Rogue waves and entropy consumption

¹ Institute of Physics and ForWind, Carl-von-Ossietzky University of Oldenburg - Oldenburg, Germany
² Institute of Physics, University of Osnabrück - Osnabrück, Germany
³ Disaster Prevention Research Institute (DPRI), Kyoto University - Kyoto, Japan
⁴ Hamburg University of Technology - 21073 Hamburg, Germany
⁵ Imperial College - London SW7 2AZ, UK

Received: 19 September 2017
Accepted: 9 January 2018

Abstract

Based on data from the Sea of Japan and the North Sea the occurrence of rogue waves is analyzed by a scale-dependent stochastic approach, which interlinks fluctuations of waves for different spacings. With this approach we are able to determine a stochastic cascade process, which provides information of the general multipoint statistics. Furthermore the evolution of single trajectories in scale, which characterize wave height fluctuations in the surroundings of a chosen location, can be determined. The explicit knowledge of the stochastic process enables to assign entropy values to all wave events. We show that for these entropies the integral fluctuation theorem, a basic law of non-equilibrium thermodynamics, is valid. This implies that positive and negative entropy events must occur. Extreme events like rogue waves are characterized as negative entropy events. The statistics of these entropy fluctuations changes with the wave state, thus for the Sea of Japan the statistics of the entropies has a more pronounced tail for negative entropy values, indicating a higher probability of rogue waves.