48 



THEORY OF SEAKEEPING 



Increase of Waves 



Fig. 50 Typical change of wave energy in build-up 

 and decay of waves (from Ijima, 1957) 



compounded of several generating causes. Most im- 

 portant of all, however, is the fact that a sea spectrum is 

 a statistical concept. Waves are expected to conform 

 to the predicted spectrum on the average, and it should 

 not be expected that an isolated record will conform 

 exactly. Conversely, an isolated record should be con- 

 sidered of little value in (|ualifying a spectrum formida- 

 tion. The rare occurrence of the ideal conditions in na- 

 ture, ho\ve\'er, makes it very difficult to collect sufficient 

 data for a statistical evaluation. Also, until recently, 

 Darbyshire's (1955) data were the only ones obtained by 

 instrumental measurements in the open ocean. 



In regard to the spectrum area, i.e., significant wave 

 height prediction, the subject is further complicated by 

 the indeterminateness of the wind specification. Various 

 formulations indicate that spectrum area is proportional 

 to either the fourth or fifth power of wind velocity. 

 Small differences in measured wind \'elocity will, there- 

 fore, strongly affect the relative position of the spectral 

 curve on such plots as Figs. 40 and 51. Yet winds are 

 measured indiscriminately at various "anemometer 

 heights," and no standard for such measurements has 

 been established. Aerodynamic experience also has in- 

 dicated that interference of a body with an air stream 

 extends for a considerable distance. In calibrating air- 



craft speed, a "bomb" carrying the speed pick up has 

 sometimes been suspended on a cable many feet below 

 the aircraft. The conclusion is inevitable that wind- 

 s]K»od measurement at practical locations on a ship is 

 faulty. C'oncei\-ably a kite or a small balloon could be 

 used (jn weather ships. 



Apparently the only a\-ailable data from sea recording 

 and analysis for spectrum \-erification were obtained in 

 project SWOP (Chase, et al., 1957). This project will 

 be described more completely in Section 8 in connection 

 with directional wave spectrum. For the present it is 

 sufficient to sa,v that two stereophotographs of an open- 

 sea area were taken from two airplanes simultaneously 

 within a 20-min period of wa\e-pole recording. Two 

 spectra were computed, one from the stereophotographic 

 analysis and the other from the wa\'e-pole analysis. 

 One of these is reprotluced in I'ig. 51 for comparison with 

 other spectra. 



A discussion of the discrepancies among the spectra 

 shown in Fig. 51 will be found in Xeumann and Pierson 

 (1957). 



6.52 Wove development with time. Some of the ap- 

 palling differences among the spectra shown in Figs. 46 

 and 51 are compensated by the differences in their rates of 

 growth. An abnormally high Neumann spectrum is de- 

 \'eloping so slowly that its full wave height is hardly ever 

 reached in practice in strong winds. The much lower 

 wave height indicated l)y Darl\vshire's (1955) spectrum, 

 on the other hand, is ciuickl^y attained. The differences 

 among the different formulations are therefore much re- 

 duced for the wind durations most frequently found in 

 practice. 



The mean of Ho highest waves in a 40-knot wind is 

 shown in Fig. 47 as a function of wind duration. This 

 figure shows the wave heights expected in idealized condi- 

 tions of uniform wind over unlimited fetch. Walden 

 (1953/54) collected the material to show what was ac- 

 tually observed. Weather and \'isual wave-observation 

 data had been radioed at regular intervals by ten 

 weather-obser\'ation ships in the Atlantic Ocean. This in- 

 formation was systematicall,v collected at the sea- 

 weather bvu-eau (Seewetteramt) in Hamburg, Germany. 

 These records, covering the period from February to 

 December 1953, were examined in conjunction with 

 working weather maps. 



Out of a very large number of records, 515 suitable for 

 wind-duration effects, and 264 suitable for fetch-effect 

 e\'aluation were chosen. In these records the wind 

 started suddenly, reached full force in a short time and 

 then lilew for a long time with approximately uniform 

 \'elocity. In addition, in the records chosen, the sea was 

 calm before the wind started. The conditions were suf- 

 ficiently close to the ideal ones implied in spectrum 

 formulations so that only minor computational correc- 

 tions were necessary. The results of these investigations 

 (for winds of 26 and 30 knots) are shown in Figs. 52 

 and 53 for the effect of wind duration and Figs. 54 and 55 

 for the effect of the fetch. Of the wave-forecasting 



