The origin of localized snakes-and-ladders solutions of plane Couette flow
arXiv:1906.06277 · doi:10.1103/PhysRevE.100.031102
Abstract
Spatially localized exact solutions of plane Couette flow are organized in a snakes-and-ladders structure strikingly similar to that observed for simpler pattern-forming partial differential equations. [PRL 104,104501 (2010)]. We demonstrate the mechanism by which these snaking solutions originate from well-known periodic states of the Taylor-Couette system. They are formed by a localized slug of Wavy-Vortex flow that emerges from a background of Taylor vortices via a modulational sideband instability. This mechanism suggests a deep connection between pattern-formation theory and Navier-Stokes flow.
arXiv comment5 pages
References in corpus (21)
- Visualizing the geometry of state space in plane Couette flow
- Computational Study of Turbulent-Laminar Patterns in Couette Flow
- Streamwise-localized solutions at the onset of turbulence in pipe flow
- Equilibrium and traveling-wave solutions of plane Couette flow
- Snakes and ladders: localized solutions of plane Couette flow
- Localised edge states nucleate turbulence in extended plane Couette cells
- Spatially localized solutions of shear flows
- The genesis of streamwise-localized solutions from globally periodic travelling waves in pipe flow
- Streamwise and doubly-localised periodic orbits in plane Poiseuille flow
- A doubly-localized equilibrium solution of plane Couette flow
- Invariant Solution underlying Oblique Stripe Patterns in Plane Couette Flow
- Transition to magnetorotational turbulence in Taylor--Couette flow with imposed azimuthal magnetic field
- Periodically bursting edge states in plane Poiseuille flow
- Long wavelength instability of coherent structures in plane Couette flow
- Defect-like structures and localized patterns in SH357
- Homoclinic snaking in plane Couette flow: bending, skewing, and finite-size effects
- Optimising energy growth as a tool for finding exact coherent structures
- Localized travelling waves in the asymptotic suction boundary layer
- Localization in a spanwise-extended model of plane Couette flow
- Analysis and modeling of localized invariant solutions in pipe flow
- Transition in the asymptotic suction boundary layer over a heated plate