Revealing the shape of turbulence in channel flows

The proposed research focuses on a novel geometric approach to study Navier- Stokes turbulence. In the last century, the study of turbulence has been ap- proached 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. This 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 a 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. Removing the translational (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, or geometric velocity. Thus, in strong turbulence, the Taylor’s hypothesis (Taylor, 1938) of frozen vortices is not satisfied because the geometric velocities can be significant. In my PhD work, I aim at revealing the shape of turbulence in channel flows. In particular, I study how vortices change shape as they are transported by the mean flow, and how these shape- changing dynamics influence their own motion. This study yields the discovery that the geometric velocity, induced by vortex shape changes, is the physical manifestation of hidden wave-like dispersion properties of turbulence.