206 Long Waves in Canals and Standing Waves in Closed Basins 



which has as its boundary condition that all transverse motion v disap- 

 pears at its walls, with motion in the .v-direction only. One obtains for 

 the Northern Hemisphere: 



u = (g/c)rj , v = and 7) = Ae- lflc)!y cos(ot — xx) , (VI. 103) 



in which c = \>gh. 



The wave velocity is not influenced by the earth's rotation, but the wave 

 height is not the same everywhere in a cross-section of the canal. The wave- 

 height increases from the side of the canal preceding the rotation to the 

 other side in an exponential function. If on one side it is r) , then on the other 

 side it is 



Voe- 



■iflc)a 



Table 27 shows this influence for two cases. The velocity of the water in 

 the ^-direction of the canal — there are no transverse movements — has 



Table 27. Amplitude across a canal for Kelvin waves 

 (In percent of the amplitude at that side of the canal succeeding rotation) 



always the same phase as the vertical displacement, to which the amplitude 

 is proportional. The wave preferably limits itself, in case of wide canals, 

 to one side of the canal, namely the one which follows the rotation. These 

 Kelvin (1879) waves named after their discoverer, are characterized by great 

 amplitudes on the right-hand side and by small amplitudes on the left-hand 

 side, looking in the direction of travel of the wave. At high water, when the 

 current flows in the direction of progress, the wave crest slopes down from 

 right to left, and the component of gravity acting down that slope is exactly 

 balanced by the deflecting force of the earth's rotation acting in the opposite 

 direction. At low water, the directions of the slope and of the current are 

 reversed. 



The peculiarity that transverse oscillations do not occur with Kelvin waves 

 is only valid in rectangular canals, in which the Coriolis force is balanced 

 at any time by the transverse slope of the surface. If the cross-section of 

 the canal is of a different shape, there will be periodical transverse motions 

 which — as proven by Proudman (1925, p. 465) — are not symmetrical to 



