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A new probabilistic description for intermittent turbulence: Internal time

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  • Nagata, Ken-ichi
  • Katsuyama, Tomoo

Abstract

A new fractal model for intermittent turbulence is constructed on the basis of a hierarchical velocity-correlation function which represents a self-similar structure of turbulence. The hierarchy is assumed to be obtained by a class of transformations, such as the baker transformation. The hierarchical function allows describing stochastically the nonlinear dissipative dynamics of intermittent turbulence. The probabilistic description is done with time scales which have such a concept of age that the stronger the fluctuation is the younger it is in age. The velocity-correlation function which is observed in turbulent flow is expressed as having statistical weights proportional to the time scales. We propose that the time scale, called “internal time”, exists in the nonlinear dissipative dynamics of turbulence. A degree of intermittency is governed by the internal time. The numerical results of the one-dimensional energy spectrum function agree well over equilibrium range with experimental results. Mandelbrot's fractal dimension takes values ranging from 2.3 to 2.7 for the experimental results.

Suggested Citation

  • Nagata, Ken-ichi & Katsuyama, Tomoo, 1989. "A new probabilistic description for intermittent turbulence: Internal time," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 155(3), pages 585-603.
    • Handle: RePEc:eee:phsmap:v:155:y:1989:i:3:p:585-603
    DOI: 10.1016/0378-4371(89)90007-1
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    References listed on IDEAS

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    1. Misra, B. & Prigogine, I. & Courbage, M., 1979. "From deterministic dynamics to probabilistic descriptions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 98(1), pages 1-26.
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