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Soliton models of long internal waves

Published online by Cambridge University Press:  20 April 2006

Harvey Segur  and
J. L. Hammack
Harvey Segur
Affiliation:
Aeronautical Research Associates of Princeton, Inc., P.O. Box 2229, Princeton, New Jersey 08540, U.S.A.
J. L. Hammack
Affiliation:
Department of Civil Engineering, University of California, Berkeley, California 94720, U.S.A. Present address: Dept of Engng Sciences, University of Florida, Gainesville, Fla 32611.
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Abstract

The Korteweg-de Vries (KdV) equation and the finite-depth equation of Joseph (1977) and Kubota, Ko & Dobbs (1978) both describe the evolution of long internal waves of small but finite amplitude, propagating in one direction. In this paper, both theories are tested experimentally by comparing measured and theoretical soliton shapes. The KdV equation predicts the shapes of our measured solitons with remarkable accuracy, much better than does the finite-depth equation. When carried to second-order, the finite-depth theory becomes about as accurate as (first-order) KdV theory for our experiments. However, second-order corrections to the finite-depth theory also identify a bound on the range of validity of that entire expansion. This range turns out to be rather small; it includes only about half of the experiments reported by Koop & Butler (1981).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 118 , May 1982 , pp. 285 - 304
Copyright
© 1982 Cambridge University Press

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References

Ablowitz, M. J., Fokas, A. S., Satsuma, J. & Segur, H. 1982 On the periodic intermediate long wave equation J. Phys. A:. Math. & Gen. (to appear).Google Scholar
Abramowitz, M. & Stegun, L. A. 1964 Handbook of Mathematical Functions. N.B.S., Washington, D.C.
Benjamin, T. B. 1966 J. Fluid Mech. 25, 241.
Benjamin, T. B. 1967 J. Fluid Mech. 29, 559.
Benney, D. J. 1966 J. Math. & Phys. 45, 52.
Chen, H. H. & Lee, Y. C. 1979 Phys. Rev. Lett. 43, 264.
Djordjevic, V. D. & Redekopp, L. G. 1978 J. Phys. Oceanog. 8, 1016.
Hammack, J. L. 1972 Tsunamis - a model of their generation and propagation. W. M. Keck Lab., Caltech Rep. KH-R-28.Google Scholar
Hammack, J. L. 1980 J. Phys. Oceanog. 10, 1455.
Hammack, J. L. & Segur, H. 1974 J. Fluid Mech. 65, 289.
Hammack, J. Lu & Segur, H. 1978 J. Fluid Mech. 84, 337.
Joseph, R. I. 1977 J. Phys. A, Math. & Gen. 10, L225.
Joseph, R. I. & Adams, R. C. 1981 Phys. Fluids 24, 15.
Joseph, R. I. & Egri, R. 1978 J. Phys. A, Math. & Gen. 11, L97.
Keulegan, G. H. 1953 J. Res. Nat. Bur. Stand. 51, 133.
Kodama, Y., Satsuma, J. & Ablowitz, M. J. 1981 Phys. Rev. Lett. 46, 687.
Koop, C. G. & Butler, G. 1981 J. Fluid Mech. 112, 225.
Korteweg, D. J. & De Vries, G. 1895 Phil. Mag. 39, ser. 5, 422.
Kubota, T., Ko, D. R. S. & Dobbs, L. 1978 A.I.A.A. J. Hydronaut. 12, 157.
Lamb, H. 1932 Hydrodynamics. Dover.
Leone, C., Segur, H. & Hammack, J. L. 1982 Viscous decay of long internal solitary waves, Preprint.
Long, R. R. 1956 Tellus 8, 460.
Miles, J. W. 1979 Tellus 31, 456.
Ono, H. 1975 J. Phys. Soc. Japan 39, 1082.
Osborne, A. R. & Burch, T. L. 1980 Science, 208, 451.
Peters, A. S. & Stoker, J. J. 1960 Commun. Pure Appl. Math. 13, 115.
Satsuma, J., Ablowitz, M. J. & Kodama, Y. 1979 Phys. Lett. 73A, 283.
Segur, H. 1973 J. Fluid Mech. 59, 721.
Segur, H. & Hammack, J. L. 1982 Long internal waves in layers of equal depth. Preprint.