Familiar Patterns in Strongly Viscoelastic Turbulence

We use linear stability techniques and resolvent analysis to give insight into the structure of turbulent flow of a polymer-doped fluid

The addition of minute amounts of long, flexible polymers to a liquid causes substantial turbulent drag reduction. For low enough flow rates and high enough fluid elasticity, the flow transitions to a chaotic state dubbed elastoinertial turbulence (EIT) featuring structures that are very different from those in Newtonian turbulence, most notably highly-localized ‘sheets’ of strong polymer stress fluctuations. Surprisingly, these flow patterns bear striking resemblance to critical-layer structures, i.e., structures localized at the wall-normal location where the disturbance propagation speed equals the background flow velocity, arising from the viscoelastic extension of classical Tollmien-Schlichting waves, which are closely related to the most-amplified 2D disturbances to the laminar state. This suggests the sheet-like structures that are the hallmark of EIT have their origin in similar mechanisms

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Figure: (a) DNS snapshot, (b) phase-averaged Fourier transform of DNS, (c) Tollmien-Schlichting wave, (d) most-amplified 2D disturbance. In all panels line contours are wall-normal velocity, filled contours are streamwise polymer stretching.

References

  1. Ashwin Shekar*, Ryan M McMullen, Sung-Ning Wang*, Beverley J McKeon, and Michael D Graham*. “Critical-Layer Structures and Mechanisms in Elastoinertial Turbulence". Physical Review Letters. 122, 124503 (2019). *University of Wisconsin-Madison