CHAPTER 1 



Seaway 



1 Introduction 



The wind-swept surface of an ocean usually presents a 

 very complex irregular appearance. A certain regularity 

 exists only in the broadest sense that wa\'e hollows and 

 wave crests progress in some general direction and 

 succeed each other alternately. The time between 

 passages of crests, the heights of crests, and the distances 

 between crests vary widely and erratically. It is impos- 

 sible to evaluate quantitatively by direct observation 

 the effect of such an irregular surface on the beha\'ior of 

 a ship. It is necessary to undertake a systematic analy- 

 sis or breakdown of a complex physical event into simple 

 components, to study the effect of these simple compo- 

 nents, and to add them together again in order to reach an 

 understanding of the whole. The technique of such a 

 process developed over many years in the fields of heat 

 transfer and electrical network analyses in recent years 

 has been applied to complex ocean waves. 



It has been shown that a function of any complexity 

 can be represented as the sum of a large or infinite num- 

 ber of simple harmonic functions (waves) of varying 

 periods and amplitudes. The word "simple" is applied 

 here to a uniform regular wave characterizetl by a single 

 direction of propagation, a definite frecjuency, a definite 

 wave length, and a definite amplitude, which are repeated 

 uniformly in each passing wave. The description of a 

 seaway must start then with a definition of the properties 

 of such a simple wave. This simple wa\'e does not 

 normally exist in nature, Init can be produced in a labora- 

 tory, either for investigating the properties of the wave 

 itself, or for studying its effects on ship models or on 

 harbor installations. A summary of the classical theory 

 of simple waves will be found in Appendix A. 



The classical wave theory considers only the propa- 

 gation of free waves under the action of gravitational 

 and inertial forces. Uniform distribution of air pre.ssure 

 is assumed, and neither the transfer of energy from wind 

 to water nor the mechanism of wave generation has been 

 considered. The following four sections of Chapter 1 

 will be devoted to discussing these phenomena. Theoret- 

 ical reasoning, laboratory experiments and .specially 

 designed methods for obser\'ing natural waves are 

 involved in this problem which so far has eluded a com- 

 plete .solution. Later .sections will take up the organiza- 

 tion of empirical observations in a form suitable for wave 

 forecasting and for determination of a ship's behavior at 

 sea. Finally, the mathematical sea-surface representa- 

 tion needed for the latter purpo.se will be outlined. 



'■ Throughout, References will be given bj' author and year, and 

 may be found in the alphabetical list at the end of each chapter. 



2 Generation of Waves by Wind— Elementary Rational Approach 



The problem of the generation of wa\es by wind was 

 first attacked by Lord Kelvin (Thomson, 1871),' by 

 considering the free-water surface as a dividing boundary 

 between two fluids, water and air. The motions of 

 both were considered separately; i.e., the velocity po- 

 tentials of both water and air were evaluated. Further- 

 more, it was postulated that the pressure of the air and 

 that of the adjacent water differ owing to the surface 

 tension of water. The derivation is also given in Lamb 

 (D, art. 267 and 208, pp. 458-4()2) and Motzfeld (1937, 

 pp. 205 and 206). Kelvin's .solution for waves propagat- 

 ing in one direction in deep water was extended by 

 Jeffreys (1925) to waves propagating in two directions. 

 Using the .solution of Lord Kelvin, .Jeffreys indicated that 

 at an air velocity of 640 cm/sec (about 21 fps) the water 

 surface becomes unstable, and waves develop spontane- 

 ously. These first waves have a length of 1 .8 cm (0.71 in.) 

 and a celerity of 23.2 cm/sec (0.76 fps) which was shown 

 to be the least possible wave celerity. This wa\'e repre- 

 sents a borderline between longer waves due to gravity, 

 and the shorter (but faster traveling) waves due to the 

 surface tension of water; i.e., the capillaiy waves. 



The foregoing conclusion does not agree with observa- 

 tions of nature, which indicate that waves begin to de- 

 velop at much lower wind A^elocities. .leffreys (1925, 

 1926) by observation of waves due to light winds on a 

 pond arrived at the conclusion that waves begin to 

 form at a wind \-elocity of about 110 cm/sec (3.6 fps), 

 have an initial length of 6 to 8 cm (2.4 to 3.1 in.) and a 

 celerity of about 30 cm/sec (about 1 fps). Stanton 

 (1932) found by experiments in a wind flume that 

 graA'ity wa\'cs first form at an air speed of 250 cm/sec 

 (8.2 fps) and are cm (2.4 in.) long. He emphasized the 

 uncertainty of such observations and wrote: "The mini- 

 mum velocity of the wind required to cause the formation 

 of waves has been observed, although as has been pointed 

 out, the value obtained will depend to a great extent on 

 the conditions of the experiment." 



The general picture is made much clearer by Roll 

 (1951) who observed and measured wind and waves on 

 a large shallow pond left on a low sea shore by the reced- 

 ing tide. Fig. 1 shows the frequency distribution of the 

 various wa\'es plotted versus the wind velocity. It is 

 impossible to name with certainty the wind velocity 

 connected with the first formation of waves. By taking 

 the 50 per cent proluibility of occurrence of gravity waves 

 Roll estimated the minimum nece.s.sary wind velocity at 

 60 to 80 cm/sec (2 to 2.6 fps). He made the very 

 important observation that from the beginning there are 



1 



