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Spectrograms of ship wakes: identifying linear and nonlinear wave signals

  • Ravindra Pethiyagoda (a1), Scott W. McCue (a1) and Timothy J. Moroney (a1)

Abstract

A spectrogram is a useful way of using short-time discrete Fourier transforms to visualise surface height measurements taken of ship wakes in real-world conditions. For a steadily moving ship that leaves behind small-amplitude waves, the spectrogram is known to have two clear linear components, a sliding-frequency mode caused by the divergent waves and a constant-frequency mode for the transverse waves. However, recent observations of high-speed ferry data have identified additional components of the spectrograms that are not yet explained. We use computer simulations of linear and nonlinear ship wave patterns and apply time–frequency analysis to generate spectrograms for an idealised ship. We clarify the role of the linear dispersion relation and ship speed on the two linear components. We use a simple weakly nonlinear theory to identify higher-order effects in a spectrogram and, while the high-speed ferry data are very noisy, we propose that certain additional features in the experimental data are caused by nonlinearity. Finally, we provide a possible explanation for a further discrepancy between the high-speed ferry spectrograms and linear theory by accounting for ship acceleration.

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Corresponding author

Email address for correspondence: scott.mccue@qut.edu.au

References

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Benassai, G., Piscopo, V. & Scamardella, A. 2015 Spectral analysis of waves produced by HSC for coastal management. J. Mar. Sci. Technol. 112.
Brown, E. D., Buchsbaum, S. B., Hall, R. E., Penhune, J. P., Schmitt, K. F., Watson, K. M. & Wyatt, D. C. 1989 Observations of a nonlinear solitary wave packet in the Kelvin wake of a ship. J. Fluid Mech. 204, 263293.
Chung, Y. K. & Lim, J. S. 1991 A review of the Kelvin ship wave pattern. J. Ship Res. 35, 191197.
Cohen, L. 1989 Time-frequency distributions – a review. Proc. IEEE 77, 941981.
Darmon, A., Benzaquen, M. & Raphaël, E. 2014 Kelvin wake pattern at large Froude numbers. J. Fluid Mech. 738, R3.
Darrigol, O. 2003 The spirited horse, the engineer, and the mathematician: water waves in nineteenth-century hydrodynamics. Arch. Hist. Exact Sci. 58, 2195.
Didenkulova, I., Sheremet, A., Torsvik, T. & Soomere, T. 2013 Characteristic properties of different vessel wake signals. J. Coast. Res. SI 65, 213218.
Ellingsen, S. Å. 2014 Ship waves in the presence of uniform vorticity. J. Fluid Mech. 742, R2.
Forbes, L. K. 1989 An algorithm for 3-dimensional free-surface problems in hydrodynamics. J. Comput. Phys. 82, 330347.
Harris, F. J. 1978 On the use of windows for harmonic analysis with the discrete Fourier transform. Proc. IEEE 66, 5183.
Havelock, T. H. 1932 The theory of wave resistance. Proc. R. Soc. Lond. A 138, 339348.
Hogben, N. 1972 Nonlinear distortion of the Kelvin ship-wave pattern. J. Fluid Mech. 55, 513528.
Kurennoy, D., Soomere, T. & Parnell, K. 2009 Variability in the properties of wakes generated by high-speed ferries. J. Coast. Res. 56, 519523.
Li, Y. & Ellingsen, S. Å. 2016 Ship waves on uniform shear current at finite depth: wave resistance and critical velocity. J. Fluid Mech. 791, 539567.
MarineTraffic AIS Vessel Tracking – AIS Positions Maps. Retrieved 26 February 2016, from http://www.marinetraffic.com/en/ais/home/shipid:352956/zoom:10.
Maruo, H. 1967 High-and low-aspect ratio approximation of planing surfaces. Schiffstechnik 14, 5764.
Michell, J. H. 1898 The wave-resistance of a ship. Phil. Mag. 45, 106123.
Milgram, J. H. 1988 Theory of radar backscatter from short waves generated by ships, with application to radar (SAR) imagery. J. Ship Res. 32, 5469.
Munk, W. H., Scully-Power, P. & Zachariasen, F. 1986 The Bakerian lecture, 1986. Ships from space. Proc. R. Soc. Lond. A. 412, 231254.
Noblesse, F. 1981 Alternative integral representations for the Green function of the theory of ship wave resistance. J. Engng Maths 15, 241265.
Noblesse, F., He, J., Zhu, Y., Hong, L., Zhang, C., Zhu, R. & Yang, C. 2014 Why can ship wakes appear narrower than Kelvin’s angle? Eur. J. Mech. (B/Fluids) 46, 164171.
Părău, E. & Vanden-Broeck, J.-M. 2002 Nonlinear two- and three-dimensional free surface flows due to moving disturbances. Eur. J. Mech. (B/Fluids) 21, 643656.
Părău, E., Vanden-Broeck, J.-M. & Cooker, M. J. 2007 Nonlinear three-dimensional interfacial flows with a free surface. J. Fluid Mech. 591, 481494.
Parnell, K., Delpeche, N., Didenkulova, I., Dolphin, T., Erm, A., Kask, A., Kelpšaite, L., Kurennoy, D., Quak, E. & Räämet, A. 2008 Far-field vessel wakes in Tallinn Bay. Est. J. Engng 14, 273302.
Peters, A. S. 1949 A new treatment of the ship wave problem. Commun. Pure Appl. Maths 2, 123148.
Pethiyagoda, R., McCue, S. W., Moroney, T. J. & Back, J. M. 2014a Jacobian-free Newton–Krylov methods with GPU acceleration for computing nonlinear ship wave patterns. J. Comput. Phys. 269, 297313.
Pethiyagoda, R., McCue, S. W. & Moroney, T. J. 2014b What is the apparent angle of a Kelvin ship wave pattern? J. Fluid Mech. 758, 468485.
Pethiyagoda, R., McCue, S. W. & Moroney, T. J. 2015 Wake angle for surface gravity waves on a finite depth fluid. Phys. Fluids 27, 061701.
Rabaud, M. & Moisy, F. 2013 Ship wakes: Kelvin or Mach angle? Phys. Rev. Lett. 110, 214503.
Reed, A. M. & Milgram, J. H. 2002 Ship wakes and their radar images. Annu. Rev. Fluid Mech. 34, 469502.
Sheremet, A., Gravois, U. & Tian, M. 2013 Boat-wake statistics at Jensen Beach, Florida. J. Waterways Port Coast. Ocean Engng 139, 286294.
Soomere, T. 2007 Nonlinear components of ship wake waves. Appl. Mech. Rev. 60, 120138.
Thomson, W. 1887 On ship waves. Proc. Inst. Mech. Engrs 38, 409434.
Torsvik, T., Soomere, T., Didenkulova, I. & Sheremet, A. 2015a Identification of ship wake structures by a time-frequency method. J. Fluid Mech. 765, 229251.
Torsvik, T., Herrmann, H., Didenkulova, I. & Rodin, A. 2015b Analysis of ship wake transformation in the coastal zone using time-frequency methods. Proc. Est. Acad. Sci. 64, 379388.
Tuck, E. O. 1975 Low-aspect-ratio flat-ship theory. J. Hydronaut. 9, 312.
Tuck, E. O., Collins, J. I. & Wells, W. H. 1971 On ship wave patterns and their spectra. J. Ship Res. 15, 1121.
Ursell, F. 1960 On Kelvin’s ship-wave pattern. J. Fluid Mech. 8, 418431.
Wehausen, J. V. & Laitone, E. V. 1960 Surface Waves. Springer.
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 (C11), 1413314164.
Zhu, Y., He, J., Zhang, C., Wu, H., Wan, D., Zhu, R. & Noblesse, F. 2015 Farfield waves created by a monohull ship in shallow water. Eur. J. Mech. (B/Fluids) 49, 226234.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
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