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

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
 
 
 .

Linear stability analysis and nonlinear simulations of convective dissolution in an inclined porous layer between impermeable surfaces

“…The dissolution rate, for larger inclinations angles, which is the quantity of interest for predicting the dissolution time of carbon dioxide after injection, is found to be given by the diffusive dissolution rate, F diffusive , for times up to t = 1.5 × 10 5 , in agreement with LSA results. A similar trend was also observed by Wen and Chini, 28,29 for the problem of thermal convection in an inclined porous medium subject to a constant temperature difference. In a quite similar fashion, in their first study, 28 the Nusselt number, Nu, is only weakly dependent on θ for θ < 20 • , although there is a slight increase up to a maximum around θ = 10 • .…”

“…32 The same qualitative suppression mechanism has been observed on "two-sided" systems in previous works. 28,29 In particular, Wen and Chini 28 also report a dramatic change on the dynamics of the "two-sided" system for angles θ > 30, with the complete breakdown of the columnar flow and transition to a large-scale traveling-wave convective roll state, and significant reduction of the transport.…”

“…Very relevant to the subject of the present investigation, works were performed regarding inclined porous media by Wen and Chini 28,29 for large and moderate Rayleigh numbers, addressing both numerical simulations and linear stability analysis (LSA) of the inclined problem, for a similar geometry, but considering a steady state concentration base flow, with prescribed concentration (or temperature) conditions at the top and bottom interfaces. Similarly to the problem addressed in this work, they find a limiting angle of inclination, beyond which no fingering instability is observed.…”

Three-Dimensional Convective Planforms for Inclined Darcy-Bénard Convection

“…Even when confined to two-dimensional convection, some aspect ratios (typically those where L is close to being an even integer) will exhibit a classical bifurcation from the basic state to a strongly convecting solution, but others (where L is close to being an odd integer) exhibit a smooth transition to strong convection. Another complicating factor is that the work of Wen and Chini [19] has uncovered subcritical onset of convection.…”

“…This is the case of the papers by Barletta and Storesletten [13], Rees and Barletta [14], Barletta and Rees [15], Barletta and Celli [16], Celli and Barletta [17]. Further recent studies have been reported by Rees and Bassom [18] and by Wen and Chini [19]. In the former paper, the boundary layer regime is analysed for a porous medium heated from below through an inclined isothermal boundary with uniform suction.…”