The directional spectrum is calculated as follows (Vincent and Briggs 1989),

( jσm )2 cos *j θ *-

1 j

1

D(θ) =

(

+ ∑ exp-

2*π π *j =1

2

where θm = mean wave direction = 0

= number of terms in the series (20 in numerical calculations)

σm = spreading parameter

The same functions E(f) and D(θ) were also used in the laboratory study by

Vincent and Briggs (1989) to construct a number of frequency and directional spectra (for

details, see Vincent and Briggs 1989 or Panchang et al*. *1990). One spectral case, B1,

consisted of a broad frequency spectrum; the other case, N1, had a narrow frequency

spectrum. The input data are summarized in Table 2. Two monochromatic and two

spectral cases are shown. The incident wave height is 2[2E(*f*)D(θ)∆*f*∆θ]1/2.

Table 2. Model Input Data

α

γ

σm

Input

Case ID

Period

Significant

(sec)

Wave

Height (m)

Monochromatic

M1

1.3

.0550

--

--

--

M2

1.3

.0254

--

--

--

30

Broad-directional

B1

1.3

.0775

.01440

2

10

Narrow-directional

N1

1.3

.0775

.01440

2

The discretization of the directional spectrum is summarized in Table 3. Other

researchers have used the following discretizations.

Panchang et al*. *(1990) used a

directional bin width (∆θ) of 4.39in a range from 45to +45 resulting in 39 directional

,

components for all spectra. Zhao and Anastasiou (1993) found that as many as 63

components were needed for the B1 and N1 cases. Li et al. (1993) produced results that

suggest that an adequate solution can be obtained with as few as five directional

components and five frequency components. In light of the results of Li et al. (1993), it

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