Waves, Solitons and Turbulence in Optical Systems - Abstract
Steinmeyer, Günter
Rogue waves are highly mysterious and rare phenomena in the ocean. They have been claimed to come out of nowhere and disappear without a trace. Exceeding the significant wave height by more than a factor of two, they can cause considerable damage to ships and other maritime structures. Their origin is still highly disputed. Pure linear interference of waves has been discussed as one theory, but could so far not satisfactorily explain observed probabilities for rogue wave emergence. Other models claim a leading role of nonlinearity and resulting formation of breather solitons. Here we show that rogue wave emergence can in fact be explained by simple linear interference of a small but variable number of elementary waves. We further suggest Grassberger-Procaccia dimensional analysis to extract the effective number of interfering waves immediately from time series of the wave height, measured at one fixed point in the ocean. Further analysis indicates that rogue waves can only form if there is interference of at least 10 waves. Analyzing several wave records in the literature, it is found that even under storm conditions, the rogue wave threshold is often not reached. Analyzing records of the rogue wave that was measured on January 1, 1995 on the Draupner platform, in contrast, indicates a number of at least 12 interfering waves, which clearly exceeds the statistical threshold condition. Going to even larger number of interfering waves, one can see a dramatic increase of the probability for rogue wave formation, much beyond what is predicted by longterm records or parameterless models. In turn, this critical threshold dependence allows for an effective forecast, enabling early-on detection of situations that are prone to rogue wave formation. With the information on the number of interfering waves, one can develop a simple physical model for rogue wave formation, which identifies a rare phase coincidence of waves as the origin of rogue waves. These individual waves may have been generated in remote parts of the ocean and at different propagation direction. Varying the phase diffusion in this process, one can change the depth of the preceding and trailing characteristic troughs as observed in the Draupner event or generate the characteristic wave pattern of the “three sisters”. Flipping the phase at the point of constructive interference, one can also generate the most mysterious rogue wave variant, namely, the rogue hole. Our analysis indicates varying winds and atmospheric turbulence as the real origin of these “monsters of the deep”. While nonlinearity of the ocean system certainly has a modifying influence on wave formation, rogue waves can emerge in a completely linear fashion as also witnessed by some recent new experiments on their optical counterparts. In conclusion, the answer to the ocean rogue wave mystery does not seem to lie in the depth of the ocean as was commonly believed; instead, this answer seems to be literally blowing in the wind.