Extreme long waves over a varying bathymetry

Abstract

Recent modelling work has shown that abrupt bathymetric transitions can produce dramatic amplifications of long waves, under the influence of both nonlinearity and dispersion. Here, the evolution of wave packets towards a vertical wall over a varying bathymetry is investigated with a one-dimensional conformal-mapping spectral code. In this system, wave breaking, runup and reflection, wave interference and bathymetric effects are highlighted. Wave breaking is examined with respect to geometric, kinematic and energetic conditions, with consistent results. The breaking strength is characterized for spilling and plunging based on initial wave period and amplitude. Non-breaking waves are amplified by reflection, interference and the bathymetry leading to large runups. In a typical example inspired by a real-world bathymetry, the maximum runup amplification approaches a factor of 12 – large enough for a 3 m amplitude wave to overtop a 30 m cliff.

Megagravel deposits on the west coast of Ireland show the impacts of severe storms

“…These deep‐water values translate to 9–13m SWH at the coast (Janjić, ; Cox et al ., ). Maximum wave heights (for rare individual waves) may have been as much as twice the SWH; and nonlinear interactions with uneven topography near the steep coasts may have generated additional amplifications (Brennan et al ., ; Herterich and Dias, ). The waves were big!…”

“…Observations and analysis have shown that nonlinear interactions at steep coasts can induce very large waves—‘rogue’ or ‘freak’ waves, defined as greater than twice the local significant wave height (SWH) (Didenkulova and Pelinovsky, ; Fedele et al ., ). Numerical modelling reveals that irregular bathymetry adjacent to steep coasts may drive further exceptional amplifications (Akrish et al ., ; Brennan et al ., ; Herterich and Dias, ). Finally, the photography explosion of the last decade or so has resulted in a constantly growing trove of stunning images, which is essentially a citizen‐science dataset of the extraordinary run‐up associated with storm waves at steep coasts (Figure ).…”

Breaking-wave induced pressure and acceleration on a clifftop boulder

“…The fast velocities, changing crest shape, fluid mixing and rapid development of breaking waves over a fraction of a wavelength means that, throughout breaking, the measured pressures at an impacted structure vary significantly even across globally similar waves (van Meerkerk et al 2020). Additionally, third-order wave-wave interactions at a fluid-structure interface can increase wave run-up height by twice that expected by linear wave theory (Zhao et al 2017) and the run-up of long waves can be amplified up to 12 times through nonlinear dispersion, reflection, interference and abrupt changes in bathymetry (Herterich & Dias 2019;Viotti, Carbone & Dias 2014). Abrupt changes in bathymetry that can be expected close to the coast can also trigger the formation of extreme waves through the interaction between first-order waves and their second-order bound harmonics (Li et al 2021).…”

Maximal Heights of Nearshore Storm Waves and Resultant Onshore Flow Velocities

“…In contrast to waves that shoal gradually across smooth bathymetry, and run up gentle slopes-which are well-described and amenable to mathematical modelling-waves at rocky coasts are far less studied. They are difficult to measure, and equally difficult to model (Dodet et al, 2018;Herterich and Dias, 2019). Thus, there are few data for storm-wave runup in those environments.…”