THE GENERATION OF WATER WAVES BY WIND 



by 

 Gerhard Neumann 



This paper appeared in the German publication 

 "Deutsche Hydro graphische Zeitschrif t", Vol. 2, 

 No. 5, 1949- An English translation is on file 

 at the Bsach Erosion Board Library. An ab- 

 stract of which is presented herewith. The au- 

 thor is currently a visiting professor to the 

 staff at New York University 



Classical considerations of wave formation by others have been 

 investigated by the author, and a new treatment of this problem is 

 presented. Theory is presented for computing the length and amplitude 

 of initial waves generated by incident winds of different velocities , 

 which is valid until the initial waves attain a steepness where they 

 are no longer stable and turbulence occurs. The energy supplied by 

 the wind to the water surface is computed, assuming dynamic equilibrium 

 of the effective shearing stress of the wind and resistance to this 

 stress offered by the water surface. An empirical relationship be- 

 tween the effective shearing stress of the wind and the wind velocity 

 has been determined. Surface resistance has been considered as the 

 resistance due to pressure differences for both capillary and gravity 

 waves, and that due to frictional stresses. Values of a ^resistance 

 coefficient 1 * have been computed for different values of wind velocity, 

 and this coefficient is indicated empirically to be simply proportion- 

 al to the wave steepness. The energy dissipated by the wave motion 

 is considered for a water layer of finite depth, and is computed as ■■ 

 that consumed by inner friction in the water and that dissipated 

 through bottom friction. For the generated wave to be propagated 

 and maintained, it is necessary that the energy transmitted to the 

 wave by the wind be greater than that dissipated by the wave motion. 

 From this consideration, equation 18 below is obtained. 



±_P_ 

 4- P 



where: 



XVff 



tyCxh)> ax + ^-J 



xav i 



Z s/nh(2-xh) 



(18) 



P = density of air 

 P => density of water 

 S = screening coefficient 

 Vm= wind velocity 

 C = wave transmission velocity 



V = kinematic viscosity 

 ~X = wave no . = Z7r /\ 

 h = water depth 

 CL = wave amplitude 



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