Comparison of Laboratory and Theoretical Internal Solitary Wave Kinematics
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 129, Issue 5
Abstract
An investigation into the peak velocities in internal solitary waves characteristic of those found on the ocean thermocline is described. Measurements made using particle image velocimetry in a laboratory tank are compared to the predictions of Korteweg-de Vries (KdV) theory, in both two-layer and continuously stratified forms, and to a two-layer fully nonlinear theory. The dataset comprised 60 waves, covering amplitudes in the range of layer depths in the range of and density differences of 2.5 and 7.5%. It is found that KdV theory predicts peak velocities well when the ratio of wave height to upper layer depth is less than 0.4, while the fully nonlinear theory performs better for higher ratios.
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References
Apel, J. R., Holbrook, J. R., Liu, A. K., and Tsai, J. J.(1985). “The Sulu Sea internal soliton experiment.” J. Phys. Oceanogr. 15(12), 1625–1651.
Benjamin, T. B.(1966). “Internal waves of finite amplitude and permanent form.” J. Fluid Mech., 25(2), 241–270.
Benjamin, T. B.(1967). “Internal waves of permanent form in fluids of great depth.” J. Fluid Mech., 29(3), 559–592.
Bole, J. B., Ebbesmeyer, C. C., and Romea, R. D.(1994). “Soliton currents in the South China Sea: Measurements and theoretical model-ling.” Proc., 26th Annual Offshore Technology Conf., OTC 7417, 367–376.
Curtin, T. B., and Moers, C. N. K.(1975). “Observation and interpretation of a high-frequency internal wave packet and surface slick pattern.” J. Geophys. Res., 80(6), 882–894.
Davis, R. E., and Acrivos, A.(1967). “Solitary internal waves indeep water.” J. Fluid Mech., 29(3), 593–607.
Evans, W. A. B., and Ford, M. J.(1996a). “An exact integral equation for solitary waves (with new numerical results for some ‘internal’ properties).” Proc. R. Soc. London, 452, 373–390.
Evans, W. A. B., and Ford, M. J.(1996b). “An integral equation approach to internal (2-layer) solitary waves.” Phys. Fluids, 8(8), 2032–2047.
Gray, C., and Bruce, T.(1995). “The application of particle image velocimetry (PIV) to offshore engineering.” Proc., 5th Int. Offshore and Polar Engineering Conf., ISOPE, Golden, Colo., 3, 701–708.
Grue, J., Friis, H. A., Palm, E., and Rusås, P.-O.(1997). “A method for computing unsteady fully nonlinear interfacial waves.” J. Fluid Mech., 351, 223–252.
Grue, J., Jensen, A., Rusås, P.-O., and Sveen, J. K.(1999). “Properties of large-amplitude internal waves.” J. Fluid Mech., 380, 257–278.
Hammack, J. L.(1980). “Baroclinic Tsunami generation.” J. Phys. Oceanogr., 10, 1455–1476.
Helfrich, K. R., and Melville, W. K.(1986). “On long nonlinear internal waves over slope-shelf topography.” J. Fluid Mech., 167, 285–308.
Inall, M. E., Shapiro, G. I., and Sherwin, T. J. (1999). “Mass transport by non-linear internal waves on the Malin Shelf.”
Koop, C. G., and Butler, G.(1981). “An investigation on solitary internal waves in a two-fluid system.” J. Fluid Mech., 112, 225–251.
Korteweg, D. J., and De Vries, G.(1895). “On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves.” Phil. Mag., 5(39), 422–443.
LeBlond, P. H., and Mysak, L. A. (1978). Waves in the ocean, Elsevier, Amsterdam.
Martin, A. J. (1997). “Laboratory simulation and numerical modelling of the kinematics of oceanic internal waves.” PhD thesis, Univ. of Edinburgh, Scotland, U.K.
Martin, A. J., and Easson, W. J.(1997). “Non-linear internal wave kinematics.” Proc., 7th Int. Offshore and Polar Engineering Conf., ISOPE, Golden, Colo., 3, 122–129.
Maxworthy, T.(1979). “A note on the internal solitary waves produced by tidal flow over a three-dimensional ridge.” J. Geophys. Res., 84(C1), 338–346.
Osborne, A. R., and Burch, T. L.(1980). “Internal solitons in the Andaman Sea.” Science, 208(4443), 451–460.
Perry, R. B., and Schimke, G. R.(1965). “Large amplitude internal waves observed off the Northwest coast of Sumatra.” J. Geophys. Res., 70(10), 2319–2324.
Russell, J. S. (1845). “Report on waves.” Rep. to the 14th (1844) Meeting of the British Association for the Advancement of Science, London, 311–390.
Segur, H., and Hammack, J. L.(1982). “Soliton models of long internal waves.” J. Fluid Mech., 118, 285–304.
Sherwin, T. J. (1991). “Evidence of a deep internal tide in the Faeroe-Shetland channel.” Tidal hydrodynamics, B. B. Parker, ed., Wiley, New York, 469–488.
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Copyright © 2003 American Society of Civil Engineers.
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Received: Jan 13, 2000
Accepted: Mar 21, 2003
Published online: Aug 15, 2003
Published in print: Sep 2003
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