Editorial Type:
Article
Article Type:
Research Article

A Nonlinear Model of Internal Tide Transformation on the Australian North West Shelf

Peter E. Holloway School of Geography and Oceanography, University College, University of New South Wales, Australian Defence Force Academy, Canberra, Australia

Search for other papers by Peter E. Holloway in
Current site
Google Scholar
PubMed Close
,
Efim Pelinovsky Institute of Applied Physics, Russian Academy of Science, Nizhny Novgorod, Russia

Search for other papers by Efim Pelinovsky in
Current site
Google Scholar
PubMed Close
,
Tatyana Talipova Institute of Applied Physics, Russian Academy of Science, Nizhny Novgorod, Russia

Search for other papers by Tatyana Talipova in
Current site
Google Scholar
PubMed Close
, and
Belinda Barnes School of Geography and Oceanography, University College, University of New South Wales, Australian Defence Force Academy, Canberra, Australia

Search for other papers by Belinda Barnes in
Current site
Google Scholar
PubMed Close
Print Publication:
01 Jun 1997
DOI:
https://doi.org/10.1175/1520-0485(1997)027<0871:ANMOIT>2.0.CO;2
Page(s):
871–896
Restricted access

Abstract

A numerical solution to the generalized Korteweg-de Vries (K-dV) equation, including horizontal variability and dissipation, is used to model the evolution of an initially sinusoidal long internal wave, representing an internal tide. The model shows the development of the waveform to the formation of shocks and solitons as it propagates shoreward over the continental slope and shelf. The model is run using observed hydrographic conditions from the Australian North West Shelf and results are compared to current meter and thermistor observations from the shelf-break region. It is found from observations that the coefficient of nonlinearity in the K-dV equation changes sign from negative in deep water to positive in shallow water, and this plays a major role in determining the form of the internal tide transformation. On the shelf there is strong temporal variability in the nonlinear coefficient due to both background shear flow and the large amplitude of the internal tide, which distorts the density profile over a wave period. Both the model and observations show the formation of an initial shock on the leading face of the internal tide. In shallow water, the change in sign of the coefficient of nonlinearity causes the shock to evolve into a tail of short period sinusoidal waves. After further propagation a second shock forms on the back face of the wave, followed by a packet of solitons. The inclusion of bottom friction in the model is investigated along with the dependance on initial wave amplitude and variability in the coefficients of nonlinearity and dispersion. Friction is found to be important in limiting the amplitudes of the evolving waves.

Corresponding author address: Dr. Peter E. Holloway, School of Geography and Oceanography, University College, University of New South Wales, Australian Defence Force Academy, Canberra ACT 2600, Australia.

Abstract

A numerical solution to the generalized Korteweg-de Vries (K-dV) equation, including horizontal variability and dissipation, is used to model the evolution of an initially sinusoidal long internal wave, representing an internal tide. The model shows the development of the waveform to the formation of shocks and solitons as it propagates shoreward over the continental slope and shelf. The model is run using observed hydrographic conditions from the Australian North West Shelf and results are compared to current meter and thermistor observations from the shelf-break region. It is found from observations that the coefficient of nonlinearity in the K-dV equation changes sign from negative in deep water to positive in shallow water, and this plays a major role in determining the form of the internal tide transformation. On the shelf there is strong temporal variability in the nonlinear coefficient due to both background shear flow and the large amplitude of the internal tide, which distorts the density profile over a wave period. Both the model and observations show the formation of an initial shock on the leading face of the internal tide. In shallow water, the change in sign of the coefficient of nonlinearity causes the shock to evolve into a tail of short period sinusoidal waves. After further propagation a second shock forms on the back face of the wave, followed by a packet of solitons. The inclusion of bottom friction in the model is investigated along with the dependance on initial wave amplitude and variability in the coefficients of nonlinearity and dispersion. Friction is found to be important in limiting the amplitudes of the evolving waves.

Corresponding author address: Dr. Peter E. Holloway, School of Geography and Oceanography, University College, University of New South Wales, Australian Defence Force Academy, Canberra ACT 2600, Australia.

Save
Cover Journal of Physical Oceanography
Journal of Physical Oceanography

  • Benney, D. J., 1966: Long nonlinear waves in fluid flows. J. Math. Phys.,45, 52–63.

  • Berezin, Yu. A., 1987: Modelling Nonlinear Wave Processes. VNU Science Press, 182 pp.

  • Boczar-Karakiewicz, B., J. L. Bona, and B. Pelchat, 1991: Interaction of internal waves with the seabed on continental shelves. Contin. Shelf Res.,11, 1181–1197.

  • Djordjevic, V. D., and L. G. Redekopp, 1978: The fission and disintegration of internal solitary waves moving over two-dimensional topography. J. Phys. Oceanogr.,8, 1016–1024.

  • Gallagher, B. S., and W. H. Munk, 1971: Tides in shallow water: Spectroscopy. Tellus,23, 4–5.

  • Gan, J., and R. G. Ingram, 1992: Internal hydraulics, solitons and associated mixing in a stratified sound. J. Geophys. Res.,97C, 9669–9688.

  • Gear, J. A., and R. Grimshaw, 1983: A second order theory for solitary waves in shallow fluids. Phys. Fluids,26, 14–29.

  • Goryachkin, Yu. N., V. A. Ivanov, and E. N. Pelinovsky, 1992: Transformation of internal tidal waves over the Guinean Shelf. Sov. J. Phys. Oceanogr.,3(4), 309–315.

  • Grimshaw, R., 1981: Evolution equations for nonlinear internal waves in stratified shear flows. Stud. Appl. Math.,65, 159–188.

  • ——, 1983: Solitary waves in density stratified fluids. Nonlinear Deformation Waves, IUTAM Symp., Tallin, Springer, 432–447.

  • Halpern, D., 1971: Observations of short-period internal waves in Massachusetts Bay. J. Mar. Res.,29, 116–132.

  • Helfrich, K. R., W. K. Melville, and J. W. Miles, 1984: On interfacial solitary waves over slowly varying topography. J. Fluid Mech.,149, 305–317.

  • Holloway, P. E., 1984: On the semidiurnal internal tide at a shelf break location on the Australian North West Shelf. J. Phys. Oceanogr.,14, 1778–1790.

  • ——, 1987: Internal hydraulic jumps and solitons at a shelf break region on the Australian North West Shelf. J. Geophys. Res.,92, 5405–5416.

  • ——, 1994: Observations of internal tide propagation on the Australian North West Shelf. J. Phys. Oceanogr.,24, 1706–1716.

  • Huthnance, J. M., 1989: Internal tides and waves near the continental shelf edge. Geophys. Fluid Dyn.,48, 81–106.

  • Ivanov, V., E. Pelinovsky, Yu. Stepanyants, and T. Talipova, 1992: Statistical estimation of nonlinear internal long wave parameters from field measurements. Izv. Atmos. Oceanic Phys.,28, 794–798.

  • Jeans, D. R. G., 1995: Solitary internal waves in the ocean: A literature review completed as part of the internal waves contribution to Morena. Rep. U95-1, 64 pp. [Available from Unit for Coastal and Estuarine Studies, University College of North Wales, Marine Science Laboratories, Gwynedd, U.K.].

  • Klevanny, K. A., and E. N. Pelinovsky, 1978: Effect of nonlinear dissipation on the propagation of tsunamis. Izv. Atmos. Oceanic Phys.,14, 756–759.

  • Knickerbocker, C. J., and A. C. Newell, 1980: Internal solitary waves near a turning point. Phys. Lett.,75A, 326–330.

  • 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.

  • Lee, C., and R. C. Beardsley, 1974: The generation of long nonlinear internal waves in a weakly stratified shear flow. J. Geophys. Res.,79, 453–462.

  • Levitus, S., 1982: Climatological Atlas of the World Ocean. NOAA Prof. Paper No. 13, U.S. Govt. Printing Office, 173 pp.

  • Liu, A. K., 1988: Analysis of nonlinear internal waves in the New York Bight. J. Geophys. Res.,93(12), 317–329.

  • ——, J. R. Holbrook, and J. R. Apel, 1985: Nonlinear internal wave evolution in the Sulu Sea. J. Phys. Oceanogr.,15, 1613–1624.

  • Malomed, B., and V. Shrira, 1991: Soliton caustics. Physica D,53, 1–12.

  • Maslowe, S. A., and L. G. Redekopp, 1980: Long nonlinear waves in stratified shear flows. J. Fluid Mech.,101, 321–348.

  • Maxworthy, T., 1979: A note on the internal solitary waves produced by tidal flow over a three-dimensional ridge. J. Geophys. Res.,84, 338–346.

  • Miles, J. W., 1983: Solitary wave evolution over a gradual slope with turbulent friction. J. Phys. Oceanogr.,13, 551–553.

  • Morozov, E. G., 1995: Semidiurnal internal wave global field. Deep-Sea Res.,42, 135–148.

  • New, A. L., and R. D. Pingree, 1990: Large-amplitude internal soliton packets in the central Bay of Biscay. Deep-Sea Res.,37A(3), 513–524.

  • ——, and ——, 1992: Local generation of internal soliton packets in the central Bay of Biscay. Deep-Sea Res.,39A(3), 1521–1534.

  • Ostrovsky, L. A., and Yu. A. Stepanyants, 1989: Do internal solitons exist in the ocean? Rev. Geophys.,27, 293–310.

  • Pelinovsky, E., and S. Shavratsky, 1976: Propagation of nonlinear internal waves in the inhomogeneous ocean. Izv. Atmos. Oceanic Phys.,12, 41–44.

  • ——, and ——, 1977: Disintegration of cnoidal internal waves in a horizontally inhomogeneous ocean. Izv. Atmos. Oceanic Phys.,13, 455–456.

  • ——, ——, and M. A. Raevsky, 1977: The Korteweg–de Vries equation for nonstationary internal waves in an inhomogeneous ocean. Izv. Atmos. Oceanic Phys.,13, 373–376.

  • ——, Yu. A. Stepanyants, and T. G. Talipova, 1994: Modelling of the propagation of nonlinear internal waves in horizontally inhomogeneous ocean. Izv. Atmos. Oceanic Phys.,30, 79–85.

  • Sandstrom, H., and J. A. Elliot, 1984: Internal tide and solitons on the Scotian Shelf: A nutrient pump at work. J. Geophys. Res.,89(C4), 6415–6426.

  • ——, and N. S. Oakey, 1995: Dissipation in internal tides and solitary waves. J. Phys. Oceanogr.,25, 604–614.

  • Smyth, N., 1988: Dissipative effects on the resonant flow of a stratified fluid over topography. J. Fluid Mech.,192, 287–312.

  • ——, and P. Holloway, 1988: Hydraulic jump and undular bore formation on a shelf break. J. Phys. Oceanogr.,18, 947–962.

  • Voltsinger, N., K. Klevanny, and E. Pelinovsky, 1989: Long-Wave Dynamics of the Coastal Zone (in Russian). Gidrometeoisdat, Leningrad.

  • Zhou, X., and R. Grimshaw, 1989: The effect of variable currents on internal solitary waves. Dyn. Atmos. Oceans,14, 17–39.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 1997 1172 321
PDF Downloads 549 139 6