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On Moderate-Rayleigh-Number Convection in an Inclined Porous Layer

1,2,* and 3,4,*
1
Institute of Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX 78712, USA
2
Department of Geological Sciences, University of Texas at Austin, Austin, TX 78712, USA
3
Program in Integrated Applied Mathematics, University of New Hampshire, Durham, NH 03824, USA
4
Department of Mechanical Engineering, University of New Hampshire, Durham, NH 03824, USA
*
Authors to whom correspondence should be addressed.
Fluids 2019, 4(2), 101; https://doi.org/10.3390/fluids4020101
Received: 29 April 2019 / Revised: 24 May 2019 / Accepted: 28 May 2019 / Published: 31 May 2019
(This article belongs to the Special Issue Convective Instability in Porous Media, Volume II)
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Abstract

We investigate the flow structure and dynamics of moderate-Rayleigh-number ( R a ) thermal convection in a two-dimensional inclined porous layer. High-resolution numerical simulations confirm the emergence of O ( 1 ) aspect-ratio large-scale convective rolls, with one ‘natural’ roll rotating in the counterclockwise direction and one ‘antinatural’ roll rotating in the clockwise direction. As the inclination angle ϕ is increased, the background mean shear flow intensifies the natural-roll motion, while suppressing the antinatural-roll motion. Our numerical simulations also reveal—for the first time in single-species porous medium convection—the existence of spatially-localized convective states at large ϕ , which we suggest are enabled by subcritical instability of the base state at sufficiently large inclination angles. To better understand the physics of inclined porous medium convection at different ϕ , we numerically compute steady convective solutions using Newton iteration and then perform secondary stability analysis of these nonlinear states using Floquet theory. Our analysis indicates that the inclination of the porous layer stabilizes the boundary layers of the natural roll, but intensifies the boundary-layer instability of the antinatural roll. These results facilitate physical understanding of the large-scale cellular flows observed in the numerical simulations at different values of ϕ . View Full-Text
Keywords: convection; porous media; secondary stability; floquet theory; localized states convection; porous media; secondary stability; floquet theory; localized states
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Wen, B.; Chini, G.P. On Moderate-Rayleigh-Number Convection in an Inclined Porous Layer. Fluids 2019, 4, 101.

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