intervals between walls, with the number of antinodes and nodes dependent on 

 the mode of oscillation. 



The water surface in a standing wave has its greatest vertical motion at 

 antinodes. There is no vertical movement at an ideal node, but horizontal 

 velocities reach a maximum there. In terms of amplification factors, this 

 behavior gives large values of .A^^at antinodes and small values around nodes. 

 Contrary to wind waves and swell, small values of A ampl are not necessarily 

 indicative of a tranquil harbor area. 



Phases in a standing wave also behave differently than for typical wind waves 

 and swell. For example, the water surface in the fundamental mode of oscillation 

 in Figure 52 simultaneously reaches a maximum at every point to the left of the 

 node. These points are all in phase. At the same time, every point to the right of 

 the node reaches a minimum value. These points are also in phase with each 

 other but exactly out of phase with the points to the left of the node. Thus phases 

 in a simple standing wave are constant between an antinode and node. They 

 quickly change by 180 deg (or ;r radians) across the node and remain constant up 

 to the next node or boundary. 



Amplification factors for pier areas in the existing harbor are shown as a 

 function of wave frequency in Figure 53. Some frequencies produce a strong 

 resonant amplification, with peak amplification factors between about 2 and 10. 

 Many of the same resonant frequencies appear at all basins, though the strength 

 of amplification can vary considerably between basins. A large peak at very low 

 frequency (0.0007 Hz or 1,500-sec period) shows at every basin and plan. This 

 peak represents the Helmholtz (or grave) mode of oscillation, in which the entire 

 harbor rises and falls in unison. Phase is constant over the whole harbor. This 

 peak also dominates long wave spectra at the array (Figure 20). 



Amplification factor and phase contour plots for the four highest resonant 

 peaks (excluding Helmholtz resonance) show oscillation patterns in the existing 

 harbor. In the amplification factor plots, areas of high amplification are evident 

 as darker shades of gray (Figure 54). Corresponding phase contours are shown 

 in Figure 55. Areas in which phase contours are tightly bunched indicate nodal 

 areas. As would be expected for standing waves, nodal lines in Figure 55 coin- 

 cide with low amplification factors in Figure 54. The phase plots also indicate 

 areas of the harbor which rise and fall together during the resonant condition 

 (same gray shade). Thus the oscillation patterns can be interpreted. 



The 212.77-sec resonant period, peak A, shown in Figure 54 represents a 

 relatively simple rocking oscillation between Piers 1-3, the south end of the 

 harbor, and the boat ramp area A single nodal line runs across the harbor in a 

 generally east- west direction. The 176.99-sec resonance, peak B, is primarily a 

 rocking between Piers 1-3 and the coral stockpile along the west breakwater. 

 The shorter period oscillations are more complex patterns, though they generally 

 indicate a strong nodal area at or near Pier 1 and the seaward end of Pier 2. The 

 peak D resonance is an interesting pattern between the corners of Pier 1 and 

 Pier 2. 



78 



Chapter 6 Harbor Oscillations 



