From laminar to chaotic flow via stochastic resonance in viscoelastic channel flow

Abstract

Recent research indicates that low-inertia viscoelastic channel flow experiences supercritical non-normal mode elastic instability from laminar to sustained chaotic flow due to finite-size perturbations. The challenge of this study is to elucidate a realization of such a pathway when the intensity of the elastic wave is too low to amplify velocity fluctuations above the instability onset. The study identifies two subregions in the transition flow regime at Weissenberg number $Wi>Wi_c$, the instability onset. In the lower subregion at $Wi_c\leq Wi\leq 300$, we discover periodic spikes in the streamwise velocity time series $u(t)$ that appear in the chaotic power spectrum as low-frequency, high-intensity peaks resembling stochastic resonance (SR). In contrast, the spanwise velocity power spectrum, $E_w$, remains flat with low-intensity, noisy, and broad elastic wave peaks. The spikes significantly distort the probability density function of $u$, initiating and amplifying random streaks and wall-normal vorticity fluctuations. The SR appearance is similar to dynamical systems where chaotic attractor and limit cycle interact with external white noise. This similarity is confirmed by presenting a phase portrait in two subregions of the transition regime. In the upper subregion at $Wi>400$ the periodic spikes disappear and $E_w$ becomes chaotic with a large intensity elastic wave sufficient to self-organize and synchronize the streaks into cycles and to amplify the wall normal vorticity according to a recently proposed mechanism.