability of an internal gravity wave. Proceedings of the Royal Society of London A 356:411–432, https://doi.org/10.1098/rspa.1977.0142.

Fringer, O.B., and R.L. Street. 2003. The dynamics of breaking progressive interfacial waves. Journal of Fluid Mechanics 494:319–353, https://doi.org/10.1017/S0022112003006189.

Garrett, C., and W. Munk. 1979. Internal waves in the ocean. Annual Review of Fluid Mechanics 11:339–369, https://doi.org/10.1146/annurev.fl.11.010179.002011.

Gregg, M.C., D.W. Winkel, J.A. MacKinnon, and R.C. Lien. 1999. Mixing over shelves and slopes. Pp. 35–42 in Internal Wave Modeling. P. Müller and D. Henderson, eds, Proceedings of the Aha Huliko’a Hawaiian Winter Workshop.

Hosegood, P., J. Bonnin, and H. van Haren. 2004. Solibore-induced sediment resuspension in the Faeroe-Shetland Channel. Geophysical Research Letters 31, L09301, https://doi.org/10.1029/2004GL019544.

Howard, L. 1961. Note on a paper of John W. Miles. Journal of Fluid Mechanics 10:509–512, https://doi.org/10.1017/S0022112061000317.

Ivey, G.N., and R.I. Nokes. 1989. Vertical mixing due to the breaking of critical internal waves on sloping boundaries. Journal of Fluid Mechanics 204:479–500, https://doi.org/10.1017/S0022112089001849.

Klymak, J.M., and J.N. Moum. 2003. Internal solitary waves of elevation advancing on a shoaling shelf. Geophysical Research Letters 30(20), 2045, https://doi.org/10.1029/2003GL017706.

Koudella, C.R., and C. Staquet. 2006. Instability mechanisms of a two-dimensional progressive internal gravity wave. Journal of Fluid Mechanics 548:165–196, https://doi.org/10.1017/S0022112005007524.

Kunze, E., and J.M. Toole. 1997. Tidally driven vorticity, diurnal shear, and turbulence atop Fieberling Seamount. Journal of Physical Oceanography 27:2,663–2,693, https://doi.org/10.1175/1520-0485(1997)027<2663:TDVDSA>2.0.CO;2.

Ledwell, J.R., A.J. Watson, and C.S. Law. 1998. Mixing of a tracer in the pycnocline. Journal of Geophysical Research 103(C10):21,499–21,529, https://doi.org/10.1029/98JC01738.

Maxworthy, T., J. Leilich, J.E. Simpson, and E. Meiburg. 2002. The propagation of a gravity current into a linearly stratified fluid. Journal of Fluid Mechanics 453:371–394, https://doi.org/10.1017/S0022112001007054.

Miles, J. 1961. On the stability of heterogeneous shear flows. Journal of Fluid Mechanics 10:496–508, https://doi.org/10.1017/S0022112061000305.

Müller, P., G. Holloway, F. Henyey, and N. Pomphrey. 1986. Nonlinear interactions among internal gravity waves. Reviews of Geophysics 24:493–536, https://doi.org/10.1029/RG024i003p00493.

Munk, W. 1966. Abyssal recipes. Deep-Sea Research 13:707–730, https://doi.org/10.1016/0011-7471(66)90602-4.

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.

Ostrovsky, L.A., and Y.A. Stepanyants. 1989. Do internal solitons exist in the ocean? Reviews of Geophysics 27:293–310, https://doi.org/10.1029/RG027i003p00293.

Polzin, K.L., J.M. Toole, J.R. Ledwell, and R.W. Schmitt. 1997. Spatial variability of turbulent mixing in the abyssal ocean. Science 76:93–96, https://doi.org/10.1126/science.276.5309.93.

Sandstrom, H., and N.S. Oakey. 1995. Dissipation in internal tides and solitary waves. Journal of Physical Oceanography 25:604–614, https://doi.org/10.1175/1520-0485(1995)025<0604:DIITAS>2.0.CO;2.

Simpson, A.E. 1972. Effects of the lower boundary on the head of a gravity current. Journal of Fluid Mechanics 53:759–768, https://doi.org/10.1017/S0022112072000461.

Simpson, A.E. 1997. Gravity Currents. Cambridge University Press, 262 pp.

Simpson, A.E., and R.E. Britter. 1979. The dynamics of the head of a gravity current advancing over a horizontal surface. Journal of Fluid Mechanics 94:477–495, https://doi.org/10.1017/S0022112079001142.

Thorpe, S.A., and A.P. Haines. 1987. On the reflection of a train of finite-amplitude internal waves from a uniform slope. Journal of Fluid Mechanics 178:279–302, https://doi.org/10.1017/S0022112087001228.

Thorpe, S.A. 1999. The generation of alongslope currents by breaking internal waves. Journal of Physical Oceanography 29:29–45, https://doi.org/10.1175/1520-0485(1999)029<0029:TGOACB>2.0.CO;2.

Thorpe, S.A. 2004. Recent developments in the study of ocean turbulence. Annual Review of Earth and Planetary Sciences 32:91–109, https://doi.org/10.1146/annurev.earth.32.071603.152635.

Venayagamoorthy, S.K., and O.B. Fringer. 2007. On the formation and propagation of nonlinear internal boluses across a shelf break. Journal of Fluid Mechanics 577:137–159, https://doi.org/10.1017/S0022112007004624.

Zang, Y., R.L. Street, and J.R. Koseff. 1994. A non-staggered grid, fractional step method for time-dependent incompressible Navier-Stokes equations in curvilinear coordinates. Journal of Computational Physics 114:18–33, https://doi.org/10.1006/jcph.1994.1146.

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.