Higher order dynamic mode decomposition of an experimental trailing vortex

Abstract

The decay of trailing vortices is a fundamental problem in fluid mechanics and constitutes the basis of control applications that intend to alleviate the wake hazard. In order to progress, we use the recently developed modal-decomposition technique to identify the governing dynamics in an experimental trailing vortex. A particular emphasis is on the difficulty and usefulness of applying such tools to noisy experi- mental data. We conducted a water-tunnel experiment at a chord-based Reynolds number Re ¼ 4 104 using stereoscopic particle image velocimetry measurements over a downstream range of 36 chords. The downstream evolution of the maximum of vorticity suggests that the whole wake can be partitioned into three consecutive regimes. A higher-order dynamic mode decomposition of the streamwise vorticity in each such part of the wake shows that the decay is well approximated by at most three modes. Additionally, our study provides evidence for the existence of several instabilities after the vortex roll up beyond about 6.5 chords.