# Critical-Layer Structures and Mechanisms in Elastoinertial Turbulence.

@article{Shekar2018CriticalLayerSA, title={Critical-Layer Structures and Mechanisms in Elastoinertial Turbulence.}, author={Ashwin Shekar and Ryan Michael McMullen and Sung-Ning Wang and Beverley J. McKeon and Michael D. Graham}, journal={Physical review letters}, year={2018}, volume={122 12}, pages={ 124503 } }

Simulations of elastoinertial turbulence (EIT) of a polymer solution at low Reynolds number are shown to display localized polymer stretch fluctuations. These are very similar to structures arising from linear stability (Tollmien-Schlichting modes) and resolvent analyses, i.e., critical-layer structures localized where the mean fluid velocity equals the wave speed. Computations of self-sustained nonlinear Tollmien-Schlichting waves reveal that the critical layer exhibits stagnation points that…

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## References

SHOWING 1-10 OF 38 REFERENCES

### Simulations of natural transition in viscoelastic channel flow

- PhysicsJournal of Fluid Mechanics
- 2017

Orderly, or natural, transition to turbulence in dilute polymeric channel flow is studied using direct numerical simulations of a FENE-P fluid. Three Weissenberg numbers are simulated and contrasted…

### Transition to turbulence in two-dimensional Poiseuille flow

- Physics, EngineeringJournal of Fluid Mechanics
- 1990

The transition of strictly two-dimensional Poiseuille flow from laminar to chaotic behaviour is studied through full numerical simulation of spatially periodic channels with fairly large longitudinal…

### On the mechanism of elasto-inertial turbulence.

- PhysicsPhysics of fluids
- 2013

Elasto-inertial turbulence provides new insights on the nature of the asymptotic state of polymer drag reduction (maximum drag reduction), and explains the phenomenon of early turbulence, or onset of turbulence at lower Reynolds numbers than for Newtonian flows observed in some polymeric flows.

### Viscoelastic Pipe Flow is Linearly Unstable.

- Physics, EngineeringPhysical review letters
- 2018

This work reports, for the first time, a linear instability of pressure-driven pipe flow of a viscoelastic fluid, obeying the Oldroyd-B constitutive equation commonly used to model dilute polymer solutions.

### Elasto-inertial turbulence

- Physics, EngineeringProceedings of the National Academy of Sciences
- 2013

It is demonstrated here for a model system of such complex fluids that at high shear rates, turbulence is not simply modified as previously believed but is suppressed and replaced by a different type of disordered motion, elasto-inertial turbulence.

### A mechanism for streamwise localisation of nonlinear waves in shear flows

- PhysicsJournal of Fluid Mechanics
- 2015

We present the complete unfolding of streamwise localisation in a paradigm of extended shear flows, namely two-dimensional plane Poiseuille flow. Exact solutions of the Navier–Stokes equations are…

### Strong polymer-turbulence interactions in viscoelastic turbulent channel flow.

- Physics, EngineeringPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2010

An effective state-of-the-art numerical method to solve the governing equation for polymers modeled as nonlinear springs, without using any artificial assumptions as usual, was implemented here on a three-dimensional channel flow geometry, which allowed a more detailed study of the polymer-turbulence interactions.

### Two-dimensional dynamics of elasto-inertial turbulence and its role in polymer drag reduction

- Physics
- 2017

The goal of the present study is: (i) to demonstrate the two-dimensional nature of the elasto-inertial instability in elasto-inertial turbulence (EIT), (ii) to identify the role of the bi-dimensional…

### A critical layer model for turbulent pipe flow

- Physics, Environmental Science
- 2018

A model-based description of the scaling and radial location of turbulent fluctuations in turbulent pipe flow is presented and used to illuminate the scaling behaviour of the very large scale…

### A critical-layer framework for turbulent pipe flow

- Physics, Environmental ScienceJournal of Fluid Mechanics
- 2010

A model-based description of the scaling and radial location of turbulent fluctuations in turbulent pipe flow is presented and used to illuminate the scaling behaviour of the very large scale…