Maximum steepness of oceanic waves: Field and laboratory experiments

Abstract

The breaking of waves is an important mechanism for a number of physical, chemical and biological processes in the ocean. Intuitively, waves break when they become too steep. Unfortunately, a general consensus on the ultimate shape of waves has not been achieved yet due to the complexity of the breaking mechanism which still remains the least understood of all processes affecting waves. To estimate the limiting shape of ocean waves, here we present a statistical analysis of a large sample of individual wave steepness. Data were collected from measurements of the surface elevation in laboratory facilities and the open sea under a variety of sea state conditions. Observations reveal that waves are able to reach steeper profiles than the Stokes' limit for stationary waves. Due to the large number of records this finding is statistically robust.

Modeling extreme wave heights from laboratory experiments with the nonlinear Schrödinger equation

“…For the severe sea state represented by larger initial BFI, the steepness of maximum wave height is normally large. Since the mean steepness of maximum wave height in our laboratory experiment does not exceed the Stokes limit, while the exceedance has been reported in many research works, it indicates that the change of wave shape is more related to the reduction of the wave period rather than to the increase of wave height (Toffoli et al, 2010b).…”

“…Moreover, many observations have proved that the maximum wave steepness (Michell, 1893) known as the Miche-Stokes limit, which is close to 0.1429 in deep water and depicted by the dashed line in Fig. 9, could be exceeded (Toffoli et al, 2010b), but the mean steepness of maximum wave height in our laboratory experiment does not exceed the Stokes limit. Thus it reveals that the change of wave shape is more related to the reduction of the wave period rather than to the increase of wave height (Toffoli et al, 2010b).…”

“…9, could be exceeded (Toffoli et al, 2010b), but the mean steepness of maximum wave height in our laboratory experiment does not exceed the Stokes limit. Thus it reveals that the change of wave shape is more related to the reduction of the wave period rather than to the increase of wave height (Toffoli et al, 2010b).…”

Single-shot observation of optical rogue waves in integrable turbulence using time microscopy

“…Starting from random initial conditions, those hydrodynamical experiments have also demonstrated the formation of heavy-tailed statistics. Note finally that the extreme amplitudes observed in our optical fibres experiments could not be observed in water waves that are strongly limited by the wave breaking phenomenon 1,56,57 . The time-resolved direct observation of RWs presented in this letter opens the way to numerous other studies on fast dynamics in Optics.…”

Ocean Wave Rendering with Whitecap in the Visual System of a Maritime Simulator

“…However, the value is difficult to observe [48]. Therefore, some alternative criteria are often used.…”