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 *T*1 = 12 s, *T*2 =

13.46 s, and heights *H*1 = *H*2 = 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 *H*mo = 3 m, *T*p = 12 s and γ = 3.3. Figure 41 shows a

61

Chapter 5 Model Validation

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