Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

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

Version 1 : Received: 29 April 2019 / Approved: 30 April 2019 / Online: 30 April 2019 (11:20:27 CEST)

A peer-reviewed article of this Preprint also exists.

Wen, B.; Chini, G.P. On Moderate-Rayleigh-Number Convection in an Inclined Porous Layer. Fluids 2019, 4, 101. Wen, B.; Chini, G.P. On Moderate-Rayleigh-Number Convection in an Inclined Porous Layer. Fluids 2019, 4, 101.

Journal reference: Fluids 2019, 4, 101
DOI: 10.3390/fluids4020101

## Abstract

We investigate the flow structure and dynamics of moderate-Rayleigh-number ($Ra$) thermal convection in a two-dimensional inclined porous layer. Direct numerical simulations (DNS) confirm the emergence of $\mathit{O}(1)$ 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 $\phi$ is increased, the background mean shear flow intensifies the natural-roll motion, while suppressing the antinatural-roll motion. Moreover, our DNS reveal---for the first time in single-species porous medium convection---the existence of \emph{spatially-localized} convective states at large $\phi$, 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 $\phi$, 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 DNS at different values of $\phi$.

## Keywords

convection; porous media; secondary stability; Floquet theory; localized states

## Subject

PHYSICAL SCIENCES, Fluids & Plasmas

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