6^ = 5^(H,0^^,Cg) (16) 



replaces Equation (15a). If a velocity profile is needed, then the velocity 



11 12 



profiles of Coles or Thompson may be used for specified values of the 



momentum thickness 8^^ and shape factor H. Sufficient experimental data 



for three-dimensional boundary layers are not yet available for a similar 



program to be conducted. It does, however, seem that the flow in the 



streamwise direction is sufficiently similar to two-dimensional flow that 



the two-dimensional data can be directly applied to this component of the 



boundary layer flow. However, insufficient data exist for the crossflow to 



make more than a crude estimate of profile shapes. There has not even been 



a sufficiently large collection and analysis of crossflow profiles to make 



a reasonable estimate of the proper parameters [3-] that need to be 



^ j=l,...,m 

 used to approximate the crossflow. Thus, as the simplest first approxi- 

 mation of the crossflow profile shape, it is common practice to assume that 

 (1) the crossflow profile scales on the same length scale 6 as the stream- 

 wise profile and (2) the crossflow profile shape depends on only one or two 

 independent parameters, one of which is the shear stress angle 3. The fact 

 that condition (12) must be satisfied at the wall introduces the angle 3 

 into the description of the crossflow profile and also dictates (as a matter 

 of convenience) the shape assumption in the form 



y , f(A) tan 3 (17a) 



In order to satisfy condition (12) at the wall and the condition that 

 V = at A = 6 (in streamline coordinates) , the function f must satisfy 

 f(0) = 1 and f(6) = 0. 

 proximation that gives 



13 

 f(0) = 1 and f(6) = 0. The assumption by Mager is a popular first ap- 



f(A) = (1- ^) (17b) 



11 



