Log-Poisson cascade description of turbulent velocity-gradient statistics

The Log-Poisson phenomenological description of the turbulent energy cascade is evoked to discuss high-order statistics of velocity derivatives and the mapping between their probability distribution functions at different Reynolds numbers. The striking confirmation of theoretical predictions suggests that numerical solutions of the flow obtained at low/moderate Reynolds numbers can play an important quantitative role in the analysis of experimental high Reynolds number phenomena, where small scales fluctuations are in general inaccessible from direct numerical simulations.

Figure 1

(Color online) Experimental velocity-gradient pdfs for atmospheric surface layer flow with $R_{\lambda }=3.4\times {10}^3$. Black (darker) line: $s_{11}$; colored (lighter) lines: $s_{ij}$, with $i\ne j$.

Figure 2

(Color online) Numerical velocity-gradient pdfs for homogeneous isotropic turbulence with $R_{\lambda }=240$. Black lines: diagonal components $s_{ii}$; green (light gray) lines: nondiagonal components $s_{ij}$.

Figure 3

Comparison between the numerical ($R_{\lambda }=240$; solid line) and the experimental ($R_{\lambda }=3.4\times {10}^3$; dots) pdfs of $s_{11}$.

Figure 4

Comparison between the numerical ($R_{\lambda }=240$; solid line) and the experimental ($R_{\lambda }=3.4\times {10}^3$; dots) pdfs of $s_{23}$.

Figure 5

(Color online) The numerically reconstructed pdf of $s_{11}$ (black solid line) is compared to the experimental pdf (red circles).

Figure 6

(Color online) The numerically reconstructed pdf of $s_{23}$ (black solid line) is compared to the experimental pdfs of $s_{ij}$, with $i\ne j$ (colored symbols).

Figure 7

The numerically reconstructed pdf of $s_{11}$ (solid line) is compared to the experimental pdf (dots) in linear scales.

Figure 8

The numerically reconstructed pdf of $s_{23}$ is compared to the experimental pdf (dots) in linear scales.