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S.A. Hughes / Coastal Engineering 51 (2004) 10671084

parts, but no uniform, clear consensus has been

found.

The wave momentum flux parameter represent-

ing an irregular wave train is probably best

specified by direct substitution of irregular wave

parameters into the empirical Eqs. (20), (21), and

(22) developed using Fourier approximation theory.

Application is simple, and estimates of maximum

wave momentum flux should be reasonably repre-

sentative of the irregular wave train. One drawback

to this method is inconsistency between investigators

regarding which irregular wave parameters to sub-

stitute. One application may use timedomain

statistics H1/3 and Tm, while another might use

frequencydomain parameters Hmo and Tp. Thus, it

is important to specify clearly which irregular wave

representative wave height and period are substi-

tuted. For now, the direct correspondence by

substitution of irregular wave parameters Hmo and

Fig. 6. Goodness-of-fit of nonlinear momentum flux empirical

Tp is recommended for estimating a value of the

equation (Fourier wave theory).

wave momentum flux parameter representative of

irregular waves.

or slightly above the limiting relative wave height

for waves on a horizontal seabed. This problem

was likely the result of forcing the numerical

5. Maximum wave momentum flux--transient

computation beyond appropriate limits. The maxi-

waves

mum underprediction and overprediction of the

empirical curve-fit were 0.105 and 0.089, respec-

Because the maximum, depth-integrated wave

tively. The overall root-mean-squared error of the

momentum flux can be determined for any wave

curve-fit was 0.023.

form in which the kinematics are known, it is

The empirical equation represented by Eq. (20),

possible to estimate the wave momentum flux

along with Eqs. (21) and (22), provides an easy

parameter for nonperiodic waves. This may prove

method for estimating the wave momentum flux

useful for comparing coastal process responses for

parameter for finite-amplitude, steady regular waves.

different wave types.

This empirical formulation is recommended over

those provided by linear and extended linear theory

5.1. Solitary wave theory

because it better represents the momentum flux in the

wave crest which is expected to be critical for most

The maximum depth-integrated wave momentum

applications to coastal structures.

flux of a solitary wave occurs at the crest where

both the horizontal velocity and dynamic pressure

4.4. Application to irregular waves

are greatest. To first-order of approximation, the

horizontal velocity at the crest as a function of

Most coastal structure design guidance developed

elevation zs above the bottom can be approximated

in the past 2025 years use wave parameters

as (e.g., Wiegel, 1964)

representative of unidirectional irregular wave trains

or, in rarer cases, directionally spread irregular

CN

waves. Attempts have been made to relate the

umaxzs

23

1 cosMhzs Š

irregular wave parameters to regular wave counter-

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