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 .
Highlights
Buoyancy-driven convection in fluid-saturated porous media exhibits rich instability characteristics and nonlinear dynamics as the Rayleigh number Ra, a dimensionless parameter characterizing the ratio of driving to damping forces, increases [1,2,3,4,5,6,7]
High-resolution numerical simulations are performed to investigate the dynamics of convection at moderate Ra in an inclined porous layer
Our numerical simulation results indicate that the inclination of the layer modifies the boundary layer thickness of the velocity field for the natural and antinatural rolls: the former becomes thinner while the latter becomes thicker
Summary
Buoyancy-driven convection in fluid-saturated porous media exhibits rich instability characteristics and nonlinear dynamics as the Rayleigh number Ra, a dimensionless parameter characterizing the ratio of driving to damping forces, increases [1,2,3,4,5,6,7]. Some numerical simulations of porous medium convection have been performed in inclined cavities to investigate the emergent steady convective flow at small Ra [37,38,39], the side walls may significantly impact the flow structure and transport properties if the aspect ratio of the domain is not sufficiently large (e.g., in a sloping square cavity). We conduct well-resolved numerical simulations in an inclined 2D Rayleigh–Darcy domain having O(1) aspect ratio but enforce periodicity rather than sidewall conditions in the wall-parallel (x) direction, since the former enables a better approximation of the physics of convection in an extended layer.
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