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 $\rel= 110$ 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 $\delta\zeta_6^L= -0.21 \pm 0.01$ and $\dz_6^T= -0.43 \pm 0.01$, respectively, independent of $\rel$. Also the generalized extended self similarity exponents $\rho_{p,q} = (\zeta_p - \zeta_3 p/3 )/ (\zeta_q - \zeta_3 q/3 )$ 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.