ON THE EXPANSION OF SEA WAVES DUE TO THE EFFECT OF WIND 

 (based on measurements in shallow tidal waters) 



by 



Hans Ulrich BdII 



This paper appeared in the German publication 

 "•Deutsche Hydro grap hi sche Zeitschrift", Vol. 2, 

 No. 6, 1949 o An English translation is on file 

 at the Beach Erosion Board Library, An abstract 

 of which is presented herewith. 



Recent wave and wind measurements made in the tidal waters of 

 the w Neuwerk Shallows* 11 in the North Sea at the mouth of the Elbe 

 River are described and are compared with the theoretical results based 

 on the methods employed by Sverdrup and Mink. Most wave measurements 

 were made where the wave length-water depth ratio was slightly greater 

 than 2, the accepted transition value between deep and shallow water 

 wave theory. However , in slightly over 80 per cent of the cases, the 

 maximum deviations of wave height and velocity from the deep water 

 values were only 7 per cent for the wave height and U per cent for the 

 velocity, so for at least 80 per cent of the cases it should be ex- 

 pected that the relationship betwe en wav e velocity and length would be 

 satisfactorily expressed by C "V^^tt as used b y Sverdrup and Munk. 

 The wave velocity measurements have been adjusted where necessary for 

 the effect of tidal currents. 



The adjusted values of wave velocity and the measured values, of 

 wave length follow the cur ve of the theoretical relationship 

 (n=-Ji!= Qw-Ql 2tt y ) relatively well (shown in Figure 1) ex- 



cept that the main body of plotted points lies below the curve, in- 

 dicating that the theory seems to represent the upper limit of the 

 . measured values rather than their average. As shown in Figure 2 the 



author relates this negative deviation of measured thmntrtanril . wave -^ ^t/l&yyy 

 velocities as computed from the Laplace formula C=^jML -h>nh ^j^ ^AjU^ULttX^U. 



to the wave steepness and wind velocity. Empirically it is indicated 

 that this negative deviation becomes larger as the waves become steeper 

 with a fixed wave length, and becomes smaller with an increase in wind 

 velocity. 



The empirical relation between wave steepness and wave age as 

 developed by Sverdrup and Munk is compared with the measured values at 

 Neuwerk, and is shown in Figure 3. The author suggests that it 

 appears problematical that this relatively wide dispersion of plotted 



22 



