Sharp vorticity gradients in two-dimensional turbulence and the energy spectrum

    Research output: Contribution to journalJournal articleResearchpeer-review

    Abstract

    Formation of sharp vorticity gradients in two-dimensional (2D) hydrodynamic turbulence and their influence on the turbulent spectra are considered. The analog of the vortex line representation as a transformation to the curvilinear system of coordinates moving together with the di-vorticity lines is developed and compressibility of this mapping appears as the main reason for the formation of the sharp vorticity gradients at high Reynolds numbers. In the case of strong anisotropy the sharp vorticity gradients can generate spectra which fall off as k −3 at large k, which appear to take the same form as the Kraichnan spectrum for the enstrophy cascade. For turbulence with weak anisotropy the k dependence of the spectrum due to the sharp gradients coincides with the Saffman spectrum: E(k) ~ k −4. Numerical investigations of decaying turbulence reveal exponential growth of di-vorticity with a spatial distributed along straight lines. Thus, indicating strong anisotropy and accordingly the spectrum is close to the k −3-spectrum.
    Original languageEnglish
    JournalTheoretical and Computational Fluid Dynamics
    Volume24
    Issue number1-4
    Pages (from-to)253-258
    ISSN0935-4964
    DOIs
    Publication statusPublished - 2010

    Keywords

    • Fusion energy

    Cite this

    @article{be05c6f4174f499dbb4227c5ba687850,
    title = "Sharp vorticity gradients in two-dimensional turbulence and the energy spectrum",
    abstract = "Formation of sharp vorticity gradients in two-dimensional (2D) hydrodynamic turbulence and their influence on the turbulent spectra are considered. The analog of the vortex line representation as a transformation to the curvilinear system of coordinates moving together with the di-vorticity lines is developed and compressibility of this mapping appears as the main reason for the formation of the sharp vorticity gradients at high Reynolds numbers. In the case of strong anisotropy the sharp vorticity gradients can generate spectra which fall off as k −3 at large k, which appear to take the same form as the Kraichnan spectrum for the enstrophy cascade. For turbulence with weak anisotropy the k dependence of the spectrum due to the sharp gradients coincides with the Saffman spectrum: E(k) ~ k −4. Numerical investigations of decaying turbulence reveal exponential growth of di-vorticity with a spatial distributed along straight lines. Thus, indicating strong anisotropy and accordingly the spectrum is close to the k −3-spectrum.",
    keywords = "Fusion energy, Fusionsenergiforskning, Fusionsenergi",
    author = "E.A. Kuznetsov and Volker Naulin and Nielsen, {Anders Henry} and {Juul Rasmussen}, Jens",
    year = "2010",
    doi = "10.1007/s00162-009-0135-4",
    language = "English",
    volume = "24",
    pages = "253--258",
    journal = "Theoretical and Computational Fluid Dynamics",
    issn = "0935-4964",
    publisher = "Springer",
    number = "1-4",

    }

    Sharp vorticity gradients in two-dimensional turbulence and the energy spectrum. / Kuznetsov, E.A.; Naulin, Volker; Nielsen, Anders Henry; Juul Rasmussen, Jens.

    In: Theoretical and Computational Fluid Dynamics, Vol. 24, No. 1-4, 2010, p. 253-258.

    Research output: Contribution to journalJournal articleResearchpeer-review

    TY - JOUR

    T1 - Sharp vorticity gradients in two-dimensional turbulence and the energy spectrum

    AU - Kuznetsov, E.A.

    AU - Naulin, Volker

    AU - Nielsen, Anders Henry

    AU - Juul Rasmussen, Jens

    PY - 2010

    Y1 - 2010

    N2 - Formation of sharp vorticity gradients in two-dimensional (2D) hydrodynamic turbulence and their influence on the turbulent spectra are considered. The analog of the vortex line representation as a transformation to the curvilinear system of coordinates moving together with the di-vorticity lines is developed and compressibility of this mapping appears as the main reason for the formation of the sharp vorticity gradients at high Reynolds numbers. In the case of strong anisotropy the sharp vorticity gradients can generate spectra which fall off as k −3 at large k, which appear to take the same form as the Kraichnan spectrum for the enstrophy cascade. For turbulence with weak anisotropy the k dependence of the spectrum due to the sharp gradients coincides with the Saffman spectrum: E(k) ~ k −4. Numerical investigations of decaying turbulence reveal exponential growth of di-vorticity with a spatial distributed along straight lines. Thus, indicating strong anisotropy and accordingly the spectrum is close to the k −3-spectrum.

    AB - Formation of sharp vorticity gradients in two-dimensional (2D) hydrodynamic turbulence and their influence on the turbulent spectra are considered. The analog of the vortex line representation as a transformation to the curvilinear system of coordinates moving together with the di-vorticity lines is developed and compressibility of this mapping appears as the main reason for the formation of the sharp vorticity gradients at high Reynolds numbers. In the case of strong anisotropy the sharp vorticity gradients can generate spectra which fall off as k −3 at large k, which appear to take the same form as the Kraichnan spectrum for the enstrophy cascade. For turbulence with weak anisotropy the k dependence of the spectrum due to the sharp gradients coincides with the Saffman spectrum: E(k) ~ k −4. Numerical investigations of decaying turbulence reveal exponential growth of di-vorticity with a spatial distributed along straight lines. Thus, indicating strong anisotropy and accordingly the spectrum is close to the k −3-spectrum.

    KW - Fusion energy

    KW - Fusionsenergiforskning

    KW - Fusionsenergi

    U2 - 10.1007/s00162-009-0135-4

    DO - 10.1007/s00162-009-0135-4

    M3 - Journal article

    VL - 24

    SP - 253

    EP - 258

    JO - Theoretical and Computational Fluid Dynamics

    JF - Theoretical and Computational Fluid Dynamics

    SN - 0935-4964

    IS - 1-4

    ER -