Extreme waves over a shoal, and extreme forces on a submerged cylinder behind the shoal

During the last years, there has been increasing interest in freak waves and freak forces caused by change in bathymetry. Our research follows the pioneering work of Bitner (Bitner, 1980), who studied how the statistical distribution changed for waves propagating over variable depth. Laboratory data of surface waves from Marin, where waves propagated from deeper to shallower water, were analyzed in Trulsen, Zeng, and Gramstad, 2012. They found a local maximum for kurtosis at the beginning of shallower water. Experimental measurements of Raustl in Trulsen, Raustl, et al., 2020 showed an increase in kurtosis and skewness near the front of the plateau of the shoal, and a minimum in skewness at the lee side. Experimental velocity measurements of Jorde in Trulsen, Raustl, et al., 2020 led to the observation that the velocities had a local maximum and minimum in skewness at the same places as for the surface elevation, but the kurtosis had maximum on the lee side of the shoal. By numerical simulation, the same results were reached by Lawrence, Trulsen, and Gramstad, 2021. This lead us to ask if the forces on a horizontal cylinder would have a similar maximum of kurtosis behind the shoal.

We have done experiments in a wave flume measuring surface elevations and correspond-ing velocities over and behind a shoal, and the resulting forces on a horizontal cylinder behind a shoal, as sketched in fig. 1. Ultrasound probes were placed around the shoal, and an ADV could be moved horizontally over the shoal. The cylinder was equipped with force transducers, and could also be moved. The waves were generated according to the Pierson-Moskowitz spectrum, different from most earlier research that employed the JONSWAP spectrum. In the same way, as for the JONSWAP spectrum in earlier research, we observe the increase in skewness and kurtosis for surface elevation at the front end of the shoal. We also see the increase in kurtosis of the velocity field on the lee side of the shoal. Our force measurements indeed show an increase in skewness and kurtosis on the lee side of the shoal compared to over at the bottom, especially for the horizontal forces. Therefore, there might be reason to be cautious about extreme forces when placing structures behind a shoal.