of 6 near 100 meters. If the rate of boundary layer growth over water 

 shown by Wade and Debrule persists, the boundary layer thickness would 

 grow to 100 meters in a fetch of about 3 kilometers. If the air is stably 

 stratified, as it generally is, boundary layer growth will be somewhat 

 slower. 



Turbulent boundary layers are developed along the sides and ceiling 

 of the laboratory wind tunnel as specified by equation (12) as well as 

 above the air-water interface. The air-water interface is generally 

 rough; the roughness may increase with distance from the intake because 

 of wave growth. Therefore, the resulting boundary layer is thicker, 

 by an unknown amount, than indicated by equation (12). The transport 

 of air through the wind tunnel must be independent of distance from the 

 entrance. If the cross section available for airflow is also constant 

 for the length of the tank, the boundary layer growth will result in a 

 continually decreasing cross section for the flow outside the boundary 

 layer. The process is fairly well understood for laminar boundary 

 (Schlichting, 1968, pp. 176-178). The convergence of the flow results 

 in acceleration of the core flow with distance from the entrance. In 

 agreement with Bernoulli's equation, the accelerating flow is associated 

 with a decreasing pressure. This pressure gradient adds another con- 

 tribution to the pressure differential between the backface and front 

 face of each wave, and contributes to the growth of waves in the lab- 

 oratory. 



Bole (1973) discussed the importance of this pressure gradient on 

 wave growth. Harris (1975) and Bole (1976) continued the discussion. 

 Neglecting the stream-wise pressure gradient which results from boundary 

 layer growth may introduce errors in all quantitative measurements of 

 wave growth mechanisms in laboratory facilities. 



Turbulent flow with a pressure gradient is not as well understood 

 as laminar flow-, and the effects of pressure increases in the direction 

 of flow have been studied more thoroughly than the effects of pressure 

 drops (Schlichting, 1968, ch. 22). Nevertheless, a few important prin- 

 ciples have been established. The boundary layers for accelerating flow 

 are thinner than those for a zero-pressure gradient. It appears that 

 this thinner boundary layer would lead to an increase in the boundary 

 shear for a given mean speed of the airstream and a departure from the 

 logarithmic velocity profile described by equation (9), but the available 

 evidence is not clear. This possible departure of the velocity profile 

 from equation (9) is important in wind-wave laboratory studies, because 

 equation (9) is usually employed to evaluate the boundary shear and to 

 relate laboratory and field velocity measurements. 



The boundary layer growth can be accommodated with acceleration of the 

 core flow by expanding the cross section of the flow just enough to per- 

 mit constant mass flux with a constant current speed in the nonturbulent 

 region near the center of the wind tunnel. Expanding cross sections 

 through adjustable ceiling heights are used in the micrometeoro logical 

 wind tunnels at Colorado State University (Plate and Cermak, 1963) to 



28 



