where quantities with subscript r are reference quantities, and D and L are 

 reference length scales in vertical and horizontal directions. Notice that 

 (o.y) have been written into (x,y) for clarity. 



Dimensionless Equations 



Suppressing the asterisk (*) for clarity, the non-dimensional governing 

 equations in the transformed coordinates become: 



Continuity: 



3c ^ 3 3Hu ^ 3Hv ^ u 3a) _ 



. T — T ■ + M - 



3t 



M^ 3X 



3y 



do 



(2.24) 



x-Momentum: 



1 3Hu 

 H 3t 



W«3X 



+ v 



Ro / 



3Huu 3Huv 3Hua ) 

 Py3x ij^3y 3o 



A , £v j^ / 3^\ 

 7 H^^° \'^-) 



Ro 



c 2 



j^ pdc + opj + ^ 



(2.25) 



+ El 



Py3X 



3u 



Wy3X 



Wv^y 



" Py3y 



+ H.O.T. 



y„3x 14^30 \ ^ 3o 



+ B, 



y-Momentum: 



1 3Hv 

 H 3t 



_15_ 



p/y 



Ro 

 H 



3Huv ^ 3Hvv ^ 3HV(D 



p^3x 



My3y 



3a 



iv _3_ 

 / 3o 



£v 

 3o 



33 



