as "being related to the effect of tide height. Lamb (l932) has shown 

 that finite-amplitude long waves, whose elevation above Stillwater of 

 depth d is n, will propagate at the velocity 



c = /id [3(1 + n/d)^/^-2] (.38) 



which is in excess of Equation (U) when n is positive. The steepening of 

 the tide wave front is inherently related to the fact that the crest speed 

 (n positive) exceeds the trough speed (n negative). 



The essentially nondispersive nature of the tsunami is verified by 

 the fact that the period between the waves riding the second tide crest 

 is also found to be about 1.75 hours near the mouth of the Columbia River 

 (the same as the leading waves). This period decreases to l.k hours at 

 the Vancouver tide gage '(87 nautical miles from the river mouth), because 

 the second tsunami crest, having advanced through the tide crest, is 

 favored by a greater depth of water and therefore a faster speed relative 

 to the antecedent wave. 



Figures 8l b and c show the crest elevations above tide level of all 

 five tsunami waves and the tide crest elevations above MSL. At the mouth 

 of the Columbia River, Figure 8la shows that the leading tsunami crest is 

 highest and the third crest higher than the second. The beat pattern of 

 the waves for Victoria, Canada, shows this same characteristic (Figure 

 !48d). The relative prominence of the first and second waves, however, 

 reverses three times as they progress up the Columbia River. The crossing 

 points of reversal occur at about 19, ^9 and 79 nautical miles from the 

 mouth, or intervals of exactly 30 nautical miles. The significance of 

 this will be discussed after commenting on the behavior of the tide waves. 



The elevation of the tide crest first declines and then enhances as 

 the tide runs upriver (Figure 8lc ) . A pseudo-resonance effect seems to 

 cause this, and merits further attention. From Figure 80 we surmise that 

 the hydraulic gradient for the Columbia River would place normal river 

 level about 3.5 feet above MSL at 90 nautical mdles from the mouth. Tide 

 elevations relative to normal river level are then obtained from Figure 

 Blc to provide values of n for use in Equation (38) to calculate the mean 

 river depth d. From Figure 8la the gradients of the space-time propagation 

 line for the first tide crest yield values of velocity c, so that Equation 

 (38) can be solved for d. Results are shown in Figure 8ld and indicate 

 that at 65 nautical miles from the mouth, the mean depth (from the tide 

 point of view) is small. The depth profile from the mouth, in fact, is 

 closely parabolic over a length L - 65 nautical miles, with a mouth depth 

 of d-, = 50 feet. The Columbia River, then, acts as a closed-end canal 

 with the closure about 65 nautical miles upriver. 



We now use Equation (7), as for Port Alberni , to calculate the 

 fundamental period of oscillation for this system. The result is 

 startling: 



T-i = 12. lU hours (39) 



125 



