(j)

Kitaigorodoskii et al. (1975) obtained the form of depth dependence as

M*k*

Mω

Φ(ω, *d*) '

s

(II-1-159)

M*k*

Mω

(k) Thus, *Φ *is a *weighing factor *of the quantity in the bracket, which is determined from the ratio of

the quantity evaluated for finite and infinite water depth cases. Using the linear wave theory, the above

equation has been approximated by Kitaigorodoskii et. al. (1975) as

1 2

ω

2

Φ(ω,*d*) .

(II-1-160)

1

(2 & ω)2

1&

2

(l) The *TMA *spectrum was intended for wave hindcasting and forecasting in water of finite depth. This

spectrum is a modification of the *JONSWAP *spectrum simply by substituting Kitaigorodoskii's expression

for effects of the finite depth equilibrium function. By using the linear wave theory, we find the following

complete form of the *TMA *spectrum:

1

(II-1-161)

Φ(ω(,*d*) '

ω( ' ω

;

1%

sinh *K*

;

(m) In effect, this substitution transforms the decay or slope of the spectral density function of the

approximated by linear wave theory. Bouws et. al (1984) present equations for α, γ, and σ. As with the

JONSWAP, the equation may be iteratively fit to an observed spectrum and α, γ, fm , and σ may be estimated.

(n) The *PM*, *JONSWAP*, and *TMA *spectra can be estimated if something about the wind, depth and fetch

are known. Furthermore, these spectral equations can be used as target spectra whose parameters can be

varied to fit observed spectra which may have been measured. In the first situation, the value of the

parameterization is in making an educated guess at what the spectrum may have looked like. The value in

the second case is for ease of analytical representation. However, very often today engineering analyses are

made on the basis of numerical simulations of a specific event by use of a numerical model (see Part II-2).

In this case, the model estimates the spectrum and a parametric form is not required.

II-1-92

Water Wave Mechanics

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