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A note on the onset of recirculation in a 2D Couette flow over a wavy bottom

Esquivelzeta-Rabell, Francisco Martin and Figueroa-Espinoza, Bernardo and Legendre, Dominique and Salles, Paulo A note on the onset of recirculation in a 2D Couette flow over a wavy bottom. (2015) Physics of Fluids, 27 (1). 014108/1-014108/14. ISSN 1070-6631

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Official URL: http://dx.doi.org/10.1063/1.4906153

Abstract

Laminar Couette flow over a fixed wavy surface was studied with direct numerical simulation in a 2D periodic numerical domain. The mesh was generated by a conformal transformation that sets horizontal flow at the top of the domain, where a constant velocity boundary condition is given. The bottom of the domain is a wavy sinusoidal surface of wave slope 2πa/λ. The combined effect of bottom shape, inertia, and viscosity was explored using different Reynolds numbers (Re) and two dimen- sionless parameters in terms of channel width h, wavelength λ, and the amplitude of the wavy bottom a. Even if the Reynolds number was large, the simulations were not perturbed so the regime was always laminar. However, a recirculation appeared at the vicinity of the trough. The horizontal location of the eddy center was reported as a function of 2πa/λ and Reλ/h. The conditions for the onset of this recirculation were studied and compared with results from the literature. Two regimes can be clearly identified from the numerical results; a viscous regime with a weak dependence between 2πa/λ and Reλ/h for small Reynolds numbers and an inertial regime with an exponential dependence between 2πa/λ and Reλ/h for large Reynolds numbers, which presents an approximate slope of −1/3. Almost all results collapse in one single curve that characterizes the phenomenon (with the exception of some points where the flow is confined due to a large λ/h ratio).

Item Type:Article
Additional Information:Thanks to AIP editor. The original PDF of the article can be found at : https://aip.scitation.org/doi/10.1063/1.4906153
HAL Id:hal-01792943
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - INPT (FRANCE)
Other partners > Universidad Nacional Autónoma de México - UNAM (MEXICO)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UPS (FRANCE)
Laboratory name:
Funders:
UNAM Research
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Deposited By: Dominique LEGENDRE
Deposited On:16 May 2018 07:11

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