Open AccessFractional derivative dynamics of intermittent turbulence
Author(s) -
Shida Liu,
Zuntao Fu,
Liu Shi-Kuo
Publication year - 2014
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.63.074701
Subject(s) - turbulence , k epsilon turbulence model , k omega turbulence model , homogeneous isotropic turbulence , turbulence modeling , physics , fractional calculus , kolmogorov microscales , reynolds decomposition , diffusion , statistical physics , mathematical analysis , mathematics , direct numerical simulation , mechanics , thermodynamics , reynolds number , quantum mechanics
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.