Different intermittency for longitudinal and transversal turbulent fluctuations

Scaling exponents of the longitudinal and transversal velocity structure functions in numerical Navier-Stokes turbulence simulations with Taylor-Reynolds numbers up to $\text{rel}=110$ are determined by the extended self similarity method. We find significant differences in the degree of intermittency: For the sixth moments the scaling corrections to the classical Kolmogorov expectations are $\delta {\xi }_6^L=-0.21\pm 0.01$ and $\dx_6^T= -0.43 \pm 0.01$,respectively,independentof$\rel$. Also the generalized extended self similarity exponents ${\rho }_{p,q}={\text{dx}}_p\mathrm{/}{\text{dx}}_q$ differ significantly for the longitudinal and transversal structure functions. Within the She-Leveque model this means that longitudinal and transversal fluctuations obey different types of hierarchies of the moments. Moreover, the She-Leveque model hierarchy parameters ${\beta }^L$ and ${\beta }^T$ show small but significant dependences on the order of the moment.