Asymptotic behaviour for convection with anomalous diffusion

Straughan, Brian; Barletta, Antonio

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