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Energy dissipation caused by boundary layer instability at vanishing viscosity

  • Natacha Nguyen van yen (a1), Matthias Waidmann (a1), Rupert Klein (a1), Marie Farge (a2) and Kai Schneider (a3)...
  • Please note a correction has been issued for this article.

Abstract

A qualitative explanation for the scaling of energy dissipation by high-Reynolds-number fluid flows in contact with solid obstacles is proposed in the light of recent mathematical and numerical results. Asymptotic analysis suggests that it is governed by a fast, small-scale Rayleigh–Tollmien–Schlichting instability with an unstable range whose lower and upper bounds scale as $Re^{3/8}$ and $Re^{1/2}$ , respectively. By linear superposition, the unstable modes induce a boundary vorticity flux of order $Re^{1}$ , a key ingredient in detachment and drag generation according to a theorem of Kato. These predictions are confirmed by numerically solving the Navier–Stokes equations in a two-dimensional periodic channel discretized using compact finite differences in the wall-normal direction, and a spectral scheme in the wall-parallel direction.

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Copyright

This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.

Corresponding author

Email address for correspondence: marie.farge@ens.fr

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