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Lognormal hypothesis and distribution of energy dissipation in intermittent turbulence

In: Multifractals and 1/ƒ Noise

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  • Benoit B. Mandelbrot

    (Yale University, Mathematics Department
    IBM T.J. Watson Research Center)

Abstract

Obukhov, Kolmogorov and others argued that energy dissipation in intermittent turbulence is lognormally distributed. This hypothesis is shown to be untenable: depending upon the precise formulation chosen, it is either unverifiable or inconsistent. The paper proposes a variant of the generating model leading to the lognormal. This variant is consistent, appears tractable, and for sufficiently small values of its unique parameter μ it yields the lognormal hypothesis as a good approximation. As μ increases, the approximation worsens, and for high enough values of μ, the turbulence ends by concentrating in very few huge “blobs.” Still other consistent alternative models of intermittency yield distributions that differ from the lognormal in the opposite direction; these various models in combination suggest several empirical tests.

Suggested Citation

  • Benoit B. Mandelbrot, 1999. "Lognormal hypothesis and distribution of energy dissipation in intermittent turbulence," Springer Books, in: Multifractals and 1/ƒ Noise, chapter 0, pages 294-316, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-2150-0_14
    DOI: 10.1007/978-1-4612-2150-0_14
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