Weak turbulent Kolmogorov spectrum for surface gravity waves

A. I. Dyachenko; A. O. Korotkevich; V. E. Zakharov

doi:10.1103/PhysRevLett.92.134501

Weak turbulent Kolmogorov spectrum for surface gravity waves

A. I. Dyachenko, A. O. Korotkevich, V. E. Zakharov

Research output: Contribution to journal › Article › peer-review

82 Scopus citations

Abstract

The evolution of surface gravity waves on deep water excited by a stochastic external force concentrated in small wave number was studied. The primitive Eular equations were implemented for the potential flow of an ideal fluid with free surface written in hamiltonian canonical varibles. The growth of wave energy due to stochastic external force was arrested by nonlinear resonant four-wave processes, which leads to formation of powerlike Kolmogorov spectrum. It was found that, for the different pumping level surface elevation spectra differ only due to the different energy flux.

Original language	English (US)
Article number	134501
Pages (from-to)	134501-1-134501-4
Journal	Physical review letters
Volume	92
Issue number	13
DOIs	https://doi.org/10.1103/PhysRevLett.92.134501
State	Published - Apr 2 2004
Externally published	Yes

ASJC Scopus subject areas

General Physics and Astronomy

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10.1103/PhysRevLett.92.134501

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title = "Weak turbulent Kolmogorov spectrum for surface gravity waves",

abstract = "The evolution of surface gravity waves on deep water excited by a stochastic external force concentrated in small wave number was studied. The primitive Eular equations were implemented for the potential flow of an ideal fluid with free surface written in hamiltonian canonical varibles. The growth of wave energy due to stochastic external force was arrested by nonlinear resonant four-wave processes, which leads to formation of powerlike Kolmogorov spectrum. It was found that, for the different pumping level surface elevation spectra differ only due to the different energy flux.",

author = "Dyachenko, {A. I.} and Korotkevich, {A. O.} and Zakharov, {V. E.}",

note = "Funding Information: This work was supported by ONR Grant No. N00014-03-1-0648, RFBR Grant No. 03-01-00289, INTAS Grant No. 00-292, the Programme “Nonlinear dynamics and solitons” from the RAS Presidium and “Leading Scientific Schools of Russia” grant, the U.S. Army Corps of Engineers Grant No. DACW 42-03-C-0019, and the NSF Grant No. NDMS0072803. Also the authors thank the creators of the open-source fast Fourier transform library FFTW for this fast, portable, and completely free piece of software.",

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doi = "10.1103/PhysRevLett.92.134501",

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AU - Korotkevich, A. O.

AU - Zakharov, V. E.

N1 - Funding Information: This work was supported by ONR Grant No. N00014-03-1-0648, RFBR Grant No. 03-01-00289, INTAS Grant No. 00-292, the Programme “Nonlinear dynamics and solitons” from the RAS Presidium and “Leading Scientific Schools of Russia” grant, the U.S. Army Corps of Engineers Grant No. DACW 42-03-C-0019, and the NSF Grant No. NDMS0072803. Also the authors thank the creators of the open-source fast Fourier transform library FFTW for this fast, portable, and completely free piece of software.

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Y1 - 2004/4/2

N2 - The evolution of surface gravity waves on deep water excited by a stochastic external force concentrated in small wave number was studied. The primitive Eular equations were implemented for the potential flow of an ideal fluid with free surface written in hamiltonian canonical varibles. The growth of wave energy due to stochastic external force was arrested by nonlinear resonant four-wave processes, which leads to formation of powerlike Kolmogorov spectrum. It was found that, for the different pumping level surface elevation spectra differ only due to the different energy flux.

AB - The evolution of surface gravity waves on deep water excited by a stochastic external force concentrated in small wave number was studied. The primitive Eular equations were implemented for the potential flow of an ideal fluid with free surface written in hamiltonian canonical varibles. The growth of wave energy due to stochastic external force was arrested by nonlinear resonant four-wave processes, which leads to formation of powerlike Kolmogorov spectrum. It was found that, for the different pumping level surface elevation spectra differ only due to the different energy flux.

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Weak turbulent Kolmogorov spectrum for surface gravity waves

Abstract

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