Laminar-turbulent patterning in wall-bounded shear flows: a Galerkin model
arXiv:1503.06226 · doi:10.1088/0169-5983/47/3/035512
Abstract
On its way to turbulence, plane Couette flow - the flow between counter-translating parallel plates - displays a puzzling steady oblique laminar-turbulent pattern. We approach this problem via Galerkin modelling of the Navier-Stokes equations. The wall-normal dependence of the hydrodynamic field is treated by means of expansions on functional bases fitting the boundary conditions exactly. This yields a set of partial differential equations for the spatiotemporal dynamics in the plane of the flow. Truncating this set beyond lowest nontrivial order is numerically shown to produce the expected pattern, therefore improving over what was obtained at cruder effective wall-normal resolution. Perspectives opened by the approach are discussed.
arXiv commentto appear in Fluid Dynamics Research; 14 pages, 5 figures
References in corpus (12)
- Computational Study of Turbulent-Laminar Patterns in Couette Flow
- "Barber pole turbulence" in large aspect ratio Taylor-Couette flow
- Simplifying the complexity of pipe flow
- From temporal to spatiotemporal dynamics in transitional plane Couette flow
- Spatiotemporal perspective on the decay of turbulence in wall-bounded flows
- On the transition to turbulence of wall-bounded flows in general, and plane Couette flow in particular
- Modeling transitional plane Couette flow
- On modelling transitional turbulent flows using under-resolved direct numerical simulations: The case of plane Couette flow
- Large scale flow around turbulent spots
- Turbulent patterns in wall-bounded flows: a Turing instability?
- Modeling the transition to turbulence in shear flows
- Pattern fluctuations in transitional plane Couette flow