Self-similarity of wind-driven seas

S. I. Badulin, A. N. Pushkarev, D. Resio, Vladimir E Zakharov

Research output: Contribution to journalArticle

63 Citations (Scopus)

Abstract

The results of the theoretical and numerical study of the Hasselmann kinetic equation for deep water waves in presence of wind input and dissipation are presented. The guideline of the study: nonlinear transfer is the dominating mechanism of wind-wave evolution. In other words, the most important features of wind-driven sea could be understood in a framework of conservative Hasselmann equation while forcing and dissipation determine parameters of a solution of the conservative equation. The conservative Hasselmann equation has a rich family of self-similar solutions for duration-limited and fetch-limited wind-wave growth. These solutions are closely related to classic stationary and homogeneous weak-turbulent Kolmogorov spectra and can be considered as non-stationary and non-homogeneous generalizations of these spectra. It is shown that experimental parameterizations of wind-wave spectra (e.g. JONSWAP spectrum) that imply self-similarity give a solid basis for comparison with theoretical predictions. In particular, the self-similarity analysis predicts correctly the dependence of mean wave energy and mean frequency on wave age Cp/U10. This comparison is detailed in the extensive numerical study of duration-limited growth of wind waves. The study is based on algorithm suggested by Webb (1978) that was first realized as an operating code by Resio and Perrie (1989, 1991). This code is now updated: the new version is up to one order faster than the previous one. The new stable and reliable code makes possible to perform massive numerical simulation of the Hasselmann equation with different models of wind input and dissipation. As a result, a strong tendency of numerical solutions to self-similar behavior is shown for rather wide range of wave generation and dissipation conditions. We found very good quantitative coincidence of these solutions with available results on duration-limited growth, as well as with experimental parametrization of fetch-limited spectra JONSWAP in terms of wind-wave age Cp/U10.

Original languageEnglish (US)
Pages (from-to)891-945
Number of pages55
JournalNonlinear Processes in Geophysics
Volume12
Issue number6
StatePublished - 2005

Fingerprint

wind wave
dissipation
fetch
wave generation
water wave
wave spectrum
wave energy
parameterization
deep water
water waves
sea
Water waves
Parameterization
kinetics
kinetic equations
prediction
tendencies
simulation
code
Kinetics

ASJC Scopus subject areas

  • Geochemistry and Petrology
  • Geophysics
  • Statistical and Nonlinear Physics

Cite this

Badulin, S. I., Pushkarev, A. N., Resio, D., & Zakharov, V. E. (2005). Self-similarity of wind-driven seas. Nonlinear Processes in Geophysics, 12(6), 891-945.

Self-similarity of wind-driven seas. / Badulin, S. I.; Pushkarev, A. N.; Resio, D.; Zakharov, Vladimir E.

In: Nonlinear Processes in Geophysics, Vol. 12, No. 6, 2005, p. 891-945.

Research output: Contribution to journalArticle

Badulin, SI, Pushkarev, AN, Resio, D & Zakharov, VE 2005, 'Self-similarity of wind-driven seas', Nonlinear Processes in Geophysics, vol. 12, no. 6, pp. 891-945.
Badulin SI, Pushkarev AN, Resio D, Zakharov VE. Self-similarity of wind-driven seas. Nonlinear Processes in Geophysics. 2005;12(6):891-945.
Badulin, S. I. ; Pushkarev, A. N. ; Resio, D. ; Zakharov, Vladimir E. / Self-similarity of wind-driven seas. In: Nonlinear Processes in Geophysics. 2005 ; Vol. 12, No. 6. pp. 891-945.
@article{d236e2cff0da4cbf97d94aa5af13fd00,
title = "Self-similarity of wind-driven seas",
abstract = "The results of the theoretical and numerical study of the Hasselmann kinetic equation for deep water waves in presence of wind input and dissipation are presented. The guideline of the study: nonlinear transfer is the dominating mechanism of wind-wave evolution. In other words, the most important features of wind-driven sea could be understood in a framework of conservative Hasselmann equation while forcing and dissipation determine parameters of a solution of the conservative equation. The conservative Hasselmann equation has a rich family of self-similar solutions for duration-limited and fetch-limited wind-wave growth. These solutions are closely related to classic stationary and homogeneous weak-turbulent Kolmogorov spectra and can be considered as non-stationary and non-homogeneous generalizations of these spectra. It is shown that experimental parameterizations of wind-wave spectra (e.g. JONSWAP spectrum) that imply self-similarity give a solid basis for comparison with theoretical predictions. In particular, the self-similarity analysis predicts correctly the dependence of mean wave energy and mean frequency on wave age Cp/U10. This comparison is detailed in the extensive numerical study of duration-limited growth of wind waves. The study is based on algorithm suggested by Webb (1978) that was first realized as an operating code by Resio and Perrie (1989, 1991). This code is now updated: the new version is up to one order faster than the previous one. The new stable and reliable code makes possible to perform massive numerical simulation of the Hasselmann equation with different models of wind input and dissipation. As a result, a strong tendency of numerical solutions to self-similar behavior is shown for rather wide range of wave generation and dissipation conditions. We found very good quantitative coincidence of these solutions with available results on duration-limited growth, as well as with experimental parametrization of fetch-limited spectra JONSWAP in terms of wind-wave age Cp/U10.",
author = "Badulin, {S. I.} and Pushkarev, {A. N.} and D. Resio and Zakharov, {Vladimir E}",
year = "2005",
language = "English (US)",
volume = "12",
pages = "891--945",
journal = "Nonlinear Processes in Geophysics",
issn = "1023-5809",
publisher = "European Geosciences Union",
number = "6",

}

TY - JOUR

T1 - Self-similarity of wind-driven seas

AU - Badulin, S. I.

AU - Pushkarev, A. N.

AU - Resio, D.

AU - Zakharov, Vladimir E

PY - 2005

Y1 - 2005

N2 - The results of the theoretical and numerical study of the Hasselmann kinetic equation for deep water waves in presence of wind input and dissipation are presented. The guideline of the study: nonlinear transfer is the dominating mechanism of wind-wave evolution. In other words, the most important features of wind-driven sea could be understood in a framework of conservative Hasselmann equation while forcing and dissipation determine parameters of a solution of the conservative equation. The conservative Hasselmann equation has a rich family of self-similar solutions for duration-limited and fetch-limited wind-wave growth. These solutions are closely related to classic stationary and homogeneous weak-turbulent Kolmogorov spectra and can be considered as non-stationary and non-homogeneous generalizations of these spectra. It is shown that experimental parameterizations of wind-wave spectra (e.g. JONSWAP spectrum) that imply self-similarity give a solid basis for comparison with theoretical predictions. In particular, the self-similarity analysis predicts correctly the dependence of mean wave energy and mean frequency on wave age Cp/U10. This comparison is detailed in the extensive numerical study of duration-limited growth of wind waves. The study is based on algorithm suggested by Webb (1978) that was first realized as an operating code by Resio and Perrie (1989, 1991). This code is now updated: the new version is up to one order faster than the previous one. The new stable and reliable code makes possible to perform massive numerical simulation of the Hasselmann equation with different models of wind input and dissipation. As a result, a strong tendency of numerical solutions to self-similar behavior is shown for rather wide range of wave generation and dissipation conditions. We found very good quantitative coincidence of these solutions with available results on duration-limited growth, as well as with experimental parametrization of fetch-limited spectra JONSWAP in terms of wind-wave age Cp/U10.

AB - The results of the theoretical and numerical study of the Hasselmann kinetic equation for deep water waves in presence of wind input and dissipation are presented. The guideline of the study: nonlinear transfer is the dominating mechanism of wind-wave evolution. In other words, the most important features of wind-driven sea could be understood in a framework of conservative Hasselmann equation while forcing and dissipation determine parameters of a solution of the conservative equation. The conservative Hasselmann equation has a rich family of self-similar solutions for duration-limited and fetch-limited wind-wave growth. These solutions are closely related to classic stationary and homogeneous weak-turbulent Kolmogorov spectra and can be considered as non-stationary and non-homogeneous generalizations of these spectra. It is shown that experimental parameterizations of wind-wave spectra (e.g. JONSWAP spectrum) that imply self-similarity give a solid basis for comparison with theoretical predictions. In particular, the self-similarity analysis predicts correctly the dependence of mean wave energy and mean frequency on wave age Cp/U10. This comparison is detailed in the extensive numerical study of duration-limited growth of wind waves. The study is based on algorithm suggested by Webb (1978) that was first realized as an operating code by Resio and Perrie (1989, 1991). This code is now updated: the new version is up to one order faster than the previous one. The new stable and reliable code makes possible to perform massive numerical simulation of the Hasselmann equation with different models of wind input and dissipation. As a result, a strong tendency of numerical solutions to self-similar behavior is shown for rather wide range of wave generation and dissipation conditions. We found very good quantitative coincidence of these solutions with available results on duration-limited growth, as well as with experimental parametrization of fetch-limited spectra JONSWAP in terms of wind-wave age Cp/U10.

UR - http://www.scopus.com/inward/record.url?scp=30744440892&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=30744440892&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:30744440892

VL - 12

SP - 891

EP - 945

JO - Nonlinear Processes in Geophysics

JF - Nonlinear Processes in Geophysics

SN - 1023-5809

IS - 6

ER -