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Observations of a nonlinear solitary wave packet in the Kelvin wake of a ship

Published online by Cambridge University Press:  26 April 2006

Ellen D. Brown ,
Steven B. Buchsbaum ,
Robert E. Hall ,
John P. Penhune ,
Kurt F. Schmitt ,
Kenneth M. Watson  and
Donald C. Wyatt
Ellen D. Brown
Affiliation:
Science Applications International Corporation, San Diego, CA 92121, USA
Steven B. Buchsbaum
Affiliation:
Science Applications International Corporation, San Diego, CA 92121, USA Scripps Institution of Oceanography, San Diego, CA 92093, USA
Robert E. Hall
Affiliation:
Science Applications International Corporation, San Diego, CA 92121, USA
John P. Penhune
Affiliation:
Science Applications International Corporation, San Diego, CA 92121, USA
Kurt F. Schmitt
Affiliation:
Science Applications International Corporation, San Diego, CA 92121, USA
Kenneth M. Watson
Affiliation:
Scripps Institution of Oceanography, San Diego, CA 92093, USA
Donald C. Wyatt
Affiliation:
Science Applications International Corporation, San Diego, CA 92121, USA Department of Applied Mechanics and Engineering Sciences, University of California, San Diego, CA 92093, USA
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Abstract

Thirty data sets of wavestaff measurements of a solitary feature in the Kelvin wake of the Coast Guard cutter Point Brower are analysed. The average characteristics of the feature between 1 and 4 km aft of the ship are shown to be consistent with those of an oblique nonlinear solitary wave packet. The ship speed is 7.7 m/s (Froude number 0.49) and the waves that comprise the packet have an average frequency of 3.28 rad/s. The ship speed and the wave frequency, together with Kelvin wake kinematics, imply that the feature appears at an average wake half-angle of 10.9°. The packet does not exhibit linear dispersion beyond 1 km aft of the ship and its average width is 8.9 m (measured at e−1 of the peak variance). The average amplitude is 1.1 times the theoretical amplitude of an oblique nonlinear solitary wave packet with the observed width. There is considerable variability from run to run, and there is evidence of dispersive spreading before 1 km aft of the ship. An aerial photograph shows a sinuous fluctuation of the feature; possible explanations for the fluctuation include small variations in initial conditions or a sinuous instability. The solitary feature is a possible explanation for the long bright lines observed in SEASAT SAR images in light to moderate winds and observed in sun glitter photos taken from the space shuttle.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 204 , July 1989 , pp. 263 - 293
Copyright
© 1989 Cambridge University Press

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References

Akylas, T. R.: 1987 Unsteady and nonlinear effects near cusp lines of the Kelvin ship-wave pattern. J. Fluid Mech. 175, 333–342.Google Scholar
Akylas, T. R., Kung, T.-J. & Hall, R. E. 1988 Nonlinear groups in ship wakes. In Proc. Seventeenth ONR Symp. Naval Hydrodynamics. The Hague, Netherlands (to appear).
Bryant, P. J.: 1984 Oblique wave groups in deep water. J. Fluid Mech. 146, 1–20.Google Scholar
Chapman, R. B.: 1977 Survey of numerical solutions for ship free-surface problems. In Proc Second Intl. Conf. on Numerical Ship Hydrodynamics, pp. 5–16. University of Cal., Berkeley.
Clauss, G. F. & Bergmann, J., 1986 Gaussian wave packets – a new approach to seakeeping tests of ocean structures. Appl. Ocean Res. 8, 190–206.Google Scholar
Cohen, B. I., Watson, K. M. & West, B. J., 1976 Some properties of deep water solitons. Phys. Fluids 19, 345–354.Google Scholar
Dommermuth, D. G. & Yue, D. K. P. 1988 The nonlinear three-dimensional waves generated by a moving surface pressure. In Proc. Seventeenth ONR Symp. on Naval Hydrodynamics. The Hague, Netherlands (to appear).
Dysthe, K. B.: 1979 Note on a modification to the nonlinear Schrödinger equation for application to deep water waves. Proc. R. Soc. Lond. A 369, 105–114.Google Scholar
Flick, R. E., Lowe, R. L., Freilich, M. H. & Boylls, J. C., 1979 Coastal and laboratory wavestaff system. In Proceeding of Oceans, vol. 79, pp. 623–625. IEEE and Marine Tech. Society.
Fu, L. & Holt, B., 1982 SEASAT views oceans and sea ice with synthetic aperture radar. JPL Publication, 81–120. Pasadena, CA. 200 pp.
Hall, R. E., Loeser, D. J. & Wyatt, D. C., 1987 A model for the short wavelength portion of the surface wave wake of a ship and comparison with observations. Tech. Rep. SAIC-87/1794. Science Applications International Corporation, San Diego, CA. 106 pp.
Hammond, R. R., Buntzen, R. R. & Floren, E. E., 1985 Using ship wake patterns to evaluate SAR ocean wave imaging mechanisms. Tech. Rep. 978, Naval Oceans Systems Center, San Diego.
Harris, F. J.: 1978 On the use of windows for harmonic analysis with the discrete Fourier transform. Proc. IEEE 66, 51–83.Google Scholar
Hogben, N.: 1972 Nonlinear distortion of the Kelvin ship-wave pattern. J. Fluid Mech. 55, 513–528.Google Scholar
Hui, W. H. & Hamilton, J. 1979 Exact solutions of a three-dimensional nonlinear Schrödinger equation applied to gravity waves. J. Fluid Mech. 93, 117–133. Jane's Fighting Ships. 1985 London: Jane's Publishing Company.Google Scholar
Kelvin, Lord 1887 On ship waves. Proc. Inst. Mech. Engrs, pp. 409–434, Plates 80–84. Reprinted in Popular Lectures, Vol. III, pp. 450–500, Macmillan.
von Kerczek, C.: 1975 Numerical solution of naval free-surface hydrodynamics problems. In Proc. First Intl. Conf. on Numerical Ship Hydrodynamics, pp. 11–47. David W. Taylor Naval Ship Research and Development Center.
Kinsman, B.: 1974 Wind Waves. Dover, 676 pp.
Munk, W. H., Scully-Power, P. & Zachariasen, F. 1987 Ships from space. Proc. R. Soc. Lond. A 412, 231–254.Google Scholar
Rabiner, L. R. & Gold, B., 1975 Theory and Application of Digital Signal Processing. Prentice-Hall, 762 pp.
Saffman, P. G. & Yuen, H. C., 1978 Stability of a plane soliton to infinitesimal two-dimensional perturbations. Phys. Fluids 21, 1450–1451.Google Scholar
Scragg, C. A.: 1983 A numerical investigation of the Kelvin wake generated by a destroyer hull form. Rep. SAI-83/1216. Science Applications International Corporation, San Diego, CA, 46 pp.
Shum, K. T. & Melville, W. K., 1984 Estimates of the joint statistics of amplitudes and periods of ocean waves using an integral transform technique. J. Geophys. Res. 89, 6467–6476.Google Scholar
Stoker, J. J.: 1957 Water Waves. Interscience, 567 pp.
Webster, W. C. (ed.) 1986 Proc. Sixteenth Symposium on Naval Hydrodynamics. University of California, Berkeley, 613 pp.
Wehausen, J. V.: 1973 The wave resistance of ships. Adv. Appl. Mech. 13, 93–244.Google Scholar
West, B. J., Brueckner, K. A., Janda, R. S., Milder, D. M. & Milton, R. L., 1987 A new numerical method for surface hydrodynamics. J. Geophys. Res. 92, 11803–11824.Google Scholar
Wyatt, D. C. & Hall, R. E., 1988 Analysis of ship-generated surface waves using a method based upon the local Fourier transform. J. Geophys. Res. 93, 14133–14164.Google Scholar
Yeung, R. W.: 1982 Numerical methods in free-surface flows. Ann. Rev. Fluid Mech. 14, 395–442.Google Scholar
Yuen, H. C. & Lake, B. M., 1975 Nonlinear deep water waves: Theory and experiment. Phys. Fluids 18, 956–960.Google Scholar
Yuen, H. C. & Lake, B. M., 1982 Nonlinear dynamics of deep-water gravity waves. Adv. App. Mech. 22, 67–229.Google Scholar