Energy dissipation caused by boundary layer instability at vanishing viscosity. (26th June 2018)

• Record Type: Journal Article
• Authors: Nguyen van yen, Natacha; Waidmann, Matthias; Klein, Rupert; Farge, Marie; Schneider, Kai
• Is Part Of: Journal of fluid mechanics. Volume 849(2018)
• Page Start: 676
• Page End: 717
• Publication Date: 2018-06-26
• Subjects: boundary layer stability, -- vortex shedding; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2018.396
• Languages: English
• ISSNs: 0022-1120

Abstract

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.