Long Waves in Canals and Standing Waves in Closed Basins 211 



Let us add to the wave (VI. 103) travelling in the +.v-direction a wave 

 progressing in the negative direction in the form 



rj = Ae +(flc)y cos(at+xx) 



(VI. 114) 



We then obtain if A = $, x = 1 and a =f/c = 07, the distribution of 

 amplitudes and phases of the superposed waves as shown in Fig. 90. The 



Fig. 90. Superposition of two Kelvin waves travelling in opposite directions in a canal 

 with a uniform rectangular section. Period: 12 h. Amplitude of each wave: A = \, a = 0-7 

 (corresponding to a canal width of 400 km, 'depth of 40 m and <p = 44-5°). 



assumed values correspond approximately to a canal width of 400 km and 

 a depth of 40 m at 44£° latitude. The period of the wave is assumed to be 12 h. 

 The wave picture has completely lost the nature of a standing wave, as it 

 would be in a system at rest. Instead, the wave is split up in cells which 



14 = 



