coordinates, respectively; 0,,, Qo-i » ^ioj ^oo' '^i ' ^'^'^ '^9 ^^^ momentum and 



displacement thicknesses defined, respectively, by Equations (4a, 4f); and 



C, and C_ are wall skin friction coefficient components in the (J) and 6 



(J) 6 

 directions, respectively. The usual turbulent boundary layer assumptions 



of the neglect of turbulent normal stresses and the neglect of mean dif- 

 fusion in directions parallel to the hull surface are incorporated in 

 Equations (3a, 3b). 



The momentum and displacement thicknesses are defined by 



6 = ^ (U -u)dX (4a) 



u 



■IJ 



^12= "T V"^"" ^'"^ 



6 





^21= \ ^ (U^-v)dX (4c) 



~0 





®22 = ^ (Ug-v)dA (4d) 



U, - u 

 



A, = -^^^ dX (4e) 



= 1 V 



A^ = I ,, dX • (4f) 



where u and v are the components of the mean boundary layer velocity in the 

 4) and 6 directions, respectively. 



