Journal of Fluid Mechanics

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

Ellen D.  Brown a1, Steven B.  Buchsbaum a1a2, Robert E.  Hall a1, John P.  Penhune a1, Kurt F.  Schmitt a1, Kenneth M.  Watson a2 and Donald C.  Wyatt a1a3
a1 Science Applications International Corporation, San Diego, CA 92121, USA
a2 Scripps Institution of Oceanography, San Diego, CA 92093, USA
a3 Department of Applied Mechanics and Engineering Sciences, University of California, San Diego, CA 92093, USA

Article author query
brown ed   [Google Scholar] 
buchsbaum sb   [Google Scholar] 
hall re   [Google Scholar] 
penhune jp   [Google Scholar] 
schmitt kf   [Google Scholar] 
watson km   [Google Scholar] 
wyatt dc   [Google Scholar] 


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.

(Published Online April 26 2006)
(Received June 15 1988)
(Revised December 27 1988)