title: Ocean rogue waves and their phase space dynamics in the limit of a linear interference model.
abstract: We reanalyse the probability for formation of extreme waves using the simple model of linear interference of a finite number of elementary waves with fixed amplitude and random phase fluctuations. Under these model assumptions no rogue waves appear when less than 10 elementary waves interfere with each other. Above this threshold rogue wave formation becomes increasingly likely, with appearance frequencies that may even exceed long-term observations by an order of magnitude. For estimation of the effective number of interfering waves, we suggest the Grassberger-Procaccia dimensional analysis of individual time series. For the ocean system, it is further shown that the resulting phase space dimension may vary, such that the threshold for rogue wave formation is not always reached. Time series analysis as well as the appearance of particular focusing wind conditions may enable an effective forecast of such rogue-wave prone situations. In particular, extracting the dimension from ocean time series allows much more specific estimation of the rogue wave probability.
authors.affiliation: Max-Born-Institut, Max-Born-Straße 2A, 12489 Berlin, Germany.
authors.forename: Simon
authors.initials: S
authors.lastname: Birkholz
authors.affiliation: Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Germany.
authors.forename: Carsten
authors.initials: C
authors.lastname: Brée
authors.affiliation: Fakultät für Mathematik, Technische Universität Dortmund, Vogelpothsweg 87, 44221 Dortmund, Germany.
authors.forename: Ivan
authors.initials: I
authors.lastname: Veselić
authors.affiliation: Institute for Quantum Optics, Leibniz Universität Hannover, Welfengarten 1, 30167 Hannover, Germany.
authors.forename: Ayhan
authors.initials: A
authors.lastname: Demircan
authors.affiliation: Max-Born-Institut, Max-Born-Straße 2A, 12489 Berlin, Germany.
authors.forename: Günter
authors.initials: G
authors.lastname: Steinmeyer