arXiv subjects

Achim Reeh

Publications and source records attributed to Achim Reeh.

4 recordsLinked to original sources

arXiv1997

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 $δξ_6^L= -0.21 \pm 0.01$ and $\dx_6^T= -0.43 \pm 0.01$, respectively, independent of $\rel$. Also the generalized extended self similarity exponents $ρ_{p,q} = \dx_p/\dx_q$ 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 $β^L $ and $β^T$ show small but significant dependences on the order of the moment.

chao-dyn↗

arXiv1997

Scaling of the irreducible SO(3)-invariants of velocity correlations in turbulence

The scaling behavior of the SO(3) irreducible amplitudes $d_n^l(r)$ of velocity structure tensors (see L'vov, Podivilov, and Procaccia, Phys. Rev. Lett. (1997)) is numerically examined for Navier-Stokes turbulence. Here, l characterizes the irreducible representation by the index of the corresponding Legendre polynomial, and n denotes the tensorial rank, i.e., the order of the moment. For moments of different order n but with the same representation index l extended self similarity (ESS) towards large scales is found. Intermittency seems to increase with l. We estimate that a crossover behavior between different inertial subrange scaling regimes in the longitudinal and transversal structure functions will hardly be detectable for achievable Reynolds numbers.

chao-dyn↗

arXiv1997

Application of extended self similarity in turbulence

From Navier-Stokes turbulence numerical simulations we show that for the extended self similarity (ESS) method it is essential to take the third order structure function taken with the modulus and called $D_3^*(r)$, rather than the standard third order structure function $D_3(r)$ itself. If done so, we find ESS towards scales larger than roughly 10 eta, where eta is the Kolmogorov scale. If $D_3(r)$ is used, there is no ESS. We also analyze ESS within the Batchelor parametrization of the second and third order longitudinal structure function and focus on the scaling of the transversal structure function. The Re-asymptotic inertial range scaling develops only beyond a Taylor-Reynolds number of about 500.

chao-dyn↗

arXiv1996

Developed turbulence: From full simulations to full mode reductions

Developed Navier-Stokes turbulence is simulated with varying wavevector mode reductions. The flatness and the skewness of the velocity derivative depend on the degree of mode reduction. They show a crossover towards the value of the full numerical simulation when the viscous subrange starts to be resolved. The intermittency corrections of the scaling exponents of the pth order velocity structure functions seem to depend mainly on the proper resolution of the inertial subrange. Universal scaling properties (i.e., independent of the degree of mode reduction) are found for the relative scaling exponents rho which were recently defined by Benzi et al.

chao-dyn↗