Experimental and numerical study of the wave run-up along a vertical plate

Results from experiments on wave interaction with a rigid vertical plate are reported. The 5m long plate is set against the wall of a 30m wide basin, at 100m from the wavemaker. This set-up is equivalent to a 10m plate in the middle of a 60m wide basin. Regular waves are produced, with wavelengths of 1.6m, 1.8m and 2m, and steepnesses H/L (H being the double amplitude and L being the wavelength) ranging from 2% to 5%.

Free-surface elevations along the plate are measured with a row of 20 gauges. The focus is on the time evolution of the free-surface profile along the plate. At all steepnesses, strong deviations from the predictions of linear theory gradually take place as the reflected wave field develops in the basin.

This phenomenon is attributed to third-order interactions between the incoming and reflected wave systems, on the weather side of the plate. The measured profiles along the plate are compared with the predictions of two numerical models: an approximate model based on the tertiary interaction theory of Longuet-Higgins & Phillips (J.

Fluid Mech., vol. 12, 1962, p. 333) for plane waves, which provides a steady-state solution, and a fully nonlinear numerical wavetank based on extended Boussinesq equations. In most of the experimental tests, despite the large distance from the wavemaker to the plate and the small amplitude of the incident wave, no steady state is attained by the end of the exploitable part of the records.