Fabian Hennig

Analysis of structure function equations up to the seventh order

ABSTRACTWe examine balances of structure function equations up to the seventh order N = 7 for longitudinal, mixed and transverse components. Similarly, we examine the traces of the structure function equations, which are of interest because they contain invariant scaling parameters. The trace equations are found to be qualitatively similar to the individual components equations. In the even-order equations, the source terms proportional to the correlation between velocity increments and the pseudo-dissipation tensor are significant, while for odd N, source terms proportional to the correlation of velocity increments and pressure gradients are dominant. Regarding the component equations, one finds under the inertial range assumptions as many equations as unknown structure functions for even N, i.e. can solve for them as function of the source terms. On the other hand, there are more structure functions than equations for odd N under the inertial range assumptions. Similarly, there are not enough linearly ...

Statistical Description of Streamline Segments in a Turbulent Channel Flow with a Wavy Wall

In this study we investigate the statistical properties of so called streamline segments in a turbulent channel flow with one plane and one wavy wall. We give a short overview of the concept of streamline segments and recent results in description and modeling in this field. We find that streamline segments in the vicinity of the wavy wall are significantly smaller on average than in the core region. However, normalizing the length distribution with the mean segment length leads to an almost perfect collapse of the pdfs. This quasi-universal behavior is further highlighted by the comparison to statistics of streamline segments in homogeneous isotropic turbulence. Finally, we investigate the kinematic behavior of streamline segments by means of conditional moments and show differences in scaling behavior compared to the classical structure function analysis.

Geometrical Features of Streamlines and Streamline Segments in Turbulent Flows

Streamlines constitute natural geometries in turbulent flows. In this work streamlines are segmented based on local extrema of the field of the absolute value of the velocity along the streamline coordinate. Streamline segments are parameterized based on their arclength and a theoretical scaling of the mean length with the geometric mean of the Kolmogorov length and the Taylor microscale is derived and found to be in good agreement with direct numerical simulations.