Mason and Keulegan (1944) investigated waves passing into a shallower 

 water depth, with an abrupt change in depth. The condition for instabil- 

 ity obtained from their experiments was 



(a^) 1 ' 2 > 2d 2 (178) 



where aj is the wave amplitude in the deeper water, Lj the wavelength 

 in the deeper water, and d 2 the depth in the shallower water. Their 

 results were confirmed by Horikawa and Wiegel (1959), although in the 

 latter report there is an apparent discrepancy in the presentation of the 

 results; the right side of equation (178) has been multiplied by /I. 



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EXAMPLE PROBLEM 8************* 



GIVEN : A tsunami with a period of 15 minutes passes from water 3,000 

 meters deep onto a shelf where the water depth is 200 meters (656 feet) 



FIND : The maximum wave amplitude for a stable wave which will not 

 decompose into a train of waves. 



SOLUTION : The wave celerity in deep water is 



Cj = /gd 2 = /9.807 x 3,000 = 171.5 meters per second 

 and the wavelength is 



Lj = C : T = 171.5 x 15 x 60 = 154,350 meters (95.9 miles) 

 The condition for wave instability is given by equation (178) as 

 (a^) 1 ' 2 > 2d 2 



(a } x 154,350) 1/2 > 2 x 200 



a 1 > 1.04 meters (3.40 feet) 



Thus, waves with a deepwater amplitude less than 1.04 meters would not 

 decompose. 



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EXAMPLE PROBLEM 9************** 



GIVEN : A tsunami travels from a 3,000-meter water depth into a 200-meter 

 water depth. The wave period is 60 minutes. 



FIND : The maximum wave amplitude for a stable wave which will not decom- 

 pose into a train of waves. 



SOLUTION : The deepwater wave celerity is given as 



Cj = (gd x ) 1/2 = (9.807 x 3,000) 1/2 = 171.5 meters per second 



