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TMF, 2014, Volume 180, Number 1, Pages 112–124 (Mi tmf8656)  

This article is cited in 3 scientific papers (total in 3 papers)

Anomalous waves as an object of statistical topography: Problem statement

V. I. Klyatskin

Obukhov Institute for Physics of the~Atmosphere, RAS, Moscow, Russia

Abstract: Based on ideas of statistical topography, we analyze the boundary-value problem of the appearance of anomalous large waves {(}rogue waves{\rm)} on the sea surface. The boundary condition for the sea surface is regarded as a closed stochastic quasilinear equation in the kinematic approximation. We obtain the stochastic Liouville equation, which underlies the derivation of an equation describing the joint probability density of fields of sea surface displacement and its gradient. We formulate the statistical problem with the stochastic topographic inhomogeneities of the sea bottom taken into account. It describes diffusion in the phase space, and its solution must answer the question whether information about the existence of anomalous large waves is contained in the quasilinear equation under consideration.

Keywords: anomalous wave, rogue wave, Liouville equation, stochastic topography

DOI: https://doi.org/10.4213/tmf8656

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English version:
Theoretical and Mathematical Physics, 2014, 180:1, 850–861

Bibliographic databases:

Received: 17.02.2014
Revised: 04.03.2014

Citation: V. I. Klyatskin, “Anomalous waves as an object of statistical topography: Problem statement”, TMF, 180:1 (2014), 112–124; Theoret. and Math. Phys., 180:1 (2014), 850–861

Citation in format AMSBIB
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\paper Anomalous waves as an~object of statistical topography: Problem statement
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  • http://mi.mathnet.ru/eng/tmf8656
  • https://doi.org/10.4213/tmf8656
  • http://mi.mathnet.ru/eng/tmf/v180/i1/p112

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. I. Klyatskin, “Stochastic structure formation in random media”, Phys. Usp., 59:1 (2016), 67–95  mathnet  crossref  crossref  adsnasa  isi  elib
    2. V. I. Klyatskin, K. V. Koshel', “Statistical structuring theory in parametrically excitable dynamical systems with a Gaussian pump”, Theoret. and Math. Phys., 186:3 (2016), 411–429  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. V. I. Klyatskin, Fundamentals of stochastic nature sciences, Understanding Complex Systems (Springer Complexity), Springer International Publishing Ag, 2017, 190 pp.  crossref  mathscinet  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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