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Self-sustained elastoinertial Tollmien–Schlichting waves

Published online by Cambridge University Press:  09 June 2020

Ashwin Shekar ,
Ryan M. McMullen ,
Beverley J. McKeon Open the ORCID record for Beverley J. McKeon [Opens in a new window]  and
Michael D. Graham Open the ORCID record for Michael D. Graham [Opens in a new window]
Ashwin Shekar
Affiliation:
Department of Chemical and Biological Engineering, University of Wisconsin–Madison, Madison, WI53706, USA
Ryan M. McMullen
Affiliation:
Graduate Aerospace Laboratories, California Institute of Technology, Pasadena, CA91125, USA
Beverley J. McKeon
Affiliation:
Graduate Aerospace Laboratories, California Institute of Technology, Pasadena, CA91125, USA
Michael D. Graham*
Affiliation:
Department of Chemical and Biological Engineering, University of Wisconsin–Madison, Madison, WI53706, USA
*
†Email address for correspondence: mdgraham@wisc.edu
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Abstract

Direct simulations of two-dimensional plane channel flow of a viscoelastic fluid at Reynolds number $Re=3000$ reveal the existence of a family of attractors whose structure closely resembles the linear Tollmien–Schlichting (TS) mode, and in particular exhibits strongly localized stress fluctuations at the critical layer position of the TS mode. At the parameter values chosen, this solution branch is not connected to the nonlinear TS solution branch found for Newtonian flow, and thus represents a solution family that is nonlinearly self-sustained by viscoelasticity. The ratio between stress and velocity fluctuations is in quantitative agreement for the attractor and the linear TS mode, and increases strongly with Weissenberg number, $\mathit{Wi}$. For the latter, there is a transition in the scaling of this ratio as $\mathit{Wi}$ increases, and the $\mathit{Wi}$ at which the nonlinear solution family comes into existence is just above this transition. Finally, evidence indicates that this branch is connected through an unstable solution branch to two-dimensional elastoinertial turbulence (EIT). These results suggest that, in the parameter range considered here, the bypass transition leading to EIT is mediated by nonlinear amplification and self-sustenance of perturbations that excite the TS mode.

JFM classification

Flow Control: Drag reduction Turbulent Flows: Turbulent transition
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 897 , 25 August 2020 , A3
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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