ON THE TORIC SYMMETRY OF TURBULENT CHANNEL FLOWS

In the last century, the study of turbulence has been approached following the great Kolmogorov's physical insights on the inertial energy cascade and, more recently by investigating the geometry of the state space of the Navier-Stokes equations treated as a dynamical system. Such novel geometric approach arises from the evidence that what is observed in physical space sometimes is not always suggestive of the hidden laws of physics of the turbulent motion. Thus, looking at the turbulent dynamics in state space may lead to new understanding of the associated physical processes. In particular, vortices in a channel flow change shape as they are transported by the mean flow at the Taylor speed, or dynamical velocity. Reducing the translational or Toric symmetry in state space reveals that the shape-changing dynamics of vortices influences their own motion and it induces an additional self-propulsion velocity, the so-called geometric velocity. Thus, in strong turbulence the Taylor's hypothesis of frozen vortices is not satisfied because the geometric velocity can be significant.