Tollmien-Schlichting waves and the Elasto-Inertial Instability

Transition in the flow of highly viscoelastic fluids has its origins in a classical Newtonian flow pattern.

The addition of minute amounts of long, flexible polymers to a liquid causes substantial turbulent drag reduction, the upper limit of which is known as the maximum drag reduction (MDR) asymptote. For low enough flow rates and high enough fluid elasticity, the flow can transition directly from laminar to MDR. Despite the fact that the fluid is strongly viscoelastic, the instability governing this transition can be traced back to the classical Tollmien-Schlichting (TS) waves, which are not typically observed in Newtonian turbulence but are ‘unmasked’ by viscoelasticity. The figure shows a comparison between the structures observed in a direct numerical simulation (DNS) and the TS wave, as well as the most-amplified disturbance, which strongly resembles the TS wave.

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Figure: In all images, top panel: wall-normal velocity, bottom panel: streamwise polymer component. (a) DNS snapshot, (b) phase-averaged Fourier transform of DNS, (c) TS wave, (d) most-amplified 2D disturbance

RM McMullen, Caltech; BJ McKeon, Caltech; A Shekar, University of Wisconsin-Madison; MD Graham, University of Wisconsin-Madison

Funding
NSF: CBET-1510291, AFOSR: FA9550-15-1-0062 and FA9550-18-1-0174 (UW), ONR: N00014-17-1-3022 (Caltech)