Chta-Shun Yth 
ne (59) 
As before (57) and (59) imply, respectively, 
Cee aO and Pie coe, <phe) e (60) 
VI. SOME SOLUTIONS FOR ARBITRARY WAVE NUMBERS 
If the density stratification is exponential, and if the iner- 
tial effect of density variation is neglected (i.e., if the Boussinesq 
approximation is used), it is possible to obtain solutions in closed 
form for waves in a symmetric triangular channel, whatever the wave 
number may be, provided there is a free surface. 
et 
0 0 : (61) 
where y is measured from the vertex of the triangular channel, and 
let the sides of the channel be given by 
y= _ mx : (62) 
With pp given by (61), (44) becomes 
FA Z 
p # ORE AO ee Big = eg. “Sake (63) 
xX VY. bf 
in which 
Ms (64) 
1412 
