Mechanism of vorticity amplification by elastic waves in a viscoelastic channel flow

Abstract

Inertia-less viscoelastic channel flow displays a supercritical nonnormal mode elastic instability due to finite-size perturbations despite its linear stability. The nonnormal mode instability is determined mainly by a direct transition from laminar to chaotic flow, in contrast to normal mode bifurcation leading to a single fastest-growing mode. At higher velocities, transitions to elastic turbulence and further drag reduction flow regimes occur accompanied by elastic waves in three flow regimes. Here, we demonstrate experimentally that the elastic waves play a key role in amplifying wall-normal vorticity fluctuations by pumping energy, withdrawn from the mean flow, into wall-normal fluctuating vortices. Indeed, the flow resistance and rotational part of the wall-normal vorticity fluctuations depend linearly on the elastic wave energy in three chaotic flow regimes. The higher (lower) the elastic wave intensity, the larger (smaller) the flow resistance and rotational vorticity fluctuations. This mechanism was suggested earlier to explain elastically driven Kelvin–Helmholtz-like instability in viscoelastic channel flow. The suggested physical mechanism of vorticity amplification by the elastic waves above the elastic instability onset recalls the Landau damping in magnetized relativistic plasma. The latter occurs due to the resonant interaction of electromagnetic waves with fast electrons in the relativistic plasma when the electron velocity approaches light speed. Moreover, the suggested mechanism could be generally relevant to flows exhibiting both transverse waves and vortices, such as Alfven waves interacting with vortices in turbulent magnetized plasma, and Tollmien–Schlichting waves amplifying vorticity in both Newtonian and elasto-inertial fluids in shear flows.