Bvennen and Whitney 



and i is the a difference between the walls AD and BC. In 

 Figs, 5 and 6, 7 and 8, 9 and 10 the numerical and linearized free 

 surface shapes are compared for three cases of increasing wave 

 amplitude. As the amplitude increases the similarity between the 

 two diverges; both the wave velocity and the build up on the wall 

 become progressively greater In the numerical solution. Note also 

 that, especially In Fig, 10, the peak of the wave Is much sharper than 

 In the linearized solution. For amplitudes less than that of Figs, 5 

 and 6 the results were almost Identical, 



C, Example Two, Figs. 4(b), 11, and 12 



The second example. Fig, 4(b), Introduces moving and curved 

 solid boundaries; the liquid Is disturbed from rest by a bed uplift of 

 the forna: 



For XI < X < X2, Y^^= M sin [-^J sin^ [x2- Xl) 



l , 2[- Tr(X-Xl)1 ^ f. 

 ■\ ^^^ L (X2-Xi)J ^°^ ^ 



< t < T 



= M sin 



2rTr(X- XI) 



L(X2- XI) . 



for t > T 



For X<X1,X>X2, Y.^ = 



all t 



Within certain extreme limits on M and T this causes a surface 

 wave Immediately above the bed disturbance which then spreads out 

 to each side and Is followed by a depression wave over the bed uplift. 

 The linearized solution is 



Z-c = »^.i2i2jJiL).A(t) + y R, [ltanh{^)A(t) cos(ip) 



k=l 



where 



+ B,(t) sln(^)] 



(32) 



\= [-jptanh^ 

 A(K) = 2 sln^ Y- ^°^ < t < T, =2 for t > T 



B.(t) = 0-, cos V. t + 1 - (1 + 0-,) cos -^ for < t < T 



= 2+0- (cos V t + cos v^(t - T) for t > T 



k k K 



138 



