26 



THEORY OF SEAKEEPING 



Fig. 18 Relation between wave steepness and wave age. Observed values shown by symbols, assumed 

 relationship shown by full drawn line (from Sverdrup and Munk, 1947) 



2 dx 



Edc 

 2dv 



= Et ± Ep 



(57) 



Each of these independent eciuations contains two un- 

 knowns, E and c. The soUition is made possible by in- 

 troducing an assumed functional relationship 



H/\ = J(,c/U) 



(58) 



Sverdrup and Munk (1947) collected many observa- 

 tions and plotted 6 = H/\ versus ji = c/U. The first 

 quantity was called "wave steepness" and the second 

 "wave age," and these terms have since been adopted for 

 common usage. The resultant plot is shown in Fig. IS. 

 By making certain assumptions as to subdivision of 

 energy in the growth of wa\-e height and wave length, a 

 curve was obtained, which fits the observed data very 

 well. At the time the (jriginal plot was made, very few 

 data for /3 < 0.4 were available. These were obtained 

 later mo.stly by Roll (1951) and Francis (1951). Fig. 19 

 shows a plot taken from Neumann (19526). For many 

 years in the past, attempts to relate wave height directh' 

 to wind velocity were unsuccessful; a wide \-ariance 

 existed in the published literature. The parameters 

 H/\ and c/U on the other hand, fell readily into a well- 

 defined pattern for /S > 0.4. The relationship below this 

 value remains uncertain. 



Having established empirically the relation.'^hip 6 = 

 /()3), equations (56) and (57) were solved and the results 

 were plotted in the form of nondimensional ratios c/U 

 and gH/U- ver.sus gF/U- for the steady .state, and versus 



gt/U for the transient .state. Pig. 20 taken from John- 

 ,son and Rice (1952) .shows the .stead \'-state relationships 

 as developed further by Bretschneider from data which 

 became available .subsequent to the original work of 

 Sverdrup and ^lunk. The second plot taken from the 

 latter is shown in Fig. 21. These plots are of very prac- 

 tical form and ha\'e been widely used for prediction of 

 wa\'e contHtions on the basis of meteorological data. 

 For a discussion of wa\'e decay outside the generating 

 area the reader is referred to the original papers of 

 Sverdrup and Munk (1947) and Bretschneider (1952). 



5.2 Neumann's Work on Wave Generation. In this 

 section the \v(.)rk of Neumann on \va\e generation (1948, 

 1949a, h, 1950, 1952a, 6) will be outlined. He has 

 treated the matter in two different ways, considering the 

 .significant wave as did Sverdrup and ]\'Iunk (1946, 1947), 

 or taking the sea as composed of three predominating 

 wave systems. Neumann's formulation of the continuous 

 sea .spectrum (1953, 1954, and Pierson, Neumann and 

 James, H) will be the .subject of Section 6.2. 



Neumann's work on wave generation is outstanding 

 because : 



a) The experimental material, taken from pre-\'ious ob- 

 servations of other oceanographers and obtained by Neu- 

 mann himself, covers a very wide range of wind and sea 

 conditions and geographic locations. (All observations 

 were vi.sual.) 



h) A determmed attempt was made in the anal.ysis to 

 adhere as closely as possible to rational procedure. 



c) The mathematical and statistical formulations are 



