windspeeds of 3.5 to 9 meters per second (7.3 to 20 miles per hour), the 

 ratio of the water surface speed to the reference windspeed tended to 

 0.033 and was not affected by waves. No effect of fetch could be estab- 

 lished. The speed was inversely proportional to the Reynolds number 

 UH/v, where U is the reference windspeed, H the water depth, and v 

 the kinematic viscosity of the water, when the Reynolds number was less 

 than 30,000. Keulegan used the average velocity in the wind tunnel as 

 his reference velocity. Hidy and Plate (1965), Wu (1968), and other 

 investigators also reported that the ratio between surface speed of the 

 water and reference windspeed is near 0.03 in laboratory experiments. 

 Van Dorn (1953) and others reported similar ratios from observations in 

 natural flows. The close agreement in the ratio between surface water 

 speed and reference windspeed in laboratory and field, without regard to 

 the precise definition of the reference windspeed has not been satisfac- 

 torily explained. 



Keulegan reported that the reference windspeed increased with fetch 

 in his wind tunnel; the relative increase was greater in the presence of 

 waves and seemed to increase with wave height. This result has also 

 been confirmed by later investigators. Keulegan and some later investi- 

 gators attributed this increase in windspeed to a reduction in the cross 

 section of the free airflow with increasing fetch, brought about by the 

 growth of waves and the setup, i.e., the increase in water level at the 

 leeward end of the flume resulting from wind stress. 



It has long been recognized (discussed in Section IV), that an increase 

 in windspeed with fetch results from the decrease in the cross section of 

 the free airflow. Schlichting (1934) was probably the first to explain 

 that this effect results from boundary layer growth and to demonstrate 

 empirically that it is real. These results were later summarized by 

 Schlichting (1968, pp. 176-178) . In explaining the increasing windspeed 

 in wave-wind flumes, Hidy and Plate (1965) recognized that boundary layer 

 growth is a more important factor than any effect of waves or wind setup. 



b. Liang's Experiments . Liang (1972) demonstrated the effect of 

 pressure gradients on wave growth and boundary stress in a laboratory 

 facility. He used a wind tunnel 61 centimeters (24 inches) wide, 50 

 centimeters (19.7 inches) deep, and 11 meters (36 feet) long, A mean 

 water level of 19.37 centijneters (7.6 inches) was used in all experi- 

 ments. The top of the channel consisted of nine movable louvers which 

 could be opened. By allowing some air to leave the tunnel through 

 openings in the roof, it was possible to maintain a nearly constant free- 

 stream velocity and to nearly eliminate the pressure gradient in the 

 direction of airflow. As expected, the rate of wave growth and the 

 boundary stress were reduced by a reduction of the pressure gradient. 

 The bottom boundary layer thickness was less in the presence of a pressure 

 gradient. These results were expected on the basis of the theoretical 

 concepts discussed in Section IV. Liang was not able to maintain perfect 

 control over boundary layer development in this small facility, and the 

 quantitative accuracy of the results may be doubtful. 



35 



