Lower branch coherent states in shear flows: transition and control

Abstract

Lower branch coherent states in plane Couette flow have an asymptotic structure that consists of O(1) streaks, $O(R^{-1})$ streamwise rolls and a weak sinusoidal wave that develops a critical layer, for large Reynolds number $R$. Higher harmonics become negligible. These unstable lower branch states appear to have a single unstable eigenvalue at all Reynolds numbers. These results suggests that the lower branch coherent states control transition to turbulence and that they may be promising targets for new turbulence prevention strategies.

Submitted to PRL

References in corpus (5)

• Travelling waves in pipe flow
• Recurrent motions within plane Couette turbulence
• Scaling of the turbulence transition threshold in a pipe
• Low-dimensional dynamics embedded in a plane Poiseuille flow turbulence : Traveling-wave solution is a saddle point ?
• The dynamics of transition to turbulence in plane Couette flow

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• A critical layer model for turbulent pipe flow
• The Significance of Simple Invariant Solutions in Turbulent Flows
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• Turbulent drag reduction by polymer additives: Fundamentals and recent advances
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• Transition in pipe flow: the saddle structure on the boundary of turbulence
• Periodic orbits near onset of chaos in plane Couette flow
• Asymmetric, helical and mirror-symmetric travelling waves in pipe flow
• Laminar-turbulent boundary in plane Couette flow
• Active and hibernating turbulence in minimal channel flow of Newtonian and polymeric fluids
• Localised edge states nucleate turbulence in extended plane Couette cells
• Relative periodic orbits in transitional pipe flow
• Global bifurcations to subcritical magnetorotational dynamo action in Keplerian shear flow
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• Exact coherent states and connections to turbulent dynamics in minimal channel flow
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• Reduced description of exact coherent states in parallel shear flows
• From travelling waves to mild chaos: a supercritical bifurcation cascade in pipe flow
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• Subcritical dynamos in shear flows
• Takens-Bogdanov bifurcation of travelling wave solutions in pipe flow
• Stable Manifolds and the Transition to Turbulence in Pipe Flow
• Low-dimensional representations of exact coherent states of the Navier-Stokes equations from the resolvent model of wall turbulence
• Small scale exact coherent structures at large Reynolds numbers in plane Couette flow
• Exact coherent states with hairpin-like vortex structure in channel flow
• Symmetry related dynamics in parallel shear flows
• Instability of the roll/streak structure induced by free-stream turbulence in pre-transitional Couette flow
• Unstable Equilibria and Invariant Manifolds in Quasi-Two-Dimensional Kolmogorov-like Flow
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• Dynamics of laminar and transitional flows over slip surfaces: effects on the laminar-turbulent separatrix
• Laminar-turbulent separatrix in a boundary layer flow
• Self-sustainment of coherent structures in counter-rotating Taylor-Couette flow
• Heteroclinic and Homoclinic Connections in a Kolmogorov-Like Flow
• Vertically localised equilibrium solutions in large-eddy simulations of homogeneous shear flow
• An adaptive preconditioner for steady incompressible flows
• Self-similar invariant solution in the near-wall region of a turbulent boundary layer at asymptotically high Reynolds numbers
• Exact Coherent Structures in Fully Developed Two-Dimensional Turbulence
• Streamwise localization of traveling wave solutions in channel flow
• Dynamics of spatially localized states in transitional plane Couette flow
• Coherent structures in Dissipative Particle Dynamics simulations of the transition to turbulence in compressible shear flows
• High-speed shear driven dynamos. Part 1. Asymptotic analysis
• A probabilistic protocol for the assessment of transition and control
• Exact and Asymptotic Conditions on Traveling Wave Solutions of the Navier-Stokes Equations
• High-speed shear driven dynamos. Part 2. Numerical analysis
• Three-dimensional coherent structures in a curved pipe flow
• Closed-loop control of forced turbulent jets
• Transition of Planar Couette Flow at infinite Reynolds numbers
• Free-stream coherent structures in parallel compressible boundary-layer flows at subsonic Mach numbers
• Eigenvalue bounds for compressible stratified magneto-shear flows varying in two transverse directions
• Spatial marching with subgrid-scale local exact coherent structures in non-uniformly curved channel flow
• Dynamical relevance of periodic orbits under increasing Reynolds number and connections to inviscid dynamics
• Exact coherent structures in a reduced model of parallel shear flow
• Beyond secondary instability: on the emergence of finite-amplitude waves in Görtler vortices
• A self-sustaining process theory for uniform momentum zones and internal shear layers in high Reynolds number shear flows
• Dynamics-based machine learning of transitions in Couette flow
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