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Self-similar invariant solution in the near-wall region of a turbulent boundary layer at asymptotically high Reynolds numbers

Published online by Cambridge University Press:  07 February 2020

Sajjad Azimi  and
Tobias M. Schneider Open the ORCID record for Tobias M. Schneider [Opens in a new window]
Sajjad Azimi
Affiliation:
Emergent Complexity in Physical Systems Laboratory (ECPS), École Polytechnique Fédérale de Lausanne, CH-1015Lausanne, Switzerland
Tobias M. Schneider*
Affiliation:
Emergent Complexity in Physical Systems Laboratory (ECPS), École Polytechnique Fédérale de Lausanne, CH-1015Lausanne, Switzerland
*
†Email address for correspondence: [email protected]
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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 $Re=1\,000\,000$. 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.

JFM classification

Turbulent Flows: Turbulent boundary layers
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 888 , 10 April 2020 , A15
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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