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A Basing of the Diffusion Approximation Derivation for the Four-wave Kinetic Integral and Properties of the Approximation : Volume 9, Issue 3/4 (30/11/-0001)

By Polnikov, V. G.

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Book Id: WPLBN0004020034
Format Type: PDF Article :
File Size: Pages 12
Reproduction Date: 2015

Title: A Basing of the Diffusion Approximation Derivation for the Four-wave Kinetic Integral and Properties of the Approximation : Volume 9, Issue 3/4 (30/11/-0001)  
Author: Polnikov, V. G.
Volume: Vol. 9, Issue 3/4
Language: English
Subject: Science, Nonlinear, Processes
Collections: Periodicals: Journal and Magazine Collection, Copernicus GmbH
Historic
Publication Date:
-0001
Publisher: Copernicus Gmbh, Göttingen, Germany
Member Page: Copernicus Publications

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Polnikov, V. G. (-0001). A Basing of the Diffusion Approximation Derivation for the Four-wave Kinetic Integral and Properties of the Approximation : Volume 9, Issue 3/4 (30/11/-0001). Retrieved from http://www.worldebookfair.com/


Description
Description: The State Oceanographic Institute, Kropotkinskii Lane 6, Moscow, 119992 Russia. A basing of the diffusion approximation derivation for the Hasselmann kinetic integral describing nonlinear interactions of gravity waves in deep water is discussed. It is shown that the diffusion approximation containing the second derivatives of a wave spectrum in a frequency and angle (or in wave vector components) is resulting from a step-by-step analytical integration of the sixfold Hasselmann integral without involving the quasi-locality hypothesis for nonlinear interactions among waves. A singularity analysis of the integrand expression gives evidence that the approximation mentioned above is the small scattering angle approximation, in fact, as it was shown for the first time by Hasselmann and Hasselmann (1981). But, in difference to their result, here it is shown that in the course of diffusion approximation derivation one may obtain the final result as a combination of terms with the first, second, and so on derivatives. Thus, the final kind of approximation can be limited by terms with the second derivatives only, as it was proposed in Zakharov and Pushkarev (1999). For this version of diffusion approximation, a numerical testing of the approximation properties was carried out. The testing results give a basis to use this approximation in a wave modelling practice.

Summary
A basing of the diffusion approximation derivation for the four-wave kinetic integral and properties of the approximation

 

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