Internal Waves tn Channels of Vartable Depth 
and x measured across the channel. If the velocity components in 
the directions of increasing x, y and z are denoted by u, vandw, 
respectively, we have 
vie esse6r otv o= ics w= : (1) 
The equation of continuity then becomes 
5% F 32 : 34 
Sat ee 
which is the equation to be solved. 
At solid boundaries the normal velocity component vanishes, 
so that 
ag 
on 
Suen (3) 
where n is measured in a direction normal to the solid boundaries. 
At the free surface the pressure is constant, so that, with the square 
of the velocity neglected and with 7 denoting the displacement of the 
water surface from its equilibrium position, the Bernoulli equation is 
ag 
a + gn = constant, (4) 
in which t is the time. Since 
1S HOG 
Vv = A 
(4) can be written as 
1699 
