Coherent structures in plane channel flow of dilute polymer solutions with vanishing inertia
arXiv:2201.01274 · doi:10.1103/PhysRevLett.129.017801
Abstract
When subjected to sufficiently strong velocity gradients, solutions of long, flexible polymers exhibit flow instabilities and chaotic motion, often referred to as elastic turbulence. Its mechanism differs from the familiar, inertia-driven turbulence in Newtonian fluids, and is poorly understood. Here, we demonstrate that the dynamics of purely elastic pressure-driven channel flows of dilute polymer solutions are organised by exact coherent structures that take the form of two-dimensional travelling waves. Our results demonstrate that no linear instability is required to sustain such travelling wave solutions, and that their origin is purely elastic in nature. We show that the associated stress profiles are characterised by thin, filament-like arrangements of polymer stretch, which is sustained by a solitary pair of vortices. We discuss the implications of the travelling wave solutions for the transition to elastic turbulence in straight channels, and propose ways for their detection in experiments.
References in corpus (9)
- Understanding viscoelastic flow instabilities: Oldroyd-B and beyond
- Exact travelling wave solutions in viscoelastic channel flow
- A continuous pathway between the elasto-inertial and elastic turbulent states in viscoelastic channel flow
- Elastic Alfven waves in elastic turbulence
- Weakly nonlinear analysis of the viscoelastic instability in channel flow for finite and vanishing Reynolds numbers
- Elastically driven Kelvin-Helmholtz-like instability in planar channel flow
- Tollmien-Schlichting route to elastoinertial turbulence in channel flow
- Universal coherent structures of elastic turbulence in straight channel with viscoelastic fluid flow
- Non-modal elastic instability and elastic waves in weakly perturbed channel flow
Cited by in corpus (10)
- Inertial enhancement of the polymer diffusive instability
- Finite-amplitude elastic waves in viscoelastic channel flow from large to zero Reynolds number
- A unified view of elastic and elasto-inertial turbulence in channel flows at low and moderate Reynolds numbers
- Numerical Study of Viscoelastic Upstream Instability
- Preserving large-scale features in simulations of elastic turbulence
- Linear stability analysis of purely elastic travelling wave solutions in pressure driven channel flows
- On the large-Weissenberg-number scaling laws in viscoelastic pipe flows
- Uncertainty in Elastic Turbulence
- Jamming of Elastoviscoplastic fluids in Elastic Turbulence
- Coherent structures in Newtonian and viscoelastic turbulent planar jets