Internal Waves tn Channels of Vartable Depth 
dpy 
eat he es (28) 
Then the linearized equations of motion are 
3 ) 3 
Po oy (uv w) = laces Oy’ SPA: - gp, 0) , (2.9) 
where p is the pressure perturbation. The linearized equation of in- 
compressibility is 
=—— + wee =4 O =, (30) 
with the accent indicating differentiation with respect to y. The equa- 
tion of continuity is 
Oe: ORNs 
ge: a are (31) 
du 
he! 
Cross differentiation of the first and third equation in (29) 
gives 
(Sse Parse) ees (32) 
Since dependent variables will all be assumed to have the time factor 
Baler. (32) gives 
from which we have 
1405 
