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 |
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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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