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

A time series of depth-integrated wave momen-

should be possible to perform a similar derivation for

tum flux corresponding to the section of transient

higher order solitary wave theory, but estimates of

wave shown in the box in Fig. 9 was calculated

maximum depth-integrated wave momentum flux

using the local Fourier approximation method

from higher-order theory are not expected to be

described by Sobey (1992). This method is similar

markedly different from results obtained from first-

to the Fourier steady wave approximation method

order solitary theory.

discussed earlier in this paper. The measured trace of

sea surface elevations is subdivided into small

5.2. Nonlinear ship-generated waves

sections, and for each subsection a stream function

represented by a truncated Fourier series is defined.

Applying common periodic wave parameters to

An optimal solution is found within each window

transient waves such as ship-generated waves

that best satisfies the nonlinear free-surface kine-

requires that individual waves in the wave train be

matic and dynamic boundary conditions. Once kine-

identified and treated as uniform waves of perma-

matics are known throughout the water column, the

nent form. For example, Fig. 9 shows a transient

wave momentum flux can be estimated at each point.

ship-generated wave from a laboratory experiment.

One of the highest waves has been defined as the

solutions of specified test cases to existing, less

crest and trough between two successive zero

computationally intensive techniques for estimating

upcrossings of the still water level. The period for

kinematics of extreme waves. A favorable comparison

this wave is the time between the two upcrossings,

was noted for Sobey's (1992) local Fourier approx-

and the wave height is the vertical distance between

imation in the crest region near the sea surface, with

crest and following trough. However, does this

less-favorable correspondence farther down in the

nonlinear ship wave have the same effect on a

water column. Because the maximum wave momen-

coastal structure or on a shoreline as the nonlinear

tum flux is concentrated in the wave crest, the local

regular wave defined by the values of H and T?

Fourier approximation method is appropriate for

Intuitively, we might expect similar effects if the

estimating depth-integrated wave momentum flux

transient and uniform waves had similar values of

for transient wave trains.

the wave momentum flux parameter.

Fig. 7. Nonlinear curve fit to solitary wave N and M functions.

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