Mechanism of stochastic resonance in viscoelastic channel flow

Abstract

We have recently discovered stochastic resonance (SR) in chaotic inertia-less viscoelastic channel flow. SR appears just above a pure elastic instability at a critical Weissenberg number, $Wi_c=150$, of a transition regime. In this lower sub-region up to $Wi\sim 300$, only the streamwise velocity, $u$, exhibits a chaotic spectrum, $E_u$, while the spanwise velocity continues to exhibit white noise, verified by its flat spectrum, $E_w$, accompanied by weak intensity elastic waves. However, SR vanishes at the upper limit at $Wi\sim 300$, when $E_w$ becomes chaotic, indicating $Wi$ as the control parameter. Here we clarify the mechanism of SR emergence by validating the control parameters, namely $Wi$ and the rms velocity fluctuations, $u_{rms}$, measured at multiple channel locations, which determine the range of SR existence. Our experiments verify three key ingredients of the SR mechanism: chaotic $E_u$, white noise $E_w$, and weak elastic waves, which are consistent with three constituents of autonomous dynamical systems exhibiting SR.