Some remarks on modelling the PDF of the concentration of a dispersing scalar in turbulence

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Chatwin, P.C. (2002)
  • Publisher: Cambridge University Press
  • Subject:
    arxiv: Physics::Fluid Dynamics

The paper deals with the probability density function (PDF) of the concentration of a scalar within a turbulent flow. Following some comments about the overall structure of the PDF, and its approach to a limit at large times, attention focusses on the so-called small scale mixing term in the evolution equation for the PDF. This represents the effect of molecular diffusion in reducing concentration uctuations, eventually to zero. Arguments are presented which suggest that this quantity could, in certain circumstances, depend inversely upon the PDF, and a particular example of this leads to a new closure hypothesis. Consequences of this, especially similarity solutions, are explored for the case when the concentration field is statistically homogeneous.
  • References (35)
    35 references, page 1 of 4

    [1] Batchelor, G. K. (1952) The effect of homogeneous turbulence on material lines and surfaces. Proc. Roy. Soc. A 213, 349-366.

    [2] Borghi, R. (1988) Turbulent combustion modelling. Prog. Energy Combust. Sci. 14, 245-292.

    [3] Chatwin, P. C., Lewis, D. M. & Mole, N. (1996) Atmospheric diffusion: some new mathematical models. Adv. in Comp. Maths. 6, 227-242.

    [4] Chatwin, P. C., Lewis D. M. & Sullivan, P. J. (1995) Turbulent dispersion and the beta distribution. Environmetrics, 6, 395-402.

    [5] Chatwin, P. C. & Zimmerman, W. B. (1998) The probability structure associated with a simple model of turbulent dispersion. Environmetrics, 9, 131-138.

    [6] Corrsin, S. (1959) Outline of some topics in homogeneous turbulent flow. J. Geophys. Res. 64, 2134-2150.

    [7] Dahm, W. J. A., Southerland, K. B. & Buch, K. A. (1991) Direct, high resolution, fourdimensional measurements of the fine scale structure of S c ≫ 1 molecular mixing in turbulent flows. Phys. Fluids A, 3, 1115-1127.

    [8] Dopazo, C. (1975) Probability density function approach for a turbulent axisymmetric heated jet. Centreline evolution. Phys. Fluids, 18, 397-404.

    [9] Dopazo, C. (1994) Recent developments in pdf methods. In: P. A. Libby and F. A. Williams, editors, Turbulent Reacting Flows, pp. 375-474. Academic Press.

    [10] Eswaran, V. & Pope, S. B. (1988) Direct numerical simulations of the turbulent mixing of a passive scalar. Phys. Fluids, 31, 506-520.

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