All-101 Q 



A££en.dix_l . Tr aiisforaa t^qn^^of , the Differential Equations from 

 SjlhexicAl---tq..Rectanjgular Coordinates . 



Consider a rotating spherical coordinate system; let 

 r be the radial distance from the center of the sphere, the 

 colatitude, 9 the meridianal angle. The equations of motion are* 



fi^ - ^^r sin^Q - 2w^ sin Q = - 1 9P _ g. +1 ( ^ . p^ y) ^ 

 Dt p 9r p 



JZ + u|^+l|v+ _JL„™_ IZ + uy. „ w£cot_0 + ^-^2^. g^^ ^^g 

 at 8r r 99 r sin © 89 r r 



- 2wQ cos 9 = - i i 9^ + i(V Ai V) v 



p r 99 p 



aw ^ ^_aw ^ V 9w ^ w .9w ^ vm _ ZK-S.Qi-_® + 2v Q cos 9 

 9t 9r r 99 r sin 9 acp r r 



+ 2uQsin 9 = - 1 — ^4^—^ ^ 4- i(v • A. v)w 



p r sm 9 acp p -^ 



vhere 2^ is the material derivative of the radial velocity in 



terms of sphorical coordinates 



g' denotes the gravitational force 



™ V * A^ V E AV^ + 1 A (A^ ^) and V" denotes the 



Laplacian operator for the two dimensions 9 and 9 . 

 We shall neglect the radial acceleration and shear terms 

 arisinp- as a result of the velocities relative to the rotating 



* We shall not consider the non-linear terras or the viscous 

 terms in the radial equation of motion; hence, this equation 

 is written in operator form only. 



