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
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,
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.