Non-Hermitian hydrodynamics of viscoelastic channel flow

Speaker:Victor Steinberg
Affiliation:Weizmann Institute
Time:14:30 - 15:30
Location:Lidow Rosen Auditorium (323)

I present experimental results on polymer solution planar channel flow that is a development for the last several years. First, I shortly described viscoelastic flows with curved streamlines, where super- or subcritical elastic linear normal mode instabilities at Wic are observed and characterized, and the elastic instability mechanism has been explained and validated experimentally. Further, at Wi>>Wic, “elastic turbulence” (ET), a spatially smoothed chaotic flow occurred via secondary instability, is discovered, characterized experimentally and explained theoretically. However, inertia-less, viscoelastic channel flow, proven linearly stable similar to Newtonian parallel shear flows,  exhibits a non-normal mode, elastic instability, driven by finite-size perturbations from laminar directly to chaotic flow, different from ET, at Wi>Wic,, in transitional flow regime. At secondary instability also via a non-normal instability, ET is observed, and further to unexpected drag reduction (DR) flow regime. Thus, three chaotic flow regimes are observed accompanied by elastic waves discovered and characterized earlier. Furthermore, in all flow regimes, counter-propagating streaks of stream-wise velocity fluctuations self–organized into cycling self-sustained process and synchronized by the elastic waves, are noticed. This surprising finding, ET together with DR and streaks, provides the evidence that the elastic waves play the key role in energy transfer from the main flow to wall-normal fluctuating vortices. Further, we suggest and experimentally validate a mechanism of amplification of wall-normal fluctuating vortices by the elastic waves in viscoelastic channel flow, which also provides the explanation of occurring DR, where the role of the elastic waves turns out to be decisive. Finally, we report about stochastic resonance, discovered recently in inertia-less channel flow of polymer solution just above Wic, and its role in the pathway to a chaotic flow.