Invariant Solution underlying Oblique Stripe Patterns in Plane Couette Flow
arXiv:1809.02877 · doi:10.1038/s41467-019-10208-x
Abstract
When subcritical shear flows transition to turbulence, laminar and turbulent flow often coexists in space, giving rise to turbulent-laminar patterns. Most prominent are regular stripe patterns with large-scale periodicity and oblique orientation. Oblique stripes are a robust phenomenon, observed in experiments and flow simulations, yet their origin remains unclear. We demonstrate the existence of an invariant equilibrium solution of the fully nonlinear 3D Navier-Stokes equations that resembles the oblique pattern of turbulent-laminar stripes in plane Couette flow. We uncover the origin of the stripe equilibrium and show how it emerges from the well-studied Nagata equilibrium via two successive symmetry-breaking bifurcations.
References in corpus (13)
- Visualizing the geometry of state space in plane Couette flow
- Computational Study of Turbulent-Laminar Patterns in Couette Flow
- "Barber pole turbulence" in large aspect ratio Taylor-Couette flow
- Equilibrium and traveling-wave solutions of plane Couette flow
- Snakes and ladders: localized solutions of plane Couette flow
- Mean flow of turbulent-laminar patterns in plane Couette flow
- Turbulent-laminar patterns in plane Poiseuille flow
- Spatially localized solutions of shear flows
- From temporal to spatiotemporal dynamics in transitional plane Couette flow
- A doubly-localized equilibrium solution of plane Couette flow
- Growth dynamics of turbulent spots in plane Couette flow
- Homoclinic snaking in plane Couette flow: bending, skewing, and finite-size effects
- DNS of turbulent channel flow at very low Reynolds numbers
Cited by in corpus (17)
- Statistical transition to turbulence in plane channel flow
- Structured input-output analysis of transitional wall-bounded flows
- Routes to turbulence in Taylor-Couette flow
- Self-sustainment of coherent structures in counter-rotating Taylor-Couette flow
- Trigger turbulent bands directly at low Reynolds numbers in channel flow using a moving-force technique
- Linear feedback control of invariant solutions in channel flow
- Patterns in transitional shear turbulence. Part 2: Emergence and optimal wavelength
- Patterns in transitional shear turbulence. Part 1. Energy transfer and mean-flow interaction
- Self-similar invariant solution in the near-wall region of a turbulent boundary layer at asymptotically high Reynolds numbers
- The origin of localized snakes-and-ladders solutions of plane Couette flow
- Data-driven guessing and gluing of unstable periodic orbits
- Adjoint-based variational method for constructing periodic orbits of high-dimensional chaotic systems
- Modified snaking in plane Couette flow with wall-normal suction
- Model for transitional turbulence in a planar shear flow
- Localized layers of turbulence in stratified horizontally sheared Poiseuille flow
- Large-scale streak instabilities of transitional channel flow
- Natural convection in a vertical channel. Part 3. Bifurcations of many (additional) unstable periodic orbits and their dynamical relevance