only when averages are taken for large areas or longtime intervals. The 

 details of the process must be accurately scaled if model studies are to 

 be of much value in improving quantitative predictions of prototype 

 phenomena. 



IV. MODELING THE GROWTH OF WIND-GENERATED WAVES IN A WIND TUNNEL 



Several difficulties face any program for modeling the momentum 

 exchange between the atmosphere and the sea in a laboratory facility. 

 These may be grouped by: (a) The growth of boundary layers along the 

 walls, ceiling, and floor of the facility; (b) the limited fetch length 

 obtainable in the laboratory; and (c) the necessity of dealing simul- 

 taneously with several scales of motion. 



Each group of problems is described below in the light of present 

 knowledge. Their importance in modeling the momentum exchange processes 

 is demonstrated in Section V by reviewing a few reports illustrating 

 the basic principles. It is found that some carefully conducted, well- 

 documented experiments have led to significant qualitative discoveries 

 about the momentum exchange processes without adequate consideration of 

 the difficulties enumerated above. It seems unlikely, however, that 

 quantitatively accurate extrapolation to prototype scales can be achieved 

 without attaining dynamic and geometric similitude of the flow at all 

 important scales. 



1. Boundary Layer Growth in the Laboratory . 



In a laboratory facility the average thickness of the boundary layer 

 is readily shown to be a function of fetch. The equations governing the 

 formation of a steady-state viscous boundary layer on a flat plate, without 

 pressure gradients were first solved by Blasius (1910) . Schlichting 

 (1968, ch. 7) presented a review of this solution and many extensions. 

 If the thickness of the boundary layer is defined as the value of z for 

 which u = 0.99 of the free-stream velocity, u^^, 



6 = 5.0 (V x/u»)^ , (11) 



where x is the fetch length, and v is the kinematic viscosity of the 

 fluid. 



Two other definitions of the boundary layer thickness, useful in lab- 

 oratory studies, are the displacement thickness, 6j, and the momentum 

 thickness, 6^. The displacement thickness is defined as that distance 

 by which the external potential velocity field is displaced outward 

 because of the decrease in velocity in the boundary layer. That is: 



■/... 



(1-u/uoo) dz . (12) 



26 



