Stochastic resonance (SR), the phenomenon discovered more than 40 years ago in bistable nonlinear dynamical systems in the presence of weak periodic forcing and external noise, results in strong amplification of the periodic signal, though at shifted frequency. Recently we reported the SR discovery in inertialess viscoelastic channel flow just above pure elastic instability onset in a limited lower subrange of the transition chaotic flow regime, where a sharp high-energy peak in the streamwise velocity chaotic power spectrum, $E_u$, is observed unexpectedly. The spanwise velocity power spectrum, $E_w$, remains flat, indicating white noise, and is accompanied by weak intensity elastic waves. These three necessary conditions for the SR emergence are consistent with those found in autonomous deterministic dynamical systems exhibiting deterministic stochastic resonance (DSR). Notably, DSR disappears in the upper subrange of the transition regime, where $E_w$ becomes chaotic followed by strongly increased elastic wave intensity. Here we clarify the mechanism of DSR emergence by experimentally verifying three key ingredients of the DSR mechanism: chaotic $E_u$, flat white noise $E_w$, and weak elastic waves at multiple channel locations. Finally, we present a DSR existence range as a function of $\mathrm{Wi}$ and $u_{\mathrm{rms}}$, the root mean square of streamwise velocity fluctuations along the channel length, as another control parameter.

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• Elastic waves
• Low Reynolds number flows
• Nonlinear dynamics in fluids
• Shear flows
• Complex fluids
• Flow instability
• Non-Newtonian fluids
• Polymer solutions
• Rheological properties
• Viscoelasticity
• Rheology