Run-Up of Random Waves on Gentle Slopes

Abstract

This paper investigates the following characteristics of run-up of random waves on gentle slopes experimentally: (1) the run-up wave energy spectrum, (2) the ratio of the number of run-up waves to that of incident waves, (3) the relationship between the representative run-up height, the deep-water wave steepness and the beach slope, (4) the run length of run-up heights, and (5) the effect of wave grouping on representative run-up heights. Main results are summarized in the chapter of conclusions.

Wave Run-Up on a Natural Beach

“…The gradient of power density function in the saturated range at the high frequency side of the peak follows -3 power of the frequency (f~3) at the outside of the breaker zone(Sawaragi and Iwata, 1980) and follows -4 power of frequency (f~4) inside the surf zone, as reported by Mizuguchi(1984), and Mase and Iwagaki(1984).…”

An analytical model to predict dune erosion due to wave impact

“…This agreement lends credibility to the basic model formulation and derived solution, although in order to obtain a model that can be used for reliable estimates of dune erosion R and C s must be accurately predicted. Initially, several different runup height formulas were tested to predict R (e.g., Hunt, 1959;Mase and Iwagaki, 1984;Holman, 1986;Larson and Kraus, 1989a;Mayer and Kriebel, 1994), but the resulting optimum values on C s displayed a large variation between the individual cases making application of the model difficult.…”

Prediction of swash motion and run-up including the effects of swash interaction

“…Mase and Iwagaki (1984) ran a series of tests in the laboratory with random waves and found that the ratio of the number of individual run-up waves to that of incident waves decreased as the beach slope decreased. Based on additional laboratory experiments, Mase (1989) developed an empirical formula to predict the maximum run-up on a range of slopes while accounting for swash interaction between random waves.…”

“…The catch-up and absorption mechanism of swash interaction was explicitly modeled by Mase and Iwagaki (1984) employing empirical data and Mase (1988) and Baldock and Holmes (1999) by superimposing run-up parabolas using the ballistic model without friction. Mase and Iwagaki (1984) ran a series of tests in the laboratory with random waves and found that the ratio of the number of individual run-up waves to that of incident waves decreased as the beach slope decreased.…”

“…This interaction between waves continues with each incoming wave, and with respect to the hydrodynamics, the end result is that the maximum run-up will not correspond to the up-rush of the highest wave in the train. This is particularly true for mild foreshore slopes (tanbb0.1) where the time it takes for a swash lens to travel up and down is longer than for steeper slopes (Mase and Iwagaki, 1984).…”