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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