Corrsin's Hypothesis and Two-Particle Dispersion in Isotropic, Stationary Turbulence

Leif Kristensen, Peter Kirkegaard

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    Abstract

    On the basis of Corrsin’s independence hypothesis, in conjunction with specific assumptions about the form of the distance-neighbour function, an equation is derived for twoparticle dispersion in isotropic turbulence with no mean motion. It is formulated in terms of the mean-square difference between the particle positions r 1(t1) and r2(t2) at arbitrary times t1 and t2 after the release of the particles with a given initial separation. Eddy removal and eddy decay are included with wave-number dependent time scales. The equation, which in general must be solved numerically, has been considered for the scale free k−5/3 energy spectrum as well as for the von K´arm´an spectrum. The model implies that only when the outer scale is infinite, i.e. in the limit where the energy spectrum is of the form k−5/3, will there be a Cεt 3 range of the mean-square separation between the two particles. In this limiting case it is possible to estimate the dimensionless Richardson- Obukhov constant C as a function of a dimensionless eddy-decay parameter. A reasonable choice of this parameter leads to a C-value of the order 1.
    Original languageEnglish
    Place of PublicationRoskilde
    PublisherDanmarks Tekniske Universitet, Risø Nationallaboratoriet for Bæredygtig Energi
    Number of pages27
    ISBN (Print)978-87-550-3748-9
    Publication statusPublished - 2009
    SeriesDenmark. Forskningscenter Risoe. Risoe-R
    Number1691(EN)
    ISSN0106-2840

    Keywords

    • Wind energy
    • Risø-R-1691
    • Risø-R-1691(EN)

    Cite this

    Kristensen, L., & Kirkegaard, P. (2009). Corrsin's Hypothesis and Two-Particle Dispersion in Isotropic, Stationary Turbulence. Danmarks Tekniske Universitet, Risø Nationallaboratoriet for Bæredygtig Energi. Denmark. Forskningscenter Risoe. Risoe-R, No. 1691(EN)