APPENDIX B 



Neumann's 1948-1952 Work 

 on Wave Generation by Wind 



Nomenclature 



The nomenclature on page 90 of Chapter 1 apphes in 

 general to Appendix B. Additional symbols are as 

 follows : 



.-1= a coefficient; pncrsy 

 A„= energy transmitted li\- normal com])onent of drag 



force, equation ( 11)1 

 .1,= energy transmitted by tangential component of drag 

 force, equation (20) 

 B{i3)= "effective dissipative factor," ei|iiation (56) 

 C(0)= "effective friction factor" or "resistance factor" in 

 work on drag force, eipiations (37 and 38) 

 Hi, H'. Hi = e(|uivaleiit heights of three maior waves, /3,„, /5( 1 ) and 



7'i, 7'j, 7',i= characteristic mean periods of aliove waves 

 a = a coefficient 



0,n = "sea" witli r < V 

 /3(1)= intermediate 



wave c = I 

 l3,„ * = long wave 



c = 1.37 I' 



I 



Designations of waves, defined 

 as characteristic mean values 

 I for certain period intervals 

 !• when a continuous spectrum is 

 I visualized as .subdivided into 

 three major intervals (Neu- 

 mann, 11)52/)) 



fi = value of turbulent viscosity m* ( f ') in a fully developed 

 seaway with li = const 



1 Introduction 



In this Appendix the work of Xeiimaini on wave gen- 

 eration (1-1948, ll)4;)a and h, 19.50, 1952« and 6)i will 

 be outlined. This work is based either on consideration 

 of the significant wave, as by Sverdrup and Munk (1- 

 1946, 1947), or on taking the sea as composed of three 

 predominant wave systems. Xetmiann's formulation of 

 the continuous sea spectrum (l-195o, 1954, and Pierson 

 and Neumann, l-II) was presented in Section 1-6.2. 



Neumann's work on wave generation is outstanding 

 because : 



(a) The experimental material, either taken from 

 previous observations of other oceanographers or ob- 

 tained by Neumann himself, covers a very wide range of 

 wind and .sea conditions and of geographic locations. 



(5) A determined attempt is made in the analysis to 

 adhere as closely to the rational procedure as available 

 means permit. 



(c) It appears to be the only work on wa\'e develop- 

 ment in which the l)alance of energies transmitted from 

 the wind and dissipated in waves is fully discussed. 



' References to sections, equations, figures, and bibliography 

 will be designated by chapter number and section, and so on; 

 reference noted is to Xe\imann, Chapter 1 (1948). 



(d) The mathematical and statistical formulations 

 are preceded or accompanied by a large amount of physi- 

 cal description of sea conditions. 



The author considers the foregoing features (particu- 

 larly item c) to l)e of sufficient importance to warrant a 

 comprehensi\'e summary. While the detailed work based 

 on the concept of a significant wave or that of three wave 

 components is outdated, the work as a whole can still be 

 used as a valuable guide for futiu'e research. At least it 

 has to serve as such until a more modern work of com- 

 parable scope appears. Contributions to the theory of 

 wave generation found in the literature appear to be 

 concerned only with individual facets of the problem. 

 Neumann's 1948-1952 work appears to be the only one 

 treating the problem in its entirety. 



In the following exposition an attempt will be made to 

 present, in as logical and as short a form as possible, the 

 content of six of Neumann's papers published in the 

 years 1948 to 1952. While the mathematics and basic 

 concepts involved in these papers are simple, it is not 

 always easy to follow Neumann's logic. The reader is 

 warned therefore not to accept the following as an ade- 

 c}uate presentation of Neumann's work, but to consult 

 the original papers for a serious study. The difficulties 

 mentioned result primarily from two causes; The work 

 represents a transition period from the concept of a simple 

 harmonic sea to the spectral presentation developed later; 

 also it represents a gradual development of ideas from 

 paper to paper, but not (juite a continuous one. New 

 ideas appear without conspicuous announcement, older 

 ones are abandoned without a word, although a good 

 deal of the older material is used and is referred to. 

 Under no condition, however, can this set of six papers be 

 considered as being superseded by the subsecjuent work 

 on the .sea-energy spectrum. 



The work on the spectrum is concerned entirelj' with 

 the statistical study of observational material, without 

 any regard to its physical or hydro-aerodynamic proper- 

 ties. It is a good presentation of observed facts without 

 regard to the hydro-mechanical causes of their existence. 

 Contrary to this, Neumann's work of 1948-1952 repre- 

 sents the most complete investigation of the mechanics 

 of wave formation available to date, while his description 

 of the ob.servable characteristics of a .seaway must be 

 kept in mind by all theoretical investigators of lesser sea 

 experience. 



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