then it can be shown that the ratio 



2 



A 4 



(23) 



vanishes only when the wave system consists of two intersecting systems of long-crested 

 waves, and equals unity when the surface is isotropic. So this ratio is a measure of 

 the "bimodality" of the spectrum with regard to direction. Upon the same parameter 

 depend also the distribution of the "total" curvature of the surface and the number 

 of maxima, minima and saddle-points per unit horizontal area. 



Reference 1. 



Longuet-Higgins, M. S. ''The statistical analysis of a random, moving surface." Phil. Trans. 

 Roy. Soc. A. 249, p. 321 ( 1957). 



R. W. L. Gawn 



The determination of the frequency and amplitude of the complex undulations 

 of the ocean surface is of fundamental importance to those who design ships, those 

 who operate them and to those who plan operations. 



Dr. Munk mentioned the importance of the information as regards ship motion 

 but the designer's interest is much wider. The ship must stand up to all the hazards 

 of rough weather and I would like to make a few remarks on the designer's problems 

 in this connection. Gravity waves impose heavy stresses and slamming, objectionable 

 motion and speed loss and further limit efficiency if operational positions, e.g. gun 

 positions in a naval ship are exposed to water or spray. 



In the past and that not far distant the information available on ocean waves 

 was scanty and it is remarkable that the designer was able to achieve a good measure 

 of success. He assumed for strength calculations that the height of an ocean wave 

 was one twentieth the length, although later thanks to the observations of Vaughan 

 Cornish and others he could accept a smaller ratio for longer waves. 



Until a few years ago that was about all that was known of use to the designer 

 and it is refreshing now to hear of the enterprising work and the ingenious and pains- 

 taking analysis which Dr. Munk and others are carrying out. 



There is scope for a closer identification of the length or period of the wave 

 and the related height with the probability of occurrence in different oceans. While 

 height is the dominant term in the energy estimates mentioned in the paper, period or 

 length is dominant for ship motion since it influences both the excitation and the magni- 

 fication. The Authors mention that the gravity waves are centered around 10 seconds 

 period or a length of about 500 feet. It is emphasized that the range of interest to the 

 ship designer is really from about 100 to 1500 feet length or about 4 to 17 seconds 

 period and it is hoped that the Authors' further investigations will include a detailed 

 study of this particular field accordingly. It looks as though from the wonderful instru- 

 ments described by Dr. Munk and the work of the last speaker this should be realized. 



As regards instrumentation, one requirement is a handy apparatus that can be 

 taken to a ship and dropped in the water as necessary. As a matter of fact thinking on 

 these lines we have made a simple buoy at Haslar which transmits radio signals of its 

 vertical movement. Whether it is effective or not I am not yet in a position to say but 

 a preliminary trial was promising. I am hoping that it is at sea just about now so that 

 we should soon know if it is at all promising. 



/. D. Pier son 



Before proceeding to a few comments on this excellent paper, I would like to 

 bring a third party to the "marriage" of the oceanographers and ship builders. The 



58 



