1082

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

Fig. 10. Ship-generated wave sea surface (upper) and MF (lower) time series.

to nearshore coastal processes on beaches and at

An alternative estimate of maximum depth-inte-

coastal structures. The wave momentum flux param-

grated wave momentum flux for the individual wave

eter has units of force per unit crest width, and it better

defined by zero-upcrossings in Fig. 10 was calculated

characterizes the flow kinematics at a given depth

using Eqs. (20), (21), and (22) which are intended for

than other wave parameters that do not distinguish

regular steady waves. The wave parameters were

increased wave nonlinearity. The wave momentum

originally given in English units as H=0.78 ft, T=1.38

flux parameter can be defined for regular, irregular,

s, and h=9 ft. A somewhat favorable comparison to

and nonperiodic (transient) waves such as ship-

the local Fourier approximation was found. . .

generated wakes and solitary waves. Thus, if a

&

55:1 lb=f t

local approx:

nearshore process can be successfully related to the

MFmax

wave momentum flux parameter, it may be possible to

Eq: 20

48:7 lb=f t

describe the same process being forced by different

or

wave types with a similar formulation. This hypoth-

&

0:0106 local approx:

MF

esis is presently unproven.

qgh2

0:0094 Eq: 20

31

The wave momentum flux parameter was derived

max

for linear and extended linear wave theory; however,

the results do not accurately estimate the maximum

Although this is only one comparison, it may

wave momentum flux in steep, nonsinusoidal waves

indicate that treating transient wave trains as a

which are likely to be more influential for coastal

succession of uniform waves might be reasonable

process response. Fourier approximation wave theory

for those processes thought to be related to wave

for regular steady waves over a horizontal bottom was

momentum flux.

used to develop an easily applied empirical expression

giving nondimensional maximum depth-integrated

wave momentum flux as a function of relative wave

6. Summary and conclusions

height and relative water depth. For irregular wave

trains, it is recommended that H and T in the empirical

A new parameter representing the maximum depth-

formation be replaced with frequencydomain irreg-

integrated wave momentum flux occurring in a wave

ular wave parameters H mo and T p. The wave

is proposed for characterizing the wave contribution

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