Asymptotic behaviour for convection with anomalous diffusion

Straughan, Brian; Barletta, Antonio

doi:10.1007/s00161-024-01291-7

Asymptotic behaviour for convection with anomalous diffusion

Straughan, Brian; Barletta, Antonio

Authors

Brian Straughan

Antonio Barletta

Abstract

We investigate the fully nonlinear model for convection in a Darcy porous material where the diffusion is of anomalous type as recently proposed by Barletta. The fully nonlinear model is analysed but we allow for variable gravity or penetrative convection effects which result in spatially dependent coefficients. This spatial dependence usually requires numerical solution even in the linearized case. In this work, we demonstrate that regardless of the size of the Rayleigh number, the perturbation solution will decay exponentially in time for the superdiffusion case. In addition, we establish a similar result for convection in a bidisperse porous medium where both macro- and microporosity effects are present. Moreover, we demonstrate a similar result for thermosolutal convection.

Citation

Straughan, B., & Barletta, A. (2024). Asymptotic behaviour for convection with anomalous diffusion. Continuum Mechanics and Thermodynamics, 36(4), 737-743. https://doi.org/10.1007/s00161-024-01291-7

Journal Article Type	Article
Acceptance Date	Jan 25, 2024
Online Publication Date	Mar 6, 2024
Publication Date	Jul 1, 2024
Deposit Date	May 28, 2024
Publicly Available Date	May 28, 2024
Journal	Continuum Mechanics and Thermodynamics
Print ISSN	0935-1175
Electronic ISSN	1432-0959
Publisher	Springer
Peer Reviewed	Peer Reviewed
Volume	36
Issue	4
Pages	737-743
DOI	https://doi.org/10.1007/s00161-024-01291-7
Keywords	Bidispersive porous media, Thermosolutal convection, Anomalous diffusion, Thermal convection, Global nonlinear stability
Public URL	https://durham-repository.worktribe.com/output/2466473

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© The Author(s) 2024
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