Session: 02-04-01 Extreme and Freak Waves (Co-hosted with the Ian Young Honoring Symposium)

Paper Number: 107884

107884 - Slope Effect on the Evolution of Kurtosis Over a Shoal 

Shoaling surface gravity waves induce rogue wave formation. Though commonly reduced to water waves passing over a step, non-equilibrium physics allows finite slopes to be considered in this problem. Using non-homogeneous 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. In view of the central role played by the excess kurtosis of the surface elevation in estimating rare event probabilities, we translate the determined evolution of the rogue wave probability over a shoal subject to a finite slope into that of the kurtosis. We provide an effective theory that connects the non-homogeneous correction to the spectral analysis and the evolution of excess kurtosis over the shoal and find good agreement with laboratory experiments. The validated formulae allow the computation of an excess kurtosis upper bound.

 

 

Presenting Author: Saulo Mendes University of Geneva

Presenting Author Biography: Born in Northeast Brazil, Saulo Mendes earned both B.Sc. and M.Sc. in Physics in Brazil and a Ph.D. in Physical Oceanography at the University of North Carolina at Chapel Hill (USA). During his doctoral studies he performed work on theoretical and observational rogue wave data analysis, finding new empirical insights. Currently on his postdoctoral work, he is developing a framework to treat non-stationary and non-homogeneous wave fields and its impact on rogue wave occurrence and intensity.

Authors:

Saulo Mendes University of Geneva
Jérôme Kasparian University of Geneva