Journal cover Journal topic
Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union
Journal topic

Journal metrics

Journal metrics

  • IF value: 1.699 IF 1.699
  • IF 5-year value: 1.559 IF 5-year
    1.559
  • CiteScore value: 1.61 CiteScore
    1.61
  • SNIP value: 0.884 SNIP 0.884
  • IPP value: 1.49 IPP 1.49
  • SJR value: 0.648 SJR 0.648
  • Scimago H <br class='hide-on-tablet hide-on-mobile'>index value: 52 Scimago H
    index 52
  • h5-index value: 21 h5-index 21
Volume 9, issue 3/4
Nonlin. Processes Geophys., 9, 355–366, 2002
https://doi.org/10.5194/npg-9-355-2002
© Author(s) 2002. This work is licensed under
the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 License.
Nonlin. Processes Geophys., 9, 355–366, 2002
https://doi.org/10.5194/npg-9-355-2002
© Author(s) 2002. This work is licensed under
the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 License.

  31 Aug 2002

31 Aug 2002

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

V. G. Polnikov V. G. Polnikov
  • The State Oceanographic Institute, Kropotkinskii Lane 6, Moscow, 119992 Russia

Abstract. 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.

Publications Copernicus
Download
Citation