TY - JOUR

T1 - Probability Distribution Functions of Freak Waves

T2 - Nonlinear Versus Linear Model

AU - Dyachenko, Alexander I.

AU - Kachulin, Dmitriy I.

AU - Zakharov, Vladimir E.

N1 - Funding Information:
Numerical part of this work including linear and nonlinear simulation of water waves and calculating probability distribution functions of freak waves was supported by the Grant “Wave turbulence: theory, numerical simulation, experiment” #14‐22‐00174 of Russian Science Foundation. Analytical part of the article was supported by Grant of NSF 1130450.

PY - 2016/8/1

Y1 - 2016/8/1

N2 - Presented are the results of numerical experiments on calculation of probability distribution functions (PDFs) for surface elevations of water waves arising during the evolution of statistically homogeneous wave field. Extreme waves or freak waves are an integral part of ocean waving, and PDFs are compared both for nonlinear and linear models. Obviously, linear model demonstrates the Rayleigh distribution of surface elevations while PDFs for nonlinear equation have tails for large elevations similar to Rayleigh distribution, but with much larger σ.

AB - Presented are the results of numerical experiments on calculation of probability distribution functions (PDFs) for surface elevations of water waves arising during the evolution of statistically homogeneous wave field. Extreme waves or freak waves are an integral part of ocean waving, and PDFs are compared both for nonlinear and linear models. Obviously, linear model demonstrates the Rayleigh distribution of surface elevations while PDFs for nonlinear equation have tails for large elevations similar to Rayleigh distribution, but with much larger σ.

UR - http://www.scopus.com/inward/record.url?scp=84975699495&partnerID=8YFLogxK

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U2 - 10.1111/sapm.12116

DO - 10.1111/sapm.12116

M3 - Article

AN - SCOPUS:84975699495

VL - 137

SP - 189

EP - 198

JO - Studies in Applied Mathematics

JF - Studies in Applied Mathematics

SN - 0022-2526

IS - 2

ER -