Random Wave Runup Height on Gentle Slope

Abstract
An extensive series of labroatory tests were conducted and these tests led to the development of a formula to predict runup elevation of random waves on gentle, smooth and impermeable slopes, as a function of surf similarity parameter. On gentle slopes, a bore advancing into the shoreline cannot run up when the back‐rush of a preceding bore is large or when it is overtaken and captured by a subsequent large bore. No correspondence between individual running‐up bores and runup crests can be seen; the number of runup crests is reduces compared to the number of running‐up bores. This paper also proposed a formula for the ratio of the number of runup crests to that of incident waves; the formula can be used to estimate the mean repetition period of runup crests. The formulas proposed here are applicable to slopes, tan θ, ranging from 1/30 to 1/5 and to deep water significant wave steepness ranging from 0.007 to 0.07.

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