THEORY OF SEAKEEPING 



izo- 



Fig. 2 Wave profiles of models tested in a wind tunnel (from Motzfeld, 1937) 



0.4 



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0.4 



OG 



0.8 



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Fig. 3 Pressure distribution along wave profiles (from Motzfeld, 1937) 



potential flow) resulting from the action of normal pres- 

 sures is found to be small. 



The fundamental distinction just stated between the 

 kinetic energj' of nearly potential flow, and the eddy- 

 making or theimal energy of skin friction has often been 

 disregarded in the literature on wave generation and 

 propagation. A large amount ot discussion and the vari- 

 ous attempts at evaluation of the skin-friction energy in 

 this connection appear to the author to be in basic con- 

 tradiction to the laws of hydromechanics. The di.sor- 

 ganized eddy-making and thermal energies are no longer 

 available to the potential wave flow. 



One of the reasons for considering skin friction hereto- 

 fore was the necessity of explaining the experimentally 

 observed long waves which travel faster than wind. 

 Since the skin friction depends not on the wave celerity 

 but on the wind \-elocity with respect to slowly mo\'ing 

 water particles, energy transfer appears to exist even for 

 c > T^. It will be shown later, however, that the energy 

 transfer appears to depend on small steep wa\'es which 

 cover the surface of larger waves rather than on the large 

 waves themseh-es. Since the celerity of these small 

 waves is low, (F — c) has a large value for them, even 

 when c > V for the predominating large waves. The 

 energy transmitted by normal pressures on small waves 

 provides, therefore, the neces.sary explanation without 

 involving skin friction. 



2.3 Evaluation of the Drag Coefficient C : Wind- 

 Tunnel and Flume Experiments. The drag coefficient 

 L'i has been e^'aluated for difi'erent wa^'e forms by three 

 methods : (a) by wind-tunnel or flume measurements on 

 rigid-wave models, (6) by measuring the water-surface 

 inclination caused by the wind-drag force, and (c) by 

 measuring the velocity gradient of the air flow above 

 waves. 



(a) Measurements of the pressure distribution o\'er 

 the surface of wave models were made in a wind tunnel 

 by Stanton, ^Marshall and Hougton (1932) and by Motz- 

 feld (1937), and in a flume liy Thijsse (1952). Stanton, 

 et al used a wa\'e model with the excessively small length- 

 to-height ratio of 5, therefore only the more realistic 

 models of Motzfeld and Thijsse will be discussed here. 



Motzfeld had four models of waves inserted in the floor 

 of a wind tunnel, and measured the pressure distribution 

 on each model. By integration, he obtained the mean 

 horizontal force and the drag coefficient Ca. He also 

 measured pressures in the air above the model and from 

 these constructed the shapes of streamlines. A high 

 degree of initial tm'bulence was secured by the length 

 of tunnel in front of the model and by the use of A'arious 

 turbulence-stimulating devices at the entrance and m this 

 leading section of the tunnel. Four models were used: 



1 A sinusoidal wave of length/height ratio = 20 



2 A sinusoidal wave of length/height ratio = 10 



