Edge states for the turbulence transition in the asymptotic suction boundary layer
arXiv:1209.0593 · doi:10.1017/jfm.2013.212
Abstract
We demonstrate the existence of an exact invariant solution to the Navier-Stokes equations for the asymptotic suction boundary layer. The identified periodic orbit with a very long period of several thousand advective time units is found as a local dynamical attractor embedded in the stability boundary between laminar and turbulent dynamics. Its dynamics captures both the interplay of downstream oriented vortex pairs and streaks observed in numerous shear flows as well as the energetic bursting that is characteristic for boundary layers. By embedding the flow into a family of flows that interpolates between plane Couette flow and the boundary layer we demonstrate that the periodic orbit emerges in a saddle-node infinite-period (SNIPER) bifurcation of two symmetry-related travelling wave solutions of plane Couette flow. Physically, the long period is due to a slow streak instability which leads to a violent breakup of a streak associated with the bursting and the reformation of the streak at a different spanwise location. We show that the orbit is structurally stable when varying both the Reynolds number and the domain size.
Accepted for publication in journal of fluid mechanics
References in corpus (16)
- Travelling waves in pipe flow
- The Significance of Simple Invariant Solutions in Turbulent Flows
- Recurrent motions within plane Couette turbulence
- Visualizing the geometry of state space in plane Couette flow
- Turbulence transition and the edge of chaos in pipe flow
- Lower branch coherent states in shear flows: transition and control
- Equilibrium and traveling-wave solutions of plane Couette flow
- Transition in pipe flow: the saddle structure on the boundary of turbulence
- Periodic orbits near onset of chaos in plane Couette flow
- Laminar-turbulent boundary in plane Couette flow
- Localised edge states nucleate turbulence in extended plane Couette cells
- Revealing the state space of turbulent pipe flow by symmetry reduction
- Heteroclinic connections in plane Couette flow
- Statistical analysis of coherent structures in transitional pipe flow
- Basin boundary, edge of chaos, and edge state in a two-dimensional model
- Lifetime statistics in transitional pipe flow
Cited by in corpus (16)
- Streamwise and doubly-localised periodic orbits in plane Poiseuille flow
- On the transition to turbulence of wall-bounded flows in general, and plane Couette flow in particular
- Transition to turbulence in wall-bounded flows: Where do we stand?
- Edge states as mediators of bypass transition in boundary-layer flows
- Periodically bursting edge states in plane Poiseuille flow
- Long wavelength instability of coherent structures in plane Couette flow
- Symmetry related dynamics in parallel shear flows
- Travelling-wave solutions bifurcating from relative periodic orbits in plane Poiseuille flow
- Localized travelling waves in the asymptotic suction boundary layer
- Multi-scale invariant solutions in plane Couette flow: a reduced-order model approach
- Transition in the asymptotic suction boundary layer over a heated plate
- Transition to turbulence when the Tollmien-Schlichting and bypass routes coexist
- Edge state modulation by mean viscosity gradients
- Free-stream coherent structures in parallel compressible boundary-layer flows at subsonic Mach numbers
- Modified snaking in plane Couette flow with wall-normal suction
- Dynamic feedback control through wall suction in shear flows