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Steady streaming confined between three-dimensional wavy surfaces

Guibert, Romain and Plouraboué, Franck and Bergeon, Alain Steady streaming confined between three-dimensional wavy surfaces. (2010) Journal of Fluid Mechanics, vol. 657 . pp. 430-455. ISSN 0022-1120

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Official URL: http://dx.doi.org/10.1017/S0022112010001436

Abstract

We present a theoretical and numerical study of three-dimensional pulsatile confined flow between two rigid horizontal surfaces separated by an average gap h, and having three-dimensional wavy shapes with arbitrary amplitude σ h where σ ∼ O(1), but long-wavelength variations λ, with h/λ 1. We are interested in pulsating flows with moderate inertial effect arising from the Reynolds stress due to the cavity non- parallelism. We analyse the inertial steady-streaming and the second harmonic flows in a lubrication approximation. The dependence of the three-dimensional velocity field in the transverse direction is analytically obtained for arbitrary Womersley numbers and possibly overlapping Stokes layers. The horizontal dependence of the flow is solved numerically by computing the first two pressure fields of an asymptotic expansion in the small inertial limit. We study the variations of the flow structure with the amplitude, the channel’s wavelength and the Womersley number for various families of three-dimensional channels. The steady-streaming flow field in the horizontal plane exhibits a quadrupolar vortex, the size of which is adjusted to the cavity wavelength. When increasing the wall amplitude, the wavelengths characterizing the channel or the Womersley number, we find higher-order harmonic flow structures, the origin of which can either be inertially driven or geometrically induced. When some of the channel symmetries are broken, a steady-streaming current appears which has a quadratic dependence on the pressure drop, the amplitude of which is linked to the Womersley number.

Item Type:Article
Additional Information:Thanks to Cambridge University Press. The definitive version is available at http://journals.cambridge.org. The original PDF of the article can be found at Journal of Fluid Mechanics website : http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=7862904
Audience (journal):International peer-reviewed journal
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Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS
Université de Toulouse > Institut National Polytechnique de Toulouse - INPT
Université de Toulouse > Université Paul Sabatier-Toulouse III - UPS
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Deposited By:Franck PLOURABOUE

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