NEUMANN'S 1948-1952 WORK ON WAVE GENERATION BY WIND 



327 



Table 1 Sin \}/ Versus U: Observations Made in 1925; Average Depth 70 M 



[/, meters ps 1 ~ '.'i 4 o (i 7 8 !l.5 I'-'o IS 



lO'sin^J' 0.2 0,8 1.2 1.4 2.0 2.1> 3.0 3.0 4,(i 7,7 14.4 



Number of days 



olm-rved 34 50 51 G6 44 32 23 14 13 15 5 



Table 2 Sin tp Versus U: Single Observations; Average Depth 50 M 



-In a storm fnjin Octolier 4 to 0, 1936- 



Jan. 2 and 4 

 • 11135 



f/, meters p.s . 0,3 11.8 13.0 10.1 17. G 10.4 23,4 24. (i 26.0 10.5 18.0 

 lO'sin^....- 6.8 0.7 12.4 10.1 23.3 25.7 31.5 36.3 43.6 6.5 16.0 



In the Section G of Chapter 1 it wajs demonstrated that 

 large differences exist among various spectra obtained on 

 the basis of empirical data. In the intiixhiction to Chap- 

 ter 1 the author stated his behef that theptuciy empiri- 

 cal approach is inadecniate and that concurrent theoreti- 

 cal de\Tlopment is needed. The Neumann's work, here 

 outlined, can be taken as a general guide for such an ap- 

 proach. However, it has to be supplemented by, and 

 blended with, the recently developed mathematical sta- 

 tistics of irregular sea. 



2 Horizontal Drag Force 



In accordance with items (b) and (c) of the introduc- 

 tion, the cjuestion of the energy balance in wa\-e growth 

 is given a large amount of attention. The primary in- 

 formation (experimentally obtained) neeiled in this con- 

 nection is the horizontal drag exerted by wind on a water 

 surface. This forms the specific subject of Neumann 

 (1-1948). In Sections 1-2.3 and 2.7, an attempt was 

 made to correlate the drag force with the wave form 

 which, in turn, depends on wind speed, fetch, and so 

 forth. Since cjuantitative data on the wave form at sea 

 are not available, Xemnann attempts a direct correlation 

 of drag force with wind speed. For this purpo.se he ex- 

 amines the large number of observations of wind-caused 

 inclination of sea surface made by Palmen (1-1932 a and b, 

 1-1936, Palmen and Laurila, 1-1938). Observations were 

 made in the Bay of Bothnia in the northern part of the 

 Baltic Sea, where the relati\'ely miiform, small water 

 depth and steady wind conditions o\'er a large area pro- 

 vided the opportunity for the most accurate observations. 

 The mean obser\'ed data on wind and sea-surface slope 

 are given in Table 1, together with the number of ob- 

 servations involved. Table 2 gWes a set of isolated ob- 

 servations made during a storm in the Baltic Sea where 

 satisfactory observation conditions also existed. 



For observations made on land, i.e., with a constant 

 degree of roughne.ss, G. I. Taylor expressed the tangential 

 force T as 



pyU' 



(1) 



with the coefficient y between 0.0022 and 0.0032 based 

 on the wind velocity [/ measured at the height of 30 m. 

 With particular emphasis on strong winds, Palmen and 



-44 

 -4.8 

 -5.2 

 5.6 

 6,0 

 -64 

 -68 



• Ostsee (Palmen), Bo+tn Busen 



X Ostsee(Colding) 



A Erie- See 



o Center See 



® Lake Okeechobee 



I ; 7-IO,OxlO"^v"°'=^'' 



n:T= BZxio-'v-"-"" 

 in:7= 90«IO"-'--"°-^ 



04 



IG 2 24 2£ 

 en U 



3 2 3.6 4.0 4 4 



Fig. 1. Plot of log -) versus log U (from Neumann, 19-48) 



IS 20 24 28 32 3G 

 U fm sec) 



40 



Fig. 2. Variation of drag-force cofficient y with wind velocity 

 U (from Newmann, 1948) 



Laurila (1-1938) also derive the same expression with 7 

 = 0.0024 (but presumably with U measured at the 

 more usual 6 or 10-m height). Since the wave form at 

 sea is variable and depends on the wind, Neumann as- 

 sumes a relationship of the form 



/'((■) = KU" 



7 



(2) 



His plot of log 7 (observed) \-ersus log U is shown in Fig. 

 1, and his line III is found to give the simple relationship 



0.09C^-»-'' (with f in cm/sec) 



(3) 



and 



