The directional spreading function, *D*(θ)*, *describes the directional distribution

of wave energy in irregular multidirectional sea states. It can be quantified in

terms of the principal direction of wave propagation θp, and the directional spread

or standard deviation of the spreading function, σθ, which is defined as:

θp +π/ 2

∫

σθ

=

2

(C1)

θp -π/ 2

A number of parametric shapes have been proposed to describe the directional

spreading function including the cosine-power, the circular normal, and wrapped-

normal distributions. These are described in the following paragraphs.

The cosine-power function is an extended version of the cosine-squared direc-

written as*:*

Γ(*s *+ 1)

cos2*s *(θ - θ p )

for | θ - θ p | < π / 2

(C2)

π Γ(*s *+ 1/ 2)

where Γ is the gamma function. The parameter s is an index describing the degree

of directional spreading with s → ∞ representing a unidirectional wave field.

The circular normal distribution was proposed by Borgman (1969) and can be

written as:

1

References cited in this appendix are listed in the References at the end of the main text.

C1

Appendix C Directional Wave Spreading Functions

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