Ai 1-101 37 



sv/ aT •- ax ' ay ' -■ w ^ ax • ay ' ^ w 



^ _A. [ a.,^.. + „. j^v a^u . . _ a^u -] 



ws^ ax'3 ax- ay^ ax'^ay' 9y»3 



- [l + a sin i] sin nsy'. (3) 



Now, since the term (1 + a sin 'r)sin nsy' is of order 

 unity J and since this term represents the v;ind which generates 

 the velocitiesj it is appropriate to choose a dimensionless 

 velocity which will also be of order unity. Hence we select a 

 non-dimensional term containing the velocity which is presumably 

 of order one. The term suggested by an inspection of (3) is 

 pVA^ and v;e therefore put 



Y =M and U = in . 



W W 



V/e shall dr^'p the primes from the x' and y' coordinates 

 and work in the non-dimensional system henceforthi V/ith the 

 definitions, e = A/,3s-^ and & = w/ps equation (3) becomes 



- (1 + a sin T)sin nsy (k) 

 where V^ = av/ax, (V^ - Uy)^ = d^Y/dxdi - d^U/dyd%:. , etc. 



If we non-dimensionalize the momentum equations (3,22) 

 and (3.23) and the continuity equation (3.2^) by means of the 

 above definitions, v/e must introduce a nev; parameter © and a 

 variable H defined by 



q2 3' W 



p s-^ 



* As will be seen later, we shall choose a to be 0»2,- 



