Runup on a vertical column in strong water wave events

Abstract

Runup on a slender cylindrical column exposed to long, steep waves, at finite and great depth is quantified by high speed camera technique in wave channel. Ratio between water depth (h) and cylinder diameter (D) is h/D = 10, 4.16, 2.5. Breaking and non-breaking wave events are made by focusing technique. The trough-to-trough period (TTT), crest height (η0.m), frequency (ω = 2π/TTT) and reference speed (g/ω) of each wave event are defined (g denotes acceleration of gravity). Wavenumber (k) is obtained from the dispersion relation. Experimental runup maximum (Rum) is presented in terms of variable Z = [2ω2(Rum - η0,m)/g]1/2. Measurements at finite water depth collapse along a linear relationship kη0,m = a + b Z where coefficients are obtained from the experiments. Results from other studies including large scale measurements fit to this curve, for h/D < 5, kh < 2 and kD < 0.52. Results at great water depth with h/D = 10 show, beyond a threshold wave slope, a similar relationship. Growth factor (1/b) is then much stronger. Gradual transition between results at finite depth and great water depth occurs for 5 < h/D < 10 and kh > 2.5. Measured runup velocity along the column is up to 1.8 times the reference speed at great depth (h/D = 10) and up to 1.2 times the reference speed at finite depth. Wave slope kη0,m is up to 0.56.