The predicted wave heights at two gauge locations inside the basin, normal-
ized by the incident wave height, are compared with predictions from the elliptic
mild-slope model CGWAVE (Demirbilek and Panchang 1998) in Figures 37 and
38. The harbor exhibits a number of distinct periods of oscillation (60 s, 83 s,
110 s, 130 s, 143 s, and 190 s). The Helmholtz or pumping mode of the basin
occurs at a period of around 900 s. Good agreement is generally observed
between wave height amplification factors predicted by both models. It should be
pointed out that it takes longer to attain steady-state conditions in time-domain
models, especially for resonant oscillations. Figure 39 shows a plot of the time
history at Gauge 5 for one of the resonance periods (T = 60 s). Steady-state
conditions are attained approximately 30 wave periods after the waves initially
arrived at the gauge location.
Although linear, frequency-domain models are computationally more effi-
cient at predicting harbor resonance periods and amplification factors, they
cannot predict the magnitude of the long-period wave energy inside a harbor
from a given offshore wind-wave spectrum. To overcome this deficiency,
Okihiro, Guza, and Seymour (1993) used an ad-hoc coupling of a nonlinear
model for the generation of bound long waves outside a harbor with a linear
model for the amplification of long waves inside the harbor. The complex nature
of bathymetry outside Barbers Point Harbor makes it difficult to quantify the
relative amount of long-wave energy outside the harbor that is freely propagating
into the harbor. The entrance channel is much deeper than the surrounding areas.
Free long waves would be generated along the steep side slopes of the entrance
channel as well as reflected from shoreline. The long waves would thus be propa-
gating over a wide range of directions.
We investigated the ability of the Boussinesq model to simultaneously model
the nonlinear generation of long waves by storm waves propagating from deep to
shallow water, the diffraction of both short and long period waves into the harbor
basin, and the resonant amplification of long waves inside a harbor. We initially
considered a bichromatic wave train with component periods T1 = 12 s, T2 =
13.46 s, and heights H1 = H2 = 1.5 m. The group period of 110 s corresponds to
one of the natural periods of oscillation of the basin. Numerical simulations were
carried out with ∆x = ∆y = 10 m and ∆t = 0.2 s. The simulated surface elevation
time-histories at the offshore Gauge 1, harbor entrance Gauge 2, and harbor basin
Gauges 3 and 5 are shown in Figure 40. The long-period component, obtained by
applying a low-pass filter (T > 25 s), is also shown in the figures. It can be seen
that nonlinear interactions during the shoaling process lead to an amplification of
the long-period wave component between the offshore Gauge 1 which is in 50 m
of water, and the harbor entrance Gauge 2 which is 7 m of water. Inside the
harbor basin, the long waves are further amplified and dominate the harbor
response at Gauge 5.
Although bichromatic waves are useful for demonstrating the importance of
nonlinear wave-wave interactions in harbor response, natural sea states are
irregular with wave energy distributed over a large number of frequency com-
ponents. We simulated the response of the harbor to an irregular wave train.
Numerical simulations were carried out for an incident sea state characterized by
a JONSWAP spectrum with Hmo = 3 m, Tp = 12 s and γ = 3.3. Figure 41 shows a
61
Chapter 5 Model Validation
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