Repository: Freie Universität Berlin, Math Department

Energy dissipation caused by boundary layer instability at vanishing viscosity

Nguyen van yen, N. and Waidmann, M. and Klein, R. and Farge, M. (2018) Energy dissipation caused by boundary layer instability at vanishing viscosity. Journal of Fluid Mechanics, 849 . pp. 676-717.

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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 and , respectively. By linear superposition, the unstable modes induce a boundary vorticity flux of order , 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.

Item Type:Article
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics > Geophysical Fluid Dynamics Group
ID Code:2311
Deposited By: Ulrike Eickers
Deposited On:15 Mar 2019 15:54
Last Modified:15 Mar 2019 15:54

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