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

Abstract

Bathymetric changes have been experimentally shown to affect the occurrence of rogue waves. We recently derived a non-homogeneous correction to the spectral analysis, allowing us to describe the evolution of the rogue wave probability over a shoal. Here, we extend this work to the evolution of the excess kurtosis of the surface elevation, that plays a central role in estimating rare event probabilities. Furthermore, we provide an upper bound to the excess kurtosis. In intermediate and deep water regimes, a shoal does not affect wave steepness nor bandwidth significantly, so that the vertical asymmetry between crests and troughs, the excess kurtosis and the exceedance probability of wave height stay rather constant. In contrast, in shallower water, a sharp increase in wave steepness increases the vertical asymmetry, resulting in a growth of both the tail of the exceedance probability and the excess kurtosis.

Effects of a liquid metal co‐filler on the properties of epoxy/binary filler composites

“…20,47,48 Larger LM droplets generally featured highly distorted shapes and could no longer be characterized as spheres, attributed to the easier deformation of larger droplets with higher Deborah numbers. 49 Figure 8 shows the measured TC values of the composites cured at various Al 2 O 3 :EGaIn ratios. Given that the TC of EGaIn (26.4 W/mK) is lower than that of Al 2 O 3 ($30 W/mK), it is not surprising that the TC of the LM-free composite (Al 2 O 3 :EGaIn = 50:0) is higher than those of the binary filler systems.…”