However, the slight truncation of the vertex of the triangle by land 

 (Figure T2b), reduces these periods by the factor 0.92, to 



T;j_ = 19.2, T2 = 10. i+, T3 = 7.2, and T^^ = 5-^ minutes (30) 



Further, assuming partial truncation of the bay due to the breakwater of 

 Hilo Harbor (Figures 72 a and b), the fundamental period T^ is reduced 

 (cf. Keulegan, I962) to 



Tj = 1U.5 minutes (3l) 



For each of the modes of oscillation a node occurs across the mouth 

 of the bay and the niimber of nodes is represented by the integer n\ 

 (Figures 72 c and d). Thus for the second mode oscillation (T2 = 10. U 

 minutes) there are two nodes, one located at 0.293L or 8200 feet from the 

 head of the bay, almost exactly at the position of Hilo Harbor breakwater. 



From our subjective analysis of the Hilo marigram (Figure 59) it 

 appears that there was immediate development of an oscillation 13 feet 

 high of about 20 minutes period which drained energy from the main 

 tsunami (Table III). The fifth harmonic of the main tsunami period of 

 1.8 hours is 21.6 minutes, so that the natural tendency for the tsunami 

 to develop odd harmonics through its convergence in Hilo Bay apparently 

 found a sympathetic response from the fundamental eigenperiod for the 

 bay. The enormous wave of 20-minute period was clearly a resonance 

 effect. The effect, however, was rapidly broken by interference from 

 other oscillations of about 15 minutes and 30 minutes period (Table III), 

 the shorter oscillation probably associated with the truncation effect 

 of the breakwater (Equation tSl)). 



For a more exacting examination of the responses we refer to the 

 wave energy spectra of Figure 67a. In the first 8 hours, the tsunami 

 apparently excited pseudo-resonant responses from all four of the modes 

 suggested by Equation (30). However, it drew a large response from a 

 33-minute oscillation (which is close to being the third harmonic of the 

 fundamental tsunami period). A free oscillation of this period must 

 represent the coupled bay-shelf oscillation for that area, for it is 

 noted from Figure 72a that the insular shelf has a peculiar convex shape 

 that would help to trap energy between the continental slope and the 

 bay-head. The spectra of Figure 67a show that the peak at 33 minutes 

 tends to become dominant with time as the other oscillations damp out. 



Hilo Bay then appears peculiarly attuned to resonance effects from 

 great tsunamis. Since we conclude from Figure 71 that a great earth- 

 quake of magnitude M = 8.5 always will tend to develop a tsunami of 

 period approximating 1.8 hours, Hilo will always respond in the same 

 way, regardless of the origin of the earthquake. Differences, of course, 

 would be expected on the basis of direction. The lesser effects experi- 

 enced at Hilo from the Alaskan tsunami, as compared with the Chilean 

 tsunami of May, I96O, or the Aleutian tsunami of April, 19^6, are 



108 



