ERDC/CHL CHETN-III-67
September 2003
Wave Momentum Flux Parameter
for Coastal Structure Design
by Steven A. Hughes
provides information about a new wave parameter for characterizing wave processes at coastal
structures. A description of the parameter is given along with sample calculations for periodic waves
and solitary waves. The first application of this physically relevant parameter has been development
of new empirical relationships for irregular wave runup on smooth, impermeable slopes described in
CHETN-III-68 (Hughes 2003).
COMMON WAVE PARAMETERS: Coastal engineers have established useful design guidance
by augmenting theoretical reasoning with empirical coefficients determined from small-scale
laboratory testing. Waves are usually included in empirical design relationships via one or more
wave parameters considered to be representative of the incident wave condition. Common regular
and irregular wave parameters are listed in Table 1.
Table 1
Common Wave and Fluid Parameters
Regular Wave Parameters
H = wave height
Ho = deepwater wave height
L = local wavelength
Lo = deepwater wavelength
T = wave period
k = wave number [= 2π/L]
Irregular Wave Parameters
Hmo
=
zeroth-moment wave height
Hs =
significant wave height [= H1/3]
Hrms
=
root-mean-squared wave height
H10% =
10% of waves are higher
Tp
=
spectral peak wave period
Tm =
mean wave period
Lp
=
wavelength associated with Tp
Lop =
deepwater wavelength associated with Tp
Lm
=
wavelength associated with Tm
Lom =
deepwater wavelength associated with Tm
Fluid and Other Parameters
ρ = fluid density
= coefficient of dynamic viscosity
ν = coefficient of kinematic viscosity
h = water depth
α = beach or structure slope
Sometimes, these wave parameters are combined to form dimensionless variables that may include
relevant fluid and other parameters such as those given in Table 1. The more common dimensionless
wave parameters that have appeared in coastal structure design guidance are shown in Table 2. Note
that relative wave height H/h is the only parameter that does not contain wave period or wavelength.
Hence, H/h is the only parameter listed that is applicable to solitary waves.
The dimensionless wave parameters listed in Table 2 strictly pertain to uniform, periodic waves of
permanent form (i.e., regular waves); and it is customary to use first-order wave theory to calculate
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