Mechanism of stochastic resonance in viscoelastic channel flow
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866911873485504512 |
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| author | Li, Yuke Steinberg, Victor |
| author_facet | Li, Yuke Steinberg, Victor |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_10288 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Mechanism of stochastic resonance in viscoelastic channel flow Li, Yuke Steinberg, Victor Fluid Dynamics 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. |
| title | Mechanism of stochastic resonance in viscoelastic channel flow |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2312.10288 |