Newman 



The classical analysis of ship waves using linearized inviscid 

 wave theory, originated in the nineteenth century by Kelvin and 

 Mitchell, has enabled us to understand and predict the qualitative 

 features of ship waves. The period since 1900 has seen a wide vari- 

 ety of refinements and applications of this basic model, and the 

 present unsatisfactory state-of-the-art in no way detracts from the 

 dedicated contributions of Havelock and others, some of whom are 

 in this audience, who labored with ship-wave theory before it was 

 facilitated by digital computers and a more widespread understand- 

 ing of the methods of mathematical physics. 



As in most other branches of ship hydrodynamics, our present 

 knowledge of ship waves is sufficient only for a qualitative under- 

 standing of the phenomena, and does not permit quantitative predic- 

 tions with the accuracy required by most engineering situations. In 

 the past decade many ambitious scientists and engineers have, there- 

 fore, abandoned the assumptions of linearization, or of an inviscid 

 fluid. Some of these attempts at fundamental improvements of the 

 Kelvin-Michell approach were summarized by the author in a Panel 

 Report (Newman [ 1968]) to the Seventh Symposium on Naval Hydro- 

 dynamics. The present paper is not intended to cover such a broad 

 range of contributions, but only to report on my own recent and very 

 limited activities in this area, both experimental and theoretical. In 

 the experimental domain, photographic observations have been made 

 of the Ferry Boat UNCATENA and of a small scale model of the same 

 vessel, in order to verify the Kelvin wave pattern prediction and to 

 search for variations in the wave system resulting from scale effects. 

 In addition, a series of experiments have been made in a towing tank 

 with the objective of confirming the striking nonlinear phase-jumps 

 predicted by Howe [ 1967, 1968] , Finally, in an extensive theoretical 

 investigation, which is reported upon in more detail elsewhere 

 (Newman [ 1 971] ) , we consider the possibility of third-order nonlinear 

 resonant interactions in ship waves, motivated by the importance of 

 these interactions in the field of ocean waves (Phillips [ 1966]). For 

 the sake of completeness, we shall first give a brief outline of the 

 classical Kelvin ship-wave system. 



II. THE KELVIN SHIP- WAVE PATTERN 



Disregarding the local effects close to a ship hull, we can 

 assume that ship waves are a distribution, in wavenumber space, of 

 Individual plane water waves. Generally speaking, these are ob- 

 served to be of small amplitude relative to their wavelength, and the 

 relevant Reynolds numbers are of order 10 to 10', so that we are 

 led to a linear potential -flow model. The individual plane wave 

 system can then be described by the free- surface elevation 



Ux,,y,)=Ae'*^^''oCOs5.yoSin«)-ia,t ^^^ 



520 



