Rogue wave occurrence over planar coastal bathymetries

Rogue waves have received considerable attention in recent years, with major advancements in their generation mechanisms having been defined. However, the focus of most investigations has been related to rogue wave occurrence in deep water. In contrast, far fewer results are available in shallower water depths. As such, the present work focuses on exploring the occurrence probabilities of rogue waves in coastal waters, as well as the physical mechanisms that lead to their formation. This is achieved by a thorough analysis of a very extensive experimental dataset of random waves propagating over planar beaches. More specifically, long simulations of realistic JONSWAP spectra arising in intermediate water depths have been generated at the deep end of the Coastal Flume at Imperial College London. These propagate over 3 uniform slopes with inclinations varying between 1:15 and 1:50, while being sampled by a dense array of wave gauges. The fine spatial resolution of wave gauges allows for a detailed description of large wave evolution as they travel towards the shoreline. Importantly, a parametric approach in defining the offshore forcing conditions has been adopted and covers a wide range of sea-state steepnesses and effective water depths. Taken together, 15 different storm conditions, each consisting of approximately 20,000 waves, have been considered for each bed slope configuration.

In analysing these results, the occurrence of rogue waves is examined at all spatial locations across the coastal zone. We observe a considerable increase in rogue wave occurrence for reducing water depths which has not been found previously. This is particularly the case for moderately mild offshore storms. In exploring the shape of rogue waves arising at different water depth regimes, the relative importance of dispersion and nonlinearity is defined. While rogue waves arising at the deeper end of the coast resemble NewWave type events, solitary-type events become more pronounced at the shallower end. The occurrence of rogue waves in shallow water is suppressed once extensive wave breaking arises. While this is expected as a result of depth-induced wave breaking, interesting results arise for the steepest offshore conditions. Evidence suggests that waves breaking at the outer edge of the surf zone, regroup and give rise to rogue waves closer to the shoreline.

Taken together, the rogue wave investigation within the present extensive experimental dataset provides evidence for their increased importance in coastal waters which has not been broadly considered so far.