Saturation of rogue wave amplification over steep shoals

Abstract

Shoaling surface gravity waves induce rogue wave formation. Though commonly reduced to water waves passing over a step, nonequilibrium physics allows finite slopes to be considered in this problem. Using nonhomogeneous spectral analysis of a spatially varying energy density ratio, we describe the dependence of the amplification as a function of the slope steepness. Increasing the slope increases the amplification of rogue wave probability until this amplification saturates at steep slopes. In contrast, the increase of the down slope of a subsequent de-shoal zone leads to a monotonic decrease in the rogue wave probability, thus featuring a strong asymmetry between shoaling and de-shoaling zones. Due to the saturation of the rogue wave amplification at steep slopes, our model is applicable beyond its range of validity up to a step, thus elucidating why previous models based on a step could describe the physics of steep finite slopes. We also explain why the rogue wave probability increases over a shoal while it is lower in shallower water.

Non-homogeneous approximation for the kurtosis evolution of shoaling rogue waves

“…When solving for second-order irregular waves, we assume that the shoal is linear , the length of the shoal is relatively short and we deal with small amplitude waves only (). These assumptions greatly simplify the problem, but are also representative of real ocean bathymetry(Mendes & Kasparian 2022). Furthermore, we have recently demonstrated that as the slope magnitude increases the rogue wave occurrence follows suit.…”

“…Furthermore, we have recently demonstrated that as the slope magnitude increases the rogue wave occurrence follows suit. However, if we assume a small effect of reflection due to a small surf similarity parameter among spectral components (Battjes 1974), the increase in rogue wave occurrence saturates for slopes larger than or equal to (Mendes & Kasparian 2022). The evolution of the exceedance probability in (2.2) can be generalized to any arbitrary incoming statistics (Mendes et al.…”

“…(2020) provided experimental data with the broadest set of conditions and widest range of relative water depths. As reviewed in Mendes & Kasparian (2022), three complementary theoretical models for the wave statistics have emerged, albeit they tend to focus on either the surface elevation (Moore et al. 2020), the crest height (Li et al.…”

Non-homogeneous approximation for the kurtosis evolution of shoaling rogue waves

“…Dashed vertical lines mark the shoaling and de-shoaling zones (see figure 1). Solid curves include the slope effect [26].…”

Novel methods for coupled prediction of extreme wind speeds and wave heights

“…In addition, spectrum bandwidth seems to have different types of effects in extreme wave distribution depending on whether they are in deep [25][26][27][28] or shallow water 13 . Furthermore, ocean processes such as shoaling or wave-current systems that drive wave trains out of equilibrium have been experimentally 22,25,[29][30][31][32][33][34][35][36][37] associated with increasing the occurrence of extreme waves by order of magnitude. However, it has been recently found that no established theoretical distribution to date, neither universal as Gumbel nor based on physical principles, can describe extreme wave statistics in a wide range of conditions .…”