Energy dissipation caused by boundary layer instability at vanishing viscosity. (26th June 2018) - Nguyen van yen, Natacha; Waidmann, Matthias; Klein, Rupert; Farge, Marie; Schneider, Kai
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.