Nonlinear hydrodynamic instability and turbulence in pulsatile flow

Abstract

<jats:p>Pulsating flows through tubular geometries are laminar provided that velocities are moderate. This in particular is also believed to apply to cardiovascular flows where inertial forces are typically too low to sustain turbulence. On the other hand, flow instabilities and fluctuating shear stresses are held responsible for a variety of cardiovascular diseases. Here we report a nonlinear instability mechanism for pulsating pipe flow that gives rise to bursts of turbulence at low flow rates. Geometrical distortions of small, yet finite, amplitude are found to excite a state consisting of helical vortices during flow deceleration. The resulting flow pattern grows rapidly in magnitude, breaks down into turbulence, and eventually returns to laminar when the flow accelerates. This scenario causes shear stress fluctuations and flow reversal during each pulsation cycle. Such unsteady conditions can adversely affect blood vessels and have been shown to promote inflammation and dysfunction of the shear stress-sensitive endothelial cell layer.</jats:p>

Non-modal transient growth of disturbances in pulsatile and oscillatory pipe flows

“…Xu et al. (2020) showed that initializing direct numerical simulations with the linear optimal helical disturbance can trigger turbulent flow patterns as those observed in their experiments. In experiments of oscillatory pipe flow, the transition threshold is independent of (with different critical numbers depending on the set-up, see Sergeev 1966; Merkli & Thomann 1975; Hino et al.…”

“…Thomas et al (2011) showed that the linear instability of oscillatory pipe flow persists also for pulsatile flow; however, in experiments, transition occurs much earlier (see e.g. Sarpkaya 1966;Stettler & Hussain 1986;Xu et al 2017Xu et al , 2020. Taken together, these results suggest that pulsatile pipe flow undergoes a subcritical transition to turbulence in all regimes.…”

“…Sarpkaya 1966; Stettler & Hussain 1986; Xu et al. 2017, 2020). Taken together, these results suggest that pulsatile pipe flow undergoes a subcritical transition to turbulence in all regimes.…”

“…Taken together, these results suggest that pulsatile pipe flow undergoes a subcritical transition to turbulence in all regimes. Xu et al (2020) recently reported on a nonlinear instability of pulsatile pipe flow, which occurs at pulsation amplitudes relevant for arterial flow. In their experiments, geometric imperfections triggered a helical wave pattern which emerged cyclically during the deceleration phase and broke down into turbulence, before decaying.…”

Active open-loop control of elastic turbulence

“…Active or dynamic control requires auxiliary energy, while passive or static control requires none 17 . Both control schemes applied to flow patterns and fluid instabilities in Newtonian fluids have extensively been studied [18][19][20][21][22][23][24][25] . Also, passive control of viscoelastic fluid flow has been examined [26][27][28][29][30][31] using either geometric modifications 28,29 including spatially modulated cylinders in a Taylor-Couette geometry 30 and disorder in microfluidic flows to inhibit elastic turbulence 31 , or soft boundaries 27 , as well as thermal control 26 .…”