Prandtl Lecture

Norbert Peters (RWTH Aachen): Turbulence statistics along gradient trajectories

Monday, April 18, 2011, 10:00 - 10:45, Stefaniensaal

Kolmogorov's 1941 theory predicts that in isotropic homogeneous turbulence the two-point difference of velocity fluctuations ∆u, the so-called velocity increment, taken at a sufficiently large distance apart, scales with the third root of that distance. Since then this scaling prediction has been confirmed by comparison with many straight-line experimental data sets in turbulent flows. Only recently have high resolution Direct Numerical Simulations made it possible to test this scaling for curved lines such as gradient trajectories which are determined by the flow itself. Exploring the two-point correlation of the scalar gradient along such trajectories, which decorrelates at large distances, and using arguments very similar to those that led to Kolmogorov's 4/5 law, it was recently found by Lipo Wang [1] that ∆u scales linearly with the arclength distance along the trajectory. This has consequences for the modeling of the length distribution of dissipation elements [2], [3].

Dissipation elements are defined as the spatial region from which the same pair of maximum and minimum points in a scalar field is reached.

By calculating gradient trajectories starting from every grid cell in direction of ascending and descending scalar gradients a local maximum and a local minimum point is reached.

In the seminar the motivation to study them and recent results are presented. In particular the derivation of an evolution equation for the length distribution function and the relation to scaling laws are discussed. A particular point of interest is the testing of the model equation for the mean dissipation, which is often used in engineering applications.

[1] L. Wang, Phys. Rev. E 79, 046325 (2009)

[2] L. Wang, N. Peters, J. Fluid Mech. 554 (2006) 457-475

[3] L. Wang. N. Peters, J. Fluid Mech. 608 (2008) 113-138