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A Non-normal-Mode Marginal State of Convection in a Porous Rectangle

Tyvand, Peder A.; Nøland, Jonas Kristiansen; Storesletten, Leiv
Journal article, Peer reviewed
Accepted version
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URI
http://hdl.handle.net/11250/2626302
Date
2019
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  • Fakultet for informasjonsteknologi og elektroteknikk (Uspesifisert) [114]
  • Publikasjoner fra CRIStin - NTNU [19849]
Original version
Transport in Porous Media. 2019, 128 (2), 633-651.   10.1007/s11242-019-01263-5
Abstract
The fourth-order Darcy–Bénard eigenvalue problem for onset of thermal convection in a 2D rectangular porous box is investigated. The conventional type of solution has normal-mode dependency in at least one of the two spatial directions. The present eigenfunctions are of non-normal-mode type in both the horizontal and the vertical direction. A numerical solution is found by the finite element method, since no analytical method is known for this non-degenerate fourth-order eigenvalue problem. All four boundaries of the rectangle are impermeable. The thermal conditions are handpicked to be incompatible with normal modes: The lower boundary and the right-hand wall are heat conductors. The upper boundary has given heat flux. The left-hand wall is thermally insulating. The computed eigenfunctions have novel types of complicated cell structures, with intricate internal cell walls.
Publisher
Springer Verlag
Journal
Transport in Porous Media

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