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

D A S Rees; Eugen Magyari

doi:10.3390/fluids2020027

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

D A S Rees, Eugen Magyari

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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 language	English
Article number	27
Number of pages	12
Journal	Fluids
Volume	2
Issue number	2
DOIs	https://doi.org/10.3390/fluids2020027
Publication status	Published - 20 May 2017

Keywords

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

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10.3390/fluids2020027Licence: CC BY

fluids-02-00027-v2
The final publication is available at MDPI via https://doi.org/10.3390/fluids2020027
Accepted author manuscript, 447 KBLicence: CC BY

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title = "Hexagonal Cell Formation in Darcy–B{\'e}nard Convection with Viscous Dissipation and Form Drag",

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–B{\'e}nard 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. ",

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AU - Magyari, Eugen

N1 - This was published as part of a Special Issue on Convective Instabilities in Porous Media

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N2 - 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.

AB - 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.

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DO - 10.3390/fluids2020027

M3 - Article

SN - 2311-5521

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JO - Fluids

JF - Fluids

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M1 - 27

ER -

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

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