Hexagonal Cell Formation in Darcy–Bénard Convection with Viscous Dissipation and Form Drag

D A S Rees, Eugen Magyari

Research output: Contribution to journalArticle

4 Citations (Scopus)
126 Downloads (Pure)

Abstract

Recent interest in the effects of viscous dissipation on convective flows in porous media has centred almost exclusively on forced convection flows. In this paper, we investigate the manner in which it affects the onset and early stages of convection in Darcy–Bénard convection. A weakly nonlinear theory is described briefly, and it is shown that hexagonal cells are preferred over rolls when the Rayleigh number is sufficiently close to 4π^2. At higher Rayleigh numbers, two-dimensional rolls are preferred. When weak form drag is included, then subcritical convection eventually disappears as the Forchheimer parameter increases, yielding a highly novel situation wherein hexagonal convection arises supercritically. The range of stability of hexagons is found to increase.
Original languageEnglish
Article number27
Number of pages12
JournalFluids
Volume2
Issue number2
DOIs
Publication statusPublished - 20 May 2017

Keywords

  • convection; porous, instability, weakly nonlinear, viscous dissipation, form drag

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