with each other but exactly out of phase with the
points to the left of the node. Thus, phases in a
Fundamental Mode
simple standing wave are constant between an
antinode and node. They quickly change by
180 deg (or π radians) across the node and remain
constant up to the next node or boundary.
Node
Antinodes
Alternative harbor sites
Second Mode
Amplification factors for alternative harbor
sites in the Pago Pago Harbor embayment are
shown as a function of wave frequency in
Figure 18. The amplification factor shown at
each frequency and site is the maximum value for
all output points along the length of the site.
Some frequencies produce a strong resonant
Water Surface Positions
amplification, with peak Aamp,l values higher than
Third Mode
10, even exceeding 20 in two cases. Some of the
same resonant frequencies appear at more than
one site, though the strength of amplification can
vary considerably.
Nine of the highest resonant peaks were
selected to illustrate oscillation patterns in the
harbor. These peaks are numbered in Figure 18
for easy reference. In amplification factor plots,
Figure 17. Harbor oscillation
areas of high amplification are evident as orange
definitions
and red colors (Figures 19 through 21).
Corresponding phase contours are shown in
Figures 22-24. Areas in which Aamp,l is near zero and phase contours are tightly
bunched indicate nodal zones. Relatively strong currents would occur across
nodal lines during resonance events. The phase plots also indicate areas of the
harbor which rise and fall together during the resonant condition (areas with the
same color). Thus the oscillation patterns can be interpreted.
The 649.4-sec resonance (Peak 1) is primarily rocking between the inner
Pago Pago Harbor embayment and the outside basin formed between the entrance
and Taema Bank. Amplification factors in the funnel-shaped western end of
Pago Pago Harbor, including the Anua site, become very high. The node for this
oscillation runs from Tulutulu Point to the Anasosopo site.
The 454.6-sec resonance (Peak 2) also produces high amplification factors at
the west end of Pago Pago Harbor. However, the node for this oscillation has
moved further into the embayment to extend from Goat Island Point north near
the Leloaloa site. Another antinode lies in the outer part of the Pago Pago
Harbor embayment, giving rise to high amplification factors in the notch between
Tulutulu Point and Niuloa Point.
30
Chapter 5 Harbor Oscillations
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