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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