Phys. Rev. E 65, 027301 (2002) [2 pages]Markov process built in scale-similar multifractal energy cascades in turbulenceReceived 14 May 2001; revised 8 October 2001; published 16 January 2002 The scale-similar multifractal cascade, which is believed to describe the process of energy cascade in the inertial scale-range of isotropic turbulence, is proved to be Markovian so as to be governed by the Chapman-Kolmogorov equation, when negative logarithmic length scale is taken for time. For a limited class of cascades, the Kramers-Moyal expansion of the Chapman-Kolmogorov equation is possible and the coefficients are exactly derived from the functional form of intermittency exponents μ(q), and they are all constant if the cascade is scale similar. © 2002 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevE.65.027301
DOI:
10.1103/PhysRevE.65.027301
PACS:
47.27.Gs, 47.27.Jv, 47.53.+n, 02.50.-r
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