Asymptotics for the long-time evolution of kurtosis of narrow-band ocean waves

Peter A.E.M. Janssen (Corresponding author), Augustus J.E.M. Janssen

    Research output: Contribution to journalArticleAcademicpeer-review

    7 Citations (Scopus)
    42 Downloads (Pure)

    Abstract

    In this paper we highlight that extreme events such as freak waves are a transient phenomenon in keeping with the old fisherman tale that these extreme events seem to appear out of nowhere. Janssen (J. Phys. Oceanogr., vol. 33, 2003, pp. 863-884) obtained an evolution equation for the ensemble average of the excess kurtosis, which is a measure for the deviation from normality and an indicator for nonlinear focusing resulting in extreme events. In the limit of a narrow-band wave train, whose dynamics is governed by the two-dimensional nonlinear Schrödinger (NLS) equation, the excess kurtosis is under certain conditions seen to grow to a maximum after which it decays to zero for large times. This follows from a numerical solution of the problem and also from an analytical solution presented by Fedele (J. Fluid Mech., vol. 782, 2015, pp. 25-36). The analytical solution is not explicit because it involves an integral from initial time to actual time. We therefore study a number of properties of the integral expression in order to better understand some interesting features of the time-dependent excess kurtosis and the generation of extreme events.

    Original languageEnglish
    Pages (from-to)790-818
    Number of pages29
    JournalJournal of Fluid Mechanics
    Volume859
    DOIs
    Publication statusPublished - 25 Jan 2019

    Keywords

    • surface gravity waves
    • waves/free-surface flows

    Fingerprint Dive into the research topics of 'Asymptotics for the long-time evolution of kurtosis of narrow-band ocean waves'. Together they form a unique fingerprint.

    Cite this