shelf acting as a wave guide (Munk, Snodgrass and Carrier, 1956). Crests and troughs 

 are normal to shore, and the direction of propagation parallel to shore. Amplitudes 

 decrease rapidly seaward, and are insensible at a distance of one wave length from 

 shore. Such wave motion was theoretically described by Stokes more than one hundred 

 years ago, and referred to as "edge waves." (see also Eckart, 1951; Ursell, 1952; 

 Isaacs, Williams and Eckart, 1951.) 



Edge wave activity is related to meteorologic activity, but not in the same sense 

 as sea and swell. There is some indication that these waves are generated by traveling 

 disturbances of atmospheric pressure, such as result from internal waves in the atmos- 

 phere. If so, they represent a curious coupling of the height and sharpness of the atmos- 

 pheric inversion layer, on one hand, to the slope and width of the continental shelf 

 on the other hand. 



All our measurements so far have been confined to the continental shelf and 

 borderland. One week from today we plan to occupy a station off the coast of Mexico 

 and beyond the borderland to see whether such activity can be found also in the open 

 sea. If so, this would open up the possibility of an old dream; could deep sea surges, 

 which travel at speeds of about 400 knots, serve as a storm warning? 



SHIPS AND WAVES 



The aspect of waves which is probably of greatest interest to the present gather- 

 ing is their effect on ships. To a first order of accuracy, each degree of freedom of the 

 ship may be regarded as an independent filter which responds in a prescribed way to 

 the various wave components. For example, in its rolling motion a ship behaves rather 

 like a pendulum and responds only to those components of the complex wave pattern 

 which pass the ship with more-or-less the resonant frequency. It is obvious, however, 

 that wave frequency is not the only factor since we all know that the rolling of a ship 

 depends greatly on the direction of approach of the waves, usually being greatest when 

 the waves approach from 2 or 3 points abaft the beam. The frequency at which the 

 waves pass the ship will also depend on the ship's speed and its direction relative to 

 the direction of wave travel. 



If we regard the sea as being composed of a large number of simple sinusoidal, 

 unidirectional wavetrains (see below), it is in principle possible to calculate the response 

 of the ship to each of these, and the mean square response will be the sum of the mean 

 square amplitudes of each individual wavetrain multiplied by the appropriate response 

 factor. When generalized to a continuous spectrum, this is equivalent to regarding the 

 ship as a filter with a two-dimensional filter function depending on the ship's geometry 

 and velocity. The spectrum of the ship's motion is the integral of the appropriate 

 product of this function with the two-dimensional spectrum of the waves, and can be 

 calculated, at least in principle. From this, many useful statistical parameters can be 

 calculated by methods developed by Rice (1944) for one-dimensional problems, and 

 by Longuet-Higgins (1957) for two-dimensional problems. For example, r.m.s. 

 amplitude, mean period, greatest expected amplitude during an hour's period of observa- 

 tion, number of times a given amplitude will be exceeded and whether the cook will 

 be seasick can all be predicted. A convenient summary of these relationships is given 

 by Cartwright and Rydill (1956). 



A great deal of theoretical work has been done on the response of ships to waves, 

 the effect of a simple sinusoidal wave train traveling in a single direction having re- 

 ceived most attention, though more complicated wave patterns have recently been 

 studied by St. Denis and Pierson (1953), by Cartwright and Rydill (1956) and others. 

 (See, for example, several papers in Ships and Waves, 1954.) Considerable progress 

 has been made in checking these theoretical results using models in tanks, but the acid 

 test will be measurements using real ships in a real seaway. For these tests it will be 

 necessary to measure the characteristics of the wave pattern in both frequency and 

 direction of travel, and a knowledge of typical sea conditions based on such measure- 



49 



