EM 1110-2-1100 (Part II)
31 July 2003
1
1
R
π
' (2 π) 2
4
(II-4-27)
Ho
2β
based on criteria developed by Miche (1951) and Keller (1961) (Walton et al. 1989).
b. Irregular waves.
(1) Irregular wave runup has also been found to be a function of the surf similarity parameter (Holman
and Sallenger 1985, Mase 1989, Nielsen and Hanslow 1991), but differs from regular wave runup due to the
interaction between individual runup bores. Uprush may be halted by a large backrush from the previous
wave or uprush may be overtaken by a subsequent large bore. The ratio of the number of runup crests to the
number of incident waves increases with increased surf similarity parameter (ratios range from 0.2 to 1.0 for
ξo of 0.15 to 3.0) (Mase 1989, Holman 1986). Thus, low-frequency (infragravity) energy dominates runup
for low values of ξo. See Section II-4-5 for a discussion of infragravity waves.
(2) Mase (1989) presents predictive equations for irregular runup on plane, impermeable beaches (slopes
1/5 to 1/30) based on laboratory data. Mase's expressions for the maximum runup (Rmax), the runup exceeded
highest 1/3 of the runups (R1/3), and the mean runup ( & ) are given by
by 2 percent of the runup crests (R2%), the average of the highest 1/10 of the runups (R1/10), the average of the
R
Rmax
' 2.32 ξo0.77
(II-4-28)
Ho
R2%
' 1.86 ξo0.71
(II-4-29)
Ho
R1/10
' 1.70 ξo0.71
(II-4-30)
Ho
R1/3
' 1.38 ξo0.70
(II-4-31)
Ho
R
' 0.88 ξo0.69
(II-4-32)
Ho
for 1/30 # tan β # 1/5 and Ho/Lo $ 0.007, where Ho is the significant deepwater wave height and ξo is
calculated from the deepwater significant wave height and length. The appropriate slope for natural beaches
is the slope of the beach face (Holman 1986, Mase 1989). Wave setup is included in Equations II-4-28
through II-4-32. The effects of tide and wind setup must be calculated independently. Walton (1992)
extended Mase's (1989) analysis to predict runup statistics for any percent exceedence under the assumption
that runup follows the Rayleigh probability distribution.
(3) Field measurements of runup (Holman 1986, Nielsen and Hanslow 1991) are consistently lower than
predictions by Equations II-4-28 through II-4-32. Equation II-4-29 overpredicts the best fit to R2% by a factor
of two for Holman's data (with the slope defined as the beach face slope), but is roughly an upper envelope
of the data scatter. Differences between laboratory and field results (porosity, permeability, nonuniform
slope, wave reformation across bar-trough bathymetry, wave directionality) have not been quantified. Mase
(1989) found that wave groupiness (see Part II-1 for a discussion of wave groups) had little impact on runup
for gentle slopes.
II-4-18
Surf Zone Hydrodynamics
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