\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

Random walks, random flows, and enhanced diffusivity in advection-diffusion equations

Abstract Related Papers Cited by
  • We study the phenomenon of enhanced diffusivity, introduced by G. I.Taylor, for a class of advection-diffusion equations, modeling, for example, the spread of an ink drop in a fluid engaged in Poiseuille flow. We consider such flow in a pipe of general cross section, and compute variances and covariances of certain random flows associated with the advection-diffusion. We examine both long time behavior, including a central limit theorem, and short time asymptotics.
    Mathematics Subject Classification: Primary: 35K20, 35Q30; Secondary: 60J60.

    Citation:

    \begin{equation} \\ \end{equation}
  • [1]

    M. Avellaneda and A. Majda, An integral representation and bounds on the effective diffusivity in passive advective diffusion by laminar and turbulent flows, Commun. Math. Phys., 138 (1991), 339-391.

    [2]

    R. Camassa, Z. Lin and R. McLaughlin, The exact evolution of the scalar variance in pipe and channel flow, Commun. Math. Sci., 8 (2010), 601-626.

    [3]

    S. Goldstein, On diffusion by discontinuous movements and on the telegraph equation, Quart. J. Mech. Appl. Math., 4 (1951), 129-156.doi: 10.1093/qjmam/4.2.129.

    [4]

    R. Griego and R. Hersh, Theory of random evolutions with applications to partial differential equations, Trans. AMS, 156 (1971), 405-418.doi: 10.1090/S0002-9947-1971-0275507-7.

    [5]

    A. Majda and P. Kramer, Simplified models for turbulent diffusion: Theory, numerical modelling, and physical phenomena, Physics Reports, 314 (1999), 237-574.doi: 10.1016/S0370-1573(98)00083-0.

    [6]

    A. Mazzucato and M. Taylor, Vanishing viscosity limits for a class of circular pipe flows, Commun. PDE, 36 (2012), 328-361.doi: 10.1080/03605302.2010.505973.

    [7]

    M. Pinsky, "Lectures on Random Evolution,'' World Scientific, London, 1991.

    [8]

    G. I. Taylor, Dispersion of soluble matter in solvent flowing slowly through a tube, Proc. Roy. Soc. London A, 219 (1953), 186-203.doi: 10.1098/rspa.1953.0139.

    [9]

    M. Taylor, "Partial Differential Equations,'' Vols. 1-3, Springer-Verlag, New York, 1996.

  • 加载中
SHARE

Article Metrics

HTML views() PDF downloads(62) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return