Self-similar invariant solution in the near-wall region of a turbulent boundary layer at asymptotically high Reynolds numbers
- 10 April 2020
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Fluid Mechanics
Abstract
At sufficiently high Reynolds numbers, shear-flow turbulence close to a wall acquires universal properties. When length and velocity are rescaled by appropriate characteristic scales of the turbulent flow and thereby measured in inner units, the statistical properties of the flow become independent of the Reynolds number. We demonstrate the existence of a wall-attached non-chaotic exact invariant solution of the fully nonlinear three-dimensional Navier-Stokes equations for a parallel boundary layer that captures the characteristic self-similar scaling of near-wall turbulent structures. The branch of travelling wave solutions can be followed up to . Combined theoretical and numerical evidence suggests that the solution is asymptotically self-similar and exactly scales in inner units for Reynolds numbers tending to infinity. Demonstrating the existence of invariant solutions that capture the self-similar scaling properties of turbulence in the near-wall region is a step towards extending the dynamical systems approach to turbulence from the transitional regime to fully developed boundary layers.This publication has 28 references indexed in Scilit:
- Streamwise-Localized Solutions at the Onset of Turbulence in Pipe FlowPhysical Review Letters, 2013
- Visualizing the geometry of state space in plane Couette flowJournal of Fluid Mechanics, 2008
- Turbulence Transition and the Edge of Chaos in Pipe FlowPhysical Review Letters, 2007
- Lower Branch Coherent States in Shear Flows: Transition and ControlPhysical Review Letters, 2007
- Edge of Chaos in a Parallel Shear FlowPhysical Review Letters, 2006
- Low-dimensional dynamics of a turbulent wall flowJournal of Fluid Mechanics, 2001
- Three-dimensional finite-amplitude solutions in plane Couette flow: bifurcation from infinityJournal of Fluid Mechanics, 1990
- Turbulence statistics in fully developed channel flow at low Reynolds numberJournal of Fluid Mechanics, 1987
- NON-LINEAR INSTABILITY OF THE ASYMPTOTIC SUCTION VELOCITY PROFILEThe Quarterly Journal of Mechanics and Applied Mathematics, 1975
- The structure of turbulent boundary layersJournal of Fluid Mechanics, 1967