S.A. Hughes / Coastal Engineering 51 (2004) 10671084
1071
applied the new wave parameter to formulate equa-
stability tests could be reduced with a more physically
tions for rock armor stability of rubble-mound coastal
relevant parameter that better represents the wave
structures.
forcing.
This paper describes development of a new wave
parameter to represent the influence of nearshore
waves in correlations between wave forcing and
4. Maximum wave momentum flux--periodic
corresponding coastal processes. It is anticipated that
waves
this new wave descriptor will prove useful to depict
All wave theories are based on varying simplifica-
processes that occur when waves impinge on coastal
tions of the continuity and momentum equations, so it
structures. The new wave parameter ideally will
seems reasonable that a parameter representing the
satisfy the following criteria:
rate of change of wave momentum would be a good
candidate for use in coastal structure design and for
(1)
The parameter must be physically relevant so it
estimation of nearshore processes. Longuet-Higgins
can be incorporated into simple descriptive
and Stewart (1964) noted the relevance of wave
models of specific physical processes.
momentum flux. . .
(2) The parameter should apply to both periodic
waves and transient waves such as ship wakes
bSurface waves possess momentum which is directed
and solitary waves with the hope that results
parallel to the direction of propagation and is propor-
from one wave type might be applicable for the
tional to the square of the wave amplitude. Now if a
other type.
wave train is reflected from an obstacle, its momen-
(3) The parameter should span the range of relative
tum must be reversed. Conservation of momentum
depths from deep water to shallow water.
then requires that there be a force exerted on the
(4) The parameter should provide a better
obstacle, equal to the rate of change of wave
representation of nonbreaking and nonlinear
momentum. This force is a manifestation of the
wave processes than existing simple wave
radiation stress.Q
parameters.
Thus, wave momentum flux is the property of
(5) The parameter should provide comparable
progressive waves most closely related to force
results to established parameters such as the
loads on coastal structures or any other solid object
Iribarren number when used to predict processes
placed in the wave field. For this reason, wave
stemming from plunging and spilling wave
momentum flux is a compelling wave property for
breaking.
characterizing waves in the nearshore region, and
(6) The parameter should be easy to estimate so
potentially, for relating waves to the response of
design guidance using the parameter can be
coastal structures due to wave loading or to other
programmed into computer spreadsheets or
coastal processes.
simple programs.
The relevance of wave momentum flux to wave
runup on a beach was noted by Archetti and
The following sections introduce a new parameter
Brocchini (2002). They showed a strong correlation
based on maximum wave momentum flux, and the
between the time series of wave runup and the time
parameter is developed for linear waves, nonlinear
series of depth-integrated mass flux within the
(Fourier approximation) waves, and solitary waves.
swash zone. They also noted that the local depth-
The parameter is also estimated for a ship-generated
integrated momentum flux was balanced mainly by
wave, and use with irregular wave trains is discussed.
the weight of water in the swash zone which was
No practical applications are given in this paper; but a
approximated as a triangular wedge. Their observa-
companion paper (Hughes, 2004) demonstrates the
tion suggests that maximum wave runup on an
utility of the proposed wave parameter by develop-
impermeable slope might be directly proportional to
ment of new empirical equations for runup of regular,
the maximum depth-integrated wave momentum
irregular, and solitary waves on smooth, impermeable
flux.
plane slopes. In addition, Melby and Hughes (2003)
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