On Moderate-Rayleigh-Number Convection in an Inclined Porous Layer
Institute of Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX 78712, USA
Department of Geological Sciences, University of Texas at Austin, Austin, TX 78712, USA
Program in Integrated Applied Mathematics, University of New Hampshire, Durham, NH 03824, USA
Department of Mechanical Engineering, University of New Hampshire, Durham, NH 03824, USA
Authors to whom correspondence should be addressed.
Received: 29 April 2019 / Revised: 24 May 2019 / Accepted: 28 May 2019 / Published: 31 May 2019
PDF [1575 KB, uploaded 31 May 2019]
We investigate the flow structure and dynamics of moderate-Rayleigh-number (
) thermal convection in a two-dimensional inclined porous layer. High-resolution numerical simulations confirm the emergence of
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
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
, 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
, 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
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).
Share & Cite This Article
MDPI and ACS Style
Wen, B.; Chini, G.P. On Moderate-Rayleigh-Number Convection in an Inclined Porous Layer. Fluids 2019, 4, 101.
Wen B, Chini GP. On Moderate-Rayleigh-Number Convection in an Inclined Porous Layer. Fluids. 2019; 4(2):101.
Wen, Baole; Chini, Gregory P. 2019. "On Moderate-Rayleigh-Number Convection in an Inclined Porous Layer." Fluids 4, no. 2: 101.
Show more citation formats
Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.
[Return to top]
For more information on the journal statistics, click here
Multiple requests from the same IP address are counted as one view.