Experimental and numerical study of the effect of variable bathymetry on the slow-drift wave response of floating bodies

An experimental campaign is reported on the slow-drift motion of a rectangular barge moored at different positions along an inclined beach, at waterdepths ranging from 54 cm to 21 cm, and submitted to irregular beam seas. The beach is achieved by inclining the 24 m long false bottom of the tank at a slope of 5%, from a depth of 1.05 m. The slow-drift component of the measured sway motion is first compared with state-of-the-art calculations based on Newman's approximation. At 54 cm depth a good agreement is obtained between calculations and measurements. At 21 cm depth the Newman calculations exceed the measured values. When the flat bottom setdown contribution is added up, the calculated values become 2 to 3 times larger than the measured ones. A second-order model is proposed to predict the shoaling of a bichromatic sea-state propagating in varying water-depth. This model is validated through comparisons with an extension of Schäffer's model for a straight beach [Schäffer HA. Infragravity waves induced by short-wave groups. J Fluid Mech 1993;247:551-88] and with a fully nonlinear Boussinesq model. It appears that the long wave amplitude is much less than predicted by the flat bottom model, and that its phase difference with the short wave envelope also deviates from the flat bottom model prediction. As a result of this phase shift the actual second-order wave loads can be lower than predicted by Newman's approximation alone. Application of the shoaling model to the barge tests yields a notably better agreement between numerical and experimental values of its slow-drift sway motion.