Lagrangian Feature Extraction of the Cylinder Wake

Jens Kasten - ZIB, Berlin
Christoph Petz - ZIB, Berlin
Ingrid Hotz - ZIB, Berlin
Gilead Tadmor - Northeastern University, USA
Bernd R. Noack - TU, Berlin
Hans-Christian Hege - ZIB, Berlin

We extract Lagrangian features in the 2-D von-Kármán vortex street behind a circular cylinder. The distance of neighboring fluid particles is monitored with forward and backward time evolution over two shedding periods.

The height of the grey surface represents the maximum of the logarithm of these distances (FTLE in Kasten et al. VMV 2009). Red coloring indicates regions of particle divergence in forward time. Blue regions show convergence. The intersection of both curves marks Lagrangian saddle points (Haller 2001 Phys. D). The direction of the flow field is indicated by lines on the surface. Thus, the mixing of the von-Kármán vortex street is characterized by the Lagrangian saddle points, their attractive and separating invariant manifold "arms" mark domains of particle attraction and separation.

This project was funded by DFG (Deutsche Forschungsgemeinschaft) and the NSF (National Science Foundation).

References

G. Haller, "Distinguished material surfaces and coherent structures in three-dimensional fluid flows." Physica D (2001) 149, 248-277.

An alternative computation method of the FTLE:
Jens Kasten, Christoph Petz, Ingrid Hotz, Bernd R. Noack, Hans-Christian Hege, "Localized Finite-time Lyapunov Exponent for Unsteady Flow Analysis." Accepted for publication in Proceedings of VMV 2009 (Braunschweig, Germany).

Reporters and Editors

Reporters can freely use this image. Credit: Jens Kasten Christoph Petz Ingrid Hotz Gilead Tadmor, Bernd R. Noack, Hans-Christian Hege