Comparison of mathematical and CFD models of overwash of a step

Abstract

Overwash is the process in which waves force water onto the surface of a body that is otherwise not fully submerged. It occurs in wave interactions with thin oating plates due to their small freeboards. For example, when experimentally investigating water wave transmission by an array of thin oating plates, Bennetts & Williams (2015) reported overwash in laboratory experiments of regular incident waves interacting with an array of thin oating wooden disks. They noted shallow overwash for relatively moderate incident amplitudes, and deeper and more energetic overwash for larger incident amplitudes. Moreover, they showed that the occurrence of strong overwash was correlated to the array transmitting signi cantly less wave energy than predicted by linear potential ow theory. Skene et al. (2015) proposed a 2D (one horizontal dimension and one depth dimension) mathematical model of overwash of a thin oating plate. They separated the overwash domain from the surrounding water and plate domain; applying linear potential ow theory to the latter domain, and the nonlinear shallow water equations to the former. The potential ow model prediction of the wave elevation above the plate and velocity there was used to force the shallow water equations. Further, they compared the model predictions to measurements made during laboratory experiments. In these experiments, thin oating plastic plates were subjected to regular incident waves with steepnesses ranging from ka = 0:04 to 0:15 and wavelength to plate length ratios from 0:56 to 1:51. A depth gauge placed at the centre of the upper surface of the plate was used to measure the overwash depth. The motion of the plate was also measured, and Meylan et al. (2015) had earlier shown that linear potential ow theory accurately predicts this motion. Skene et al. (2015)'s model accurately predicted the overwash depth signals for relatively low incident steepnesses and short wavelengths, for which the mathematical model predicted a mean overwash depth of less than approximately 2 mm. However, for higher incident steepnesses and longer incident wavelengths, the model became inaccurate and overpredicted the overwash depth by a factor of up to three. The likely causes of the loss of accuracy were hypothesised to be that: (i) the shallow water equations neglect turbulence, which was visible in the experiments for the largest incident amplitudes; (ii) the model lacks back-coupling from the overwash to the plate and surrounding water; and (iii) the shallow water equations do not model the wave breaking that occurred in the experiments when bores created at the leading and trailing plate edges collided. Here, the model is applied to the problem of overwash of a step that has the height of the undisturbed water depth. The simpli ed geometry removes any errors created by (iii), and thus provides a direct means to test the impacts of (i) and (ii). The model predictions are compared to data from computational uid dynamics (CFD) models of the problem.