Self-sustained elastoinertial Tollmien–Schlichting waves

Shekar, Ashwin; McMullen, Ryan; McKeon, Beverley; Graham, Michael D.

doi:10.1017/jfm.2020.372

Cited by 35 publications

(61 citation statements)

References 46 publications

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“…Recently, in the research community of viscoelastic flows, elasto-inertial turbulence (EIT) has received much attention owing to its unique flow features relevant to the MDR (maximum drag reduction, an asymptotic statistical state first discussed by Virk 1975), and has been investigated experimentally and numerically by many researchers (Dubief, Terrapon & Soria 2013;Samanta et al 2013;Sid, Terrapon & Dubief 2018;Lopez, Choueiri & Hof 2019;Shekar et al 2019Shekar et al , 2020Page, Dubief & Kerswell 2020;Choueiri et al 2021;Shekar et al 2021), among many others. In the DNS study by Page et al (2020) the exact coherent structures were calculated in subcritical two-dimensional viscoelastic channel flows of FENE-P fluids and the authors demonstrated that the flow possesses a subcritical transition mechanism in terms of both Reynolds number and Weissenberg number.…”

Section: Recent Discussion On the Bifurcation Type In Viscoelastic Flowsmentioning

confidence: 99%

Subcritical and supercritical bifurcations in axisymmetric viscoelastic pipe flows

2021

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Axisymmetric viscoelastic pipe flow of Oldroyd-B fluids has been recently found to be linearly unstable by Garg et al. (Phys. Rev. Lett., vol. 121, 2018, 024502). From a nonlinear point of view, this means that the flow can transition to turbulence supercritically, in contrast to the subcritical Newtonian pipe flows. Experimental evidence of subcritical and supercritical bifurcations of viscoelastic pipe flows have been reported, but these nonlinear phenomena have not been examined theoretically. In this work, we study the weakly nonlinear stability of this flow by performing a multiple-scale expansion of the disturbance around linear critical conditions. The perturbed parameter is the Reynolds number with the others being unperturbed. A third-order Ginzburg–Landau equation is derived with its coefficient indicating the bifurcation type of the flow. After exploring a large parameter space, we found that polymer concentration plays an important role: at high polymer concentrations (or small solvent-to-solution viscosity ratio $\beta \lessapprox 0.785$ ), the nonlinearity stabilizes the flow, indicating that the flow will bifurcate supercritically, while at low polymer concentrations ( $\beta \gtrapprox 0.785$ ), the flow bifurcation is subcritical. The results agree qualitatively with experimental observations where critical $\beta \approx 0.855$ . The pipe flow of upper convected Maxwell fluids can be linearly unstable and its bifurcation type is also supercritical. At a fixed value of $\beta$ , the Landau coefficient scales with the inverse of the Weissenberg number ( $Wi$ ) when $Wi$ is sufficiently large. The present analysis provides a theoretical understanding of the recent studies on the supercritical and subcritical routes to the elasto-inertial turbulence in viscoelastic pipe flows.

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Section: Recent Discussion On the Bifurcation Type In Viscoelastic Flowsmentioning

confidence: 99%

Subcritical and supercritical bifurcations in axisymmetric viscoelastic pipe flows

2021

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“…(2019) and Shekar et al. (2020) proposes a two-dimensional nonlinear mechanism that entails strongly localized polymer stretch fluctuations near the ‘critical layer’ (the transverse location where the phase speed of disturbances equals the local laminar velocity) corresponding to the (least-stable) elastically modified, TS (wall) mode. The second by Page, Dubief & Kerswell (2020) (see also Dubief et al.…”

Section: Introductionmentioning

confidence: 99%

The centre-mode instability of viscoelastic plane Poiseuille flow

et al. 2021

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“…2019; Shekar et al. 2019, 2020). The kinetic energy spectrum in the EIT regime has a scaling, which is distinctly different from the Kolmogorov scaling of for IT but close to the scaling for ET (Fouxon & Lebedev 2003; Groisman & Steinberg 2004; Dubief, Terrapon & Soria 2013; Steinberg 2019).…”

Section: Introductionmentioning

confidence: 99%

A reverse transition route from inertial to elasticity-dominated turbulence in viscoelastic Taylor–Couette flow

et al. 2021

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A high-order transition route from inertial to elasticity-dominated turbulence (EDT) in Taylor–Couette flows of polymeric solutions has been discovered via direct numerical simulations. This novel two-step transition route is realized by enhancing the extensional viscosity and hoop stresses of the polymeric solution via increasing the maximum chain extension at a fixed polymer concentration. Specifically, in the first step inertial turbulence is stabilized to a laminar flow much like the modulated wavy vortex flow. The second step destabilizes this laminar flow state to EDT, i.e. a spatially smooth and temporally random flow with a $-3.5$ scaling law of the energy spectrum reminiscent of elastic turbulence. The flow states involved are distinctly different to those observed in the reverse transition route from inertial turbulence via a relaminarization of the flow to elasto-inertial turbulence in parallel shear flows, underscoring the importance of polymer-induced hoop stresses in realizing EDT that are absent in parallel shear flows.

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Self-sustained elastoinertial Tollmien–Schlichting waves

Cited by 35 publications

References 46 publications

Subcritical and supercritical bifurcations in axisymmetric viscoelastic pipe flows

Subcritical and supercritical bifurcations in axisymmetric viscoelastic pipe flows

The centre-mode instability of viscoelastic plane Poiseuille flow

A reverse transition route from inertial to elasticity-dominated turbulence in viscoelastic Taylor–Couette flow

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