ERDC/CHL CHETN-III-70
July 2005
and
Ru2% = vertical runup distance exceeded by 2 percent of wave runups
Hmo = zeroth-moment energy-based significant wave height
ξom = deepwater Iribarren number based on mean period Tm
Lom = deepwater wavelength [= (g/2π) Tm2]
Tm = mean wave period associated with wave spectrum
tan α = structure slope
The mean wave period is used instead of the peak spectral wave period, Tp, in the runup formulas to
accommodate different widths of the wave spectrum. However, in some cases, design wave
conditions are specified in terms of Tp, so it is necessary to give an estimate of Tm. The ratio of Tp /Tm
varies for different spectrum types as follows:
Tp ⎧1.15 - 1.27
for JONSWAP spectra
=⎨
(3)
Tm ⎩1.22 - 1.41
for Pierson - Moskowitz spectra
van der Meer and Stam (1992) gave the range Tp /Tm = ξop /ξom = 1.1 1.2 when they converted
Hunt's runup equation to use an Iribarren number based on peak spectral period, ξop, instead of ξom.
Using the median value in this range of ξop /ξom = 1.15, Equation 2 can be converted to a form that
uses Tp rather than Tm, i.e.,
Ru 2% ⎧0.835 ξop
for 1.15 < ξop < 1.72
⎪
=⎨
(4)
H mo ⎪1.10 (ξop )0.46
for 1.72 < ξop
⎩
where
tan α
ξop =
(5)
H mo
Lop
and Lop is the deepwater wavelength based on peak period, Tp.
Figure 1 presents the original data of van der Meer and Stam (1992) along with additional laboratory
observations reported by Ahrens and Heimbaugh (1988). The observed values of dimensionless
runup (Ru2%/Hmo) were plotted versus Iribarren number based on peak period (ξop) for structure
slopes of 1:2, 1:3, and 1:4. The experiments of van der Meer and Stam were for structures with
relatively deep water at the toe, and the maximum value of relative wave height was about
Hmo/h = 0.25. Ahrens and Heimbaugh's experiments used shallower water depths with the maximum
value of relative wave height of about Hmo/h = 0.64. The solid lines in Figure 1 were plotted using
Equation 4. Generally, the empirical runup equations represent the data well.
2
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