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Fractional derivative dynamics of intermittent turbulence

Liu Shi-Da Fu Zun-Tao Liu Shi-Kuo

Fractional derivative dynamics of intermittent turbulence

Liu Shi-Da, Fu Zun-Tao, Liu Shi-Kuo
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  • Abstract views:  1224
  • PDF Downloads:  821
  • Cited By: 0
Publishing process
  • Received Date:  04 September 2013
  • Accepted Date:  25 December 2013
  • Published Online:  05 April 2014

Fractional derivative dynamics of intermittent turbulence

  • 1. Department of Atmospheric and Oceanic Sciences and Laboratory for Climate and Ocean-Atmosphere Studies, School of Physics, Peking University, Beijing 100871, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant No. 40975027).

Abstract: Intermittent turbulence means that the turbulence eddies do not fill the space completely, so the dimension of an intermittent turbulence takes the values between 2 and 3. Turbulence diffusion is a super-diffusion, and the probability of density function is fat-tailed. In this paper, the viscosity term in the Navier-Stokes equation will be denoted as a fractional derivative of Laplatian operator. Dimensionless analysis shows that the order of the fractional derivative α is closely related to the dimension of intermittent turbulence D. For the homogeneous isotropic Kolmogorov turbulence, the order of the fractional derivatives α=2, i.e. the turbulence can be modeled by the integer order of Navier-Stokes equation. However, the intermittent turbulence must be modeled by the fractional derivative of Navier-Stokes equation. For the Kolmogorov turbulence, diffusion displacement is proportional to t3, i.e. Richardson diffusion, but for the intermittent turbulence, diffusion displacement is stronger than Richardson diffusion.

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