Effective slip law for general viscous flows over an oscillating surface

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Details zur Publikation

Autorinnen und Autoren: Mikelic A, Necasova S, Neuss-Radu M
Zeitschrift: Mathematical Methods in the Applied Sciences
Jahr der Veröffentlichung: 2013
Band: 36
Heftnummer: 15
Seitenbereich: 2086-2100
ISSN: 0170-4214


We consider the non-stationary three-dimensional viscous flow in a bounded domain, with the lateral surface containing microscopic surface irregularities. Under the assumption of a smooth flow in the domain without roughness, we prove that there is a smooth solution to a problem with the rough boundary. In the papers by Jager and Mikeli, the friction law was obtained as a perturbation of the Poiseuille flows. Here, the situation is more complicated. Nevertheless, after studying the corresponding boundary layers and using the results on solenoidal vector fields in domains with rough boundaries, we obtain rigorously the Navier friction condition. It is valid when the size and amplitude of the imperfections tend to zero. Furthermore, the friction matrix in the law is determined through a family of auxiliary boundary-layer type problems. Effective equations approximate velocity at order O(epsilon) in the H-1-norm, uniformly in time, and O(epsilon(3/2)) in the L-2-norm, also uniformly in time. Approximation for the pressure is O(epsilon(3/2)) in the L-loc(2)-norm. Copyright (c) 2013 John Wiley & Sons, Ltd.

Einrichtungen weiterer Autorinnen und Autoren

The Czech Academy of Sciences
Université Claude Bernard Lyon 1 (UCB)


Mikelic, A., Necasova, S., & Neuss-Radu, M. (2013). Effective slip law for general viscous flows over an oscillating surface. Mathematical Methods in the Applied Sciences, 36(15), 2086-2100. https://dx.doi.org/10.1002/mma.2923

Mikelic, Andro, Sarka Necasova, and Maria Neuss-Radu. "Effective slip law for general viscous flows over an oscillating surface." Mathematical Methods in the Applied Sciences 36.15 (2013): 2086-2100.


Zuletzt aktualisiert 2019-29-06 um 11:10