1

1

π

' (2 π) 2

4

(II-4-27)

2β

based on criteria developed by Miche (1951) and Keller (1961) (Walton et al. 1989).

(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

for low values of *ξ*o. 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 (*R*max), the runup exceeded

highest 1/3 of the runups (*R*1/3), and the mean runup ( & ) are given by

by 2 percent of the runup crests (*R*2%), the average of the highest 1/10 of the runups (*R*1/10), the average of the

' 2.32 ξo0.77

(II-4-28)

' 1.86 ξo0.71

(II-4-29)

' 1.70 ξo0.71

(II-4-30)

' 1.38 ξo0.70

(II-4-31)

' 0.88 ξo0.69

(II-4-32)

for 1/30 # tan *β *# 1/5 and *H*o/Lo $ 0.007, where *H*o is the significant deepwater wave height and *ξ*o 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 *R*2% 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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