Intermittency in the Navier-Stokes dynamics

Intermittency effects in high Reynolds number turbulence (Re10³–10⁶) are calculated from the Navier-Stokes equation in Fourier-Weierstrass approximation. First, the probability density functions (PDF) of scale resolved turbulent signals is found to be Gaussian for large scales, whereas for smaller scales the PDF changes (in agreement with experiment) to a more and more stretched exponential type. This is due to intermittent small scale fluctuations which are caused by the competition between turbulent energy transfer downscale and viscous energy loss. Second, we calculate the moments of ther-averaged energy dissipation rate _r (x) and theirr-scaling exponents (m/3). Our results well agree with experiment and numerical simulations of the full Navier-Stokes equations ((2)=0.29±0.02). We analytically show that the common identification between the (m/3) and the corrections (m) to classical scaling of the velocity structure functions (Kolmogorov's refined similarity hypothesis) is doubtful, because even Gaussian ₁ u ₁-PDFs (characterizing non intermittent flow) lead to (m/3)0.