NUMERICAL ANALYSIS 

 The two momentum integral Equations (3a, 3b), together with the entrain- 

 ment Equation (7), can be written completely in the form 



D(W((}),6)) 1^ + B(W((t.,e)) I?- = C(W) 



8£. 



dl. 



(35) 



where the vector W is given by 



W^ = t 



W w 



(36) 



From Equations (50) and (55) in the appendix, the coefficient matrices are 

 defined as follows: 



'11 



'11 



'11 



11 3t 11 9H 



D(W) = (D^^) = 



'21 



'21 



11 9t 

 3h 



11 



11 11 dt 



'21 



11 3H 



3h 



11 



11 3H 



(37a) 



'12 



'12 11 8t 



'12 



11 9H 



;(W) = (B^_.) = 



'22 



'22 11 St 



8h 



22 



22 11 8t 



_f22 

 11 9H 



9h 



22 



11 3H 



(37b) 



19 



