Journal
JOURNAL OF FLUID MECHANICS
Volume 849, Issue -, Pages 676-717Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.1017/jfm.2018.396
Keywords
boundary layer stability; vortex shedding
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Funding
- Humboldt Foundation
- French Research Federation for Fusion Studies
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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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