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This article is cited in 4 scientific papers (total in 4 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.
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
Linking options:
https://www.mathnet.ru/eng/tmf8656https://doi.org/10.4213/tmf8656 https://www.mathnet.ru/eng/tmf/v180/i1/p112
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