Markov process built in scale-similar multifractal energy cascades in turbulence.
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 mu(q), and they are all constant if the cascade is scale similar.
Hosokawa
Iwao
I
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