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

1083

momentum flux parameter was also derived for first-

Hrms root-mean-squared wave height for irregular

order solitary wave theory, and a time-series of depth-

wave train

integrated wave momentum flux was estimated for a

Hs

significant wave height for irregular wave train

transient ship-generated wave.

H1/3 average of the highest 1/3 waves in an irregular

It is anticipated that the wave momentum flux

wave train

parameter may prove useful for developing improved

H10% irregular wave height at which 10% of the

semiempirical formulas to describe nearshore pro-

waves are higher

wave number [=2p/L]

cesses and wave/structure interactions such as wave

k

runup, overtopping, reflection, transmission, and armor

L

local wave length

stability. Surf zone processes where waves break as

Lm

wave length associated with mean irregular

plunging or spilling breakers may not benefit from use

wave period Tm

of the wave momentum flux parameter because the

Lo

deepwater wave length

breaking processes effectively negates the advantage of

Lom deepwater wave length associated with mean

characterizing the wave nonlinearity. In these situa-

irregular wave period Tm

tions, use of the new parameter may not improve upon

Lop deepwater wave length associated with peak

existing correlations to wave parameters such as the

spectral period Tp

Iribarren number. However, for nonbreaking condi-

Lp

wave length associated with peak spectral

tions or where wave breaking occurs as surging or

period Tp

collapsing breakers on steep slopes, the wave momen-

mf

instantaneous flux of horizontal momentum

tum flux parameter should, in theory, provide a better

across a unit area

characterization of the wave forcing and lead to better

M

coefficient for solitary wave theory (function of

process response correlations. This remains to be seen.

H/h)

The optimism expressed in this paper regarding the

MF depth-integrated wave momentum flux across a

utility of the new parameter is justified initially by

unit width

reasonable correspondence of between the wave

(MF)max maximum depth-integrated wave

momentum flux parameter and wave runup on smooth,

momentum flux across a unit width

impermeable slopes (Hughes, 2004) and by new

N

coefficient for solitary wave theory (function of

expressions for rubble-mound armor layer stability as

H/h)

functions of the wave momentum flux parameter

pd

instantaneous wave dynamic pressure at a

specified position

PT

total instantaneous wave pressure

dimensionless water depth [=N2h/g]

Notation

r

a

wave amplitude

R

maximum vertical runup from SWL

a1, a2, a3 empirical coefficients

Sxx wave-averaged momentum flux (also known as

A0

radiation stress)

empirical coefficient

t

time

A1

empirical exponent

T

wave period

b1, b2 empirical coefficients

Tp

co

empirical coefficient pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

wave period associated with the spectrum peak

solitary wave celerity gH h

C

Dn50 equivalent cube length of the median armor

Tm

mean wave period in irregular wave train

stone

u

instantaneous horizontal water velocity at a

g

gravitational acceleration

specified position

h

water depth from bottom to the still water level

Vw

representative horizontal velocity near the still

H

uniform steady wave height

water level

Hlimit steepness limit wave height

x

horizontal coordinate positive in the direction

of wave propagation

Hmo zeroth-moment wave height related to the area

z

vertical coordinate directed positive upward

beneath the spectrum

with origin at the SWL

Ho

deepwater uniform wave height

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