Localized stress amplification in inertialess channel flows of viscoelastic fluids

Understanding viscoelastic flow instabilities: Oldroyd-B and beyond

“…This appears consistent with experimental observations of elastic turbulence in microchannel flows of viscoelastic fluids, where the magnitude of velocity fluctuations decreases downstream before increasing [11,12]. Notably, the large stress amplification is highly localized in space, occurs for spanwise-constant disturbances, and was overlooked in prior studies that used square-integrated measures of disturbance amplification, which are typically applied in nonmodal analysis [312]. The large stress amplification can put the flow into a regime where nonlinear terms are no longer negligible, and this could trigger a transition to elastic turbulence.…”

“…As another example of the richness of the linearized dynamics, recent calculations using localized time-periodic disturbances in plane Poiseuille flow show that polymer-stress fluctuations can be amplified by an order of magnitude while there is only negligible amplification of velocity fluctuations [312]. This appears consistent with experimental observations of elastic turbulence in microchannel flows of viscoelastic fluids, where the magnitude of velocity fluctuations decreases downstream before increasing [11,12].…”

Perspectives on viscoelastic flow instabilities and elastic turbulence

“…Perturbations of the streamwise velocity achieve growth by a factor of O(Wi), while the streamwise component of the polymer stress tensor can be amplified up to O(Wi 2 ) compared to its initial value; the time to reach the maximum val-ues scales as t max ∼ λWi, where λ is the relaxation time of the fluid. Similar to its Newtonian counterpart, the purely elastic non-normal growth theory predicts that the most amplified initial flow structures comprise (almost) streamwise-independent vortices, leading to streamwise-independent streaks [177], although other forms of stress amplification have also been examined more recently [181].…”

Perspectives on viscoelastic flow instabilities and elastic turbulence

“…Perturbations of the streamwise velocity achieve growth by a factor of O(Wi), while the streamwise component of the polymer stress tensor can be amplified up to O(Wi 2 ) compared to its initial value; the time to reach the maximum values scales as t max ∼ λWi, where λ is the relaxation time of the fluid. Similar to its Newtonian counterpart, the purely elastic non-normal growth theory predicts that the most amplified initial flow structures comprise (almost) streamwise-independent vortices, leading to streamwise-independent streaks [169], although other forms of stress amplification have also been examined more recently [173].…”