There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.
Abstract
We propose a generalization of Hopf fibrations to quotient the streamwise translation
symmetry of turbulent pipe flows viewed as dynamical systems. In particular, we exploit
the geometric structure of the associate high dimensional state space, which is that
of a principal fiber bundle. The relation between the comoving frame velocity \(U_{d}\)
associated with the dynamical phase of an orbit in the bundle and the Taylor's hypothesis
is investigated. As an application, Laser-Induced-Fluorescence techniques are exploited
to capture planar fluorescent dye concentration fields tracing a turbulent pipe flow
at the bulk Reynolds number \(\mathfrak{\mathsf{Re}}=3200\). The symmetry reduction
analysis of the experimental data reveals that the speed \(u\) of dye concentration
bursts is associated with the dynamical and geometric phases of the corresponding
orbits in the fiber bundle. In particular, in the symmetry-reduced frame we unveil
a pattern-changing dynamics of the passive scalar structures, which explains the observed
speed \(u\approx U_{d}+U_{g}\) of intense bursting events in terms of the geometric
phase velocity \(U_{g}\approx0.43U_{d}\) associated with the orbits in the bundle.