Ship wake transformation in the coastal zone is analysed based on field measurements of wave conditions at two measurement sites located about 20 m and 100 m from the shore. Analysis of single wake events recorded at both sites is carried out by transforming the time series of the wave amplitude into the time–frequency domain, using both a short-time Fourier transform and a wavelet transform. Analysis reveals that signature features of individual wake components can be tracked as the wake approaches the shore, but the wave amplitude and associated wave energy is transformed differently for different wake components. The wake energy is reduced as the waves propagate through the surf zone, which can be attributed mainly to wave breaking of the leading wave system and a significant reduction of the divergent wave system. However, the energy of transverse waves is stable or increasing, indicating that these waves undergo a non-breaking shoaling process.
1. Soomere, T., Parnell, K., and Didenkulova, I. Implications of fast ferry wakes for semi-sheltered beaches: a case study at Aegna Island, Baltic Sea. J. Coastal Res., 2009, SI 56, 128–132.
2. Soomere, T. Nonlinear components of ship wake waves. Appl. Mech. Rev., 2007, 60(1–6), 120–138.
http://dx.doi.org/10.1115/1.2730847
3. Torsvik, T., Didenkulova, I., Soomere, T., and Parnell, K. E. Variability in spatial patterns of long nonlinear waves from fast ferries in Tallinn Bay. Nonlinear Proc. Geoph., 2009, 16, 351–363.
http://dx.doi.org/10.5194/npg-16-351-2009
4. Newman, J. N. Marine Hydrodynamics. The MIT Press, 1977.
5. Stumbo, S., Fox, K., Dvorak, F., and Elliot, L. The prediction, measurement, and analysis of wake wash from marine vessels. Marine Technology, 1999, 36(4), 248–260.
6. Varyani, K. S. Full scale study of the wash of high speed craft. Ocean Eng., 2006, 33, 705–722.
http://dx.doi.org/10.1016/j.oceaneng.2005.05.007
7. Darmon, A., Benzaquen, M., and Raphael, E. Kelvin wake pattern at large Froude numbers. J. Fluid Mech., 2014, 738, R3.
http://dx.doi.org/10.1017/jfm.2013.607
8. Noblesse, F., He, J., Zhu, Y., Hong, L., Zhang, C., Zhu, R., and Yang, C. Why can ship wakes appear narrower than Kelvin’s angle? Eur. J. Mech. B-Fluid., 2014, 46, 164–171.
http://dx.doi.org/10.1016/j.euromechflu.2014.03.012
9. Lee, S., Yates, G. Y., and Wu, T. Y. Experiments and analysis of upstream-advancing solitary waves generated by moving disturbances. J. Fluid Mech., 1989, 199, 569–593.
http://dx.doi.org/10.1017/S0022112089000492
10. Akylas, T. R. On the excitation of long nonlinear water waves by a moving pressure distribution. J. Fluid Mech., 1984, 141, 455–466.
http://dx.doi.org/10.1017/S0022112084000926
11.Mei, C. C. Radiation of solitons by slender bodies advanc\-ing in a shallow channel. J. Fluid Mech., 1986, 162, 53–67.
http://dx.doi.org/10.1017/S0022112086001921
12. Didenkulova, I., Sheremet, A., Torsvik, T., and Soomere, T. Characteristic properties of different vessel wake signals. J. Coastal Res., 2013, SI 65, 213–218. ICS 2013 Proceedings, Plymouth, UK.
13. Sheremet, A., Gravois, U., and Tian, M. Boat-wake statistics at Jensen Beach, Florida. J. Waterw. Port Coast. Ocean Eng., 2013, 139(4), 286–294.
http://dx.doi.org/10.1061/(ASCE)WW.1943-5460.0000182
14. Belibassakis, K. A. A coupled-mode technique for the transformation of ship-generated waves over variable bathymetry regions. Appl. Ocean Res., 2003, 25, 321–336.
http://dx.doi.org/10.1016/j.apor.2004.05.002
15. Didenkulova, I., Parnell, K., Soomere, T., Pelinovsky, E., and Kurennoy, D. Shoaling and runup of long waves induced by high-speed ferries in Tallinn Bay. J. Coastal Res., 2009, SI 56, 491–495.
16. Didenkulova, I. and Rodin, A. A typical wave wake from high-speed vessels: its group structure and run-up. Nonlinear Proc. Geophys., 2013, 20, 179–188.
http://dx.doi.org/10.5194/npg-20-179-2013
17. Parnell, K., Delpeche, N., Didenkulova, I., Dolphin, T., Erm, A., Kask, A., et al. Far-field vessel wakes in Tallinn Bay. Estonian J. Eng., 2008, 14, 273–302.
http://dx.doi.org/10.3176/eng.2008.4.01
18. Kurennoy, D., Parnell, K. E., and Soomere, T. Fast-ferry generated waves in south-west Tallinn Bay. J. Coastal Res., 2011, SI 64, 165–169.
19. Didenkulova, I. and Soomere, T. Formation of two-section cross-shore profile under joint influence of random short waves and groups of long waves. Marine Geol., 2011, 289(1–4), 29–33.
http://dx.doi.org/10.1016/j.margeo.2011.09.011
20. R Development Core Team. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria, 2010.
21. Nason, G. P. Wavelet Methods in Statistics with R. Springer, 2008.
http://dx.doi.org/10.1007/978-0-387-75961-6
22. Nason, G. Wavethresh: Wavelets Statistics and Transforms. R package version 4.6.6. http://CRAN.R-project.org/package=wavethresh (accessed 15.12.2014).
23. Torsvik, T., Soomere, T., Didenkulova, I., and Sheremet, A. Identification of ship wake structures by a time-frequency method. J. Fluid Mech., 2015, 765, 229–251.
http://dx.doi.org/10.1017/jfm.2014.734