Recent Research on Ship Waves 



This infers a significant difference between the transverse wave 

 amplitudes for the model and full-scale, which could have important 

 ramifications on the predictions of wave resistance from conventional 

 model testing, but this tentative conclusion may be biased by minor 

 differences in camera angles or lighting , and it is felt that a quanti- 

 tative measurement of the transverse wave amplitudes for the model 

 and full-scale vessel should be made, with wave buoys or stereo 

 photographs. 



IV. TANK TESTS OF A WAVY WALL 



In perhaps the only truly nonlinear analysis of ship waves 

 carried out to date, Howe [ 1967, 1968] has considered the waves 

 generated by a "wavy wall" or ship hull form consisting of a slowly 

 damped sine wave. This geometrical form generates preferentially 

 only one wave system. By suitable choice of the hull wavelength 

 and velocity, a diverging wave system can be generated which, 

 according to Howe's theory and based on the analysis of slowly vary- 

 ing finite annplitude waves as originally developed by Whitham [ 1965] , 

 will become unstable. The most striking feature of Howe's compu- 

 tations, resulting from this Instability, is the occurrence of a shock 

 or "phase-jump" across which there is an abrupt change in phase 

 and wavenumber. Figure 11 is reproduced from Howe [ 1968] , and 

 shows the calculated wave system and the region where a phase-jump 

 is predicted. Also shown, on the abscissa and with an exaggerated 

 scale, are the waterlines of the hull form. 



Fig, 11 Cross sections of the free surface perpendicular to the 



phase-jump. The broken line segments indicate a possible 

 fornn for the free surface in the neighborhood of the phase- 

 jump (from Howe [ 1 968] ) . 



*In color slides shown during the oral presentation of this paper, 

 some weak transverse waves can be noted in the full-scale tests, 



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