A statistical theory on the turbulent diffusion of Gaussian puffs

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    Abstract

    The relative diffusion of a one-dimensional Gaussian cloud of particles is related to a two-particle covariance function Rabsij, τ) = u(xi(t))u(xi(t-τ)-ξij)  in a homogenous and stationary field of turbulence. This two-particle covariance function expresses the velocityy correlation between one particle (i) which at time t is in the position xi and another particle (j), which at the previous time t-τ is displaced the fixed distance ξij relative to xi(t-τ). For ξij = 0, Rabs redouces  to the Lagrangian covariance function of a single particle. Setting, on the other hand, the time lag T equal to zero, a pure Bulerian fixed point covariance function results. Por diffusion tiaes that are saall coapared to the integral tiae scale of the turbulence, siaple expressions are derived for the growth of the clouds standard deviation σ(t)  by assuaing that the wave nuaber spectrua corresponding to the Eulerian space covariance Rabsij,0) Can be expressed as a power law δkP where δ is a constant. For instance, by setting p = -5/3, an initially small cloud is found to growth as σ2(t) = (2r(2/3)δ)3/2 t3  in agreement with Batchelor's (1950) inertial subrange theory. Correspondingly, for the enstrophy cascade subrange in two-dinensional turbulence, for which case P = -3, the theory yields σ2(t) = σ2o exp(σt2), where σo denotes the initial size of the cloud.
    Original languageEnglish
    Place of PublicationRoskilde, Denmark
    PublisherRisø National Laboratory
    Number of pages100
    ISBN (Print)87-550-0897-6
    Publication statusPublished - 1982
    SeriesRisø-M
    Number2327
    ISSN0418-6435

    Keywords

    • Risø-M-2327

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