Inclined porous medium convection at large Rayleigh number

• Published in: Journal of fluid mechanics Vol. 837; pp. 670 - 702
• Main Authors: Wen, Baole, Chini, Gregory P.
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 25.02.2018
• Subjects: Applied mathematics; Aquifers; Columnar structure; Computational fluid dynamics; Computer simulation; Convection; Convection modes; Dimensional stability; Flow stability; Flow structures; Fluid flow; Fluid mechanics; Heat transport; Inclination angle; Instability; Investigations; JFM Papers; Linear algebra; Mechanics; Numerical analysis; Physics; Plumes; Porous media; Rayleigh number; Spatial analysis; Stability analysis; Transport; Upper bounds; United States > US; variational methods; convection in porous media; nonlinear instability
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/jfm.2017.863

High-Rayleigh-number ( $Ra$ ) convection in an inclined two-dimensional porous layer is investigated using direct numerical simulations (DNS) and stability and variational upper-bound analyses. When the inclination angle $\unicode[STIX]{x1D719}$ of the layer satisfies $0^{\circ }<\unicode[STIX]{x1D719}\lesssim 25^{\circ }$ , DNS confirm that the flow exhibits a three-region wall-normal asymptotic structure in accord with the strictly horizontal ( $\unicode[STIX]{x1D719}=0^{\circ }$ ) case, except that as $\unicode[STIX]{x1D719}$ is increased the time-mean spacing between neighbouring interior plumes also increases substantially. Both DNS and upper-bound analysis indicate that the heat transport enhancement factor (i.e. the Nusselt number) $Nu\sim CRa$ with a $\unicode[STIX]{x1D719}$ -dependent prefactor $C$ . When $\unicode[STIX]{x1D719}>\unicode[STIX]{x1D719}_{t}$ , however, where $30^{\circ }<\unicode[STIX]{x1D719}_{t}<32^{\circ }$ independently of $Ra$ , the columnar flow structure is completely broken down: the flow transitions to a large-scale travelling-wave convective roll state, and the heat transport is significantly reduced. To better understand the physics of inclined porous medium convection at large $Ra$ and modest inclination angles, a spatial Floquet analysis is performed, yielding predictions of the linear stability of numerically computed, fully nonlinear steady convective states. The results show that there exist two types of instability when $\unicode[STIX]{x1D719}\neq 0^{\circ }$ : a bulk-mode instability and a wall-mode instability, consistent with previous findings for $\unicode[STIX]{x1D719}=0^{\circ }$ (Wen et al., J. Fluid Mech., vol. 772, 2015, pp. 197–224). The background flow induced by the inclination of the layer intensifies the bulk-mode instability during its subsequent nonlinear evolution, thereby favouring increased spacing between the interior plumes relative to that observed in convection in a horizontal porous layer.