SET-UP AND RUN-UP IN SHOALING BREAKERS

William G. Van Dorn

Abstract


This paper reports the results of a series of laboratory experiments with periodic waves breaking on uniformly sloping impermeable beaches with the object of distinguishing set-up from dynamic shoreline motions due to partial reflection, the combination of which is normally referred to as 'run-up'. The principal findings are: 1. The mean set-up across the breaker zone was observed to be linear with mean slope proportional to the square of the bottom slope. The mean slope was independent of frequency over slopes of 0.04 or less, and increased with wave period over steeper slopes. 2. The dynamic run-up range was found to be proportional to the square of wave period times beach slope, in agreement with the equation of motion for a nearly frictionless block sliding on corresponding slopes under gravity. 3. The total run-up was poorly correlated with Hunt's empirical formula, nor could any reasonable deterministic justification of this formula be deduced from the present results. 4. Transient run-up was observed to considerably exceed steady-state values in most cases, suggesting that time-dependent momentum flux should be considered in the run-up of variable (natural) waves.

Keywords


set up; run up; shoaling; breaking waves; shoaling breakers

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