^= Yf [(di/T2)/s2] (36) 



which expresses the runup n in terms of the initial wave height H. 



Values of y ^'^^ available from various wave theories and are sum- 

 marized in Figure 75, revised from Wilson, et al (1962), while the value 

 of the function f is given by 



f - I/Jq (2X^/^1^/2) (3^) 



in which Jq is the zero-order Bessel function of the variable (2K^ L ' ). 

 The relationship in Equation (36) has been calculated, and is plotted in 

 Figure T6. Results all lie within the shaded band which exhibits the 

 first, second and third modes of this form of shelf resonance. Because 

 of friction (not allowed for in the simple theory), the cusps of Figure 

 76 could expect to be severely flattened, so that the runup, as a ratio 

 of wave height at the toe of the slope, may perhaps seldom exceed a value 

 of about k. 



Some data of Granthem (l953), the only experimental work on moder- 

 ately long wave runup that provides the information needed for plotting 

 in Figure 76, are included in the figure. They show some degree of accord 

 without, however, exhibiting any evidence of runup becoming especially 

 enhanced at the predicted critical mode values of (d/T )/s . There is, 

 however, an escalation of runup values in the range of (d/T'^^)/s between 

 0.02 and 2.0, in keeping with the prediction, if the damping at the 

 critical modes were severe enough to erase the cusps entirely, as well 

 as the higher mode effects shown in Figure 76. 



The subject of runup of waves on coasts is in itself so involved, 

 and the literature so extensive, that we hesitate to penetrate more 

 deeply into the question at this time. Appendix C gives merely a brief 

 review of some aspects of the problem. We may use Figure 76 to answer 

 a general question as to what runup would be caused by waves of the 

 Alaskan tsunami approaching normally on a uniformly sloping Continental 

 Shelf. Taking T == 2 hours, di^ = 6OO feet and s = 0.01, we find 

 (d-|/T2)/s2 ==0.12 feet/second2 and from Figure 76, n^/H = 0.6 to 1.2. 

 On a flatter slope s = 1/200, (d-i_/T2)/s2 = 0.5 feet/second2 and the 

 range of runup lies between Hp/H - 1.1 to 2.2. Adopting n^^/H^ = 0.5 

 and a value of n-^/E - 0.75 we obtain H^^/H - 1.5, the value used in 

 Table III. 



8. Sub-Harmonic Effects of the Alaskan Tsunami 



The subjective analyses of Figures U3 to 66 have disclosed 

 at some places low-amplitude waves of much longer period than the main 

 tsunami waves. In Table III, these are listed as secondary waves, be- 

 cause it is not known whether they represent a wave system that propa- 

 gated from the source, or whether they are locally generated through 

 some nonlinear mechanism of the coastal boundary. 



The effects are particularly strong at some of the most distant 

 places like Lyttelton, New Zealand (Figure 60c ) , Poronaysk, Sakhalin 



115 



