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arXiv · 2312.10288

Mechanism of stochastic resonance in viscoelastic channel flow

Yuke Li·Victor Steinberg
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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.

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Yuke Li, Victor Steinberg. 2023-12-16. Mechanism of stochastic resonance in viscoelastic channel flow. https://arxiv.org/abs/2312.10288

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