Long Waves in Canals and Standing Waves in Closed Basins 



05r 



209 



-10 



Fig. 89. Distribution of the transverse velocity (upper) and longitudinal velocity (below) 

 in the opposite sens of progress of the wave. The numbers along the curves correspond to 

 the values (a 2 a 2 )l(gh ). (The velocities have been multiplied by the factor (ah)l(gh ) which 



becomes zero at the border.) 



The boundary conditions at the walls of the canal y = ±a are again v = 0. 

 If n is an odd integer (n = 1, 3, 5, ...,) and if we put 



we obtain a complete solution in the form 



la nn ng . nn \ e . 



TIC 2 \ 



4aYv 



(VI. 11 la) 



f I tic 2 \ njx 



nn no . nn 



[ \ C0 *Ta y+ Wr Sm 2a y]C0S{at - 



(VI. 1116) 



The period of the «-nodal free transverse oscillation of the canal is 



12 sidereal hours 



T = 4a/nc, the period of the inertia oscillation T i = Injf = 



sin 99 



and the period of the longitudinal wave in the canal T — 2n/a. Equation 

 (VI. Ilia) then becomes 



! 



y\2 



c'x- 



(VI. 111c) 



14 



