On Gill's problem with anomalous diffusion
Abstract
The classical formulation of Gill's theorem establishing the linear stability of the buoyant flow in a vertical porous channel subject to transverse diffusion and bounded by impermeable walls is here reconsidered from the perspective of anomalous mass diffusion. Anomalous diffusion is a physical effect implying a more general formulation of the governing equations of mass transfer either in a fluid or in a fluid-saturated porous medium. Anomalous diffusion is mathematically modelled via a diffusion equation with a time-dependent mass diffusivity. In this study, the stationary and parallel buoyant flow in a vertical porous layer saturated by a fluid is investigated. The implications of the anomalous diffusion model for the proof that such a flow is always linearly stable are analysed.
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BibTeX
@misc{barletta2026gills,
title = {{On Gill's problem with anomalous diffusion}},
author = {A. Barletta},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35078},
eprint = {2610.35078},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35078},
}
RIS
TY - UNPB
TI - On Gill's problem with anomalous diffusion
AU - A. Barletta
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35078
UR - https://arxiv.org/abs/2610.35078
AB - The classical formulation of Gill's theorem establishing the linear stability of the buoyant flow in a vertical porous channel subject to transverse diffusion and bounded by impermeable walls is here reconsidered from the perspective of anomalous mass diffusion. Anomalous diffusion is a physical effect implying a more general formulation of the governing equations of mass transfer either in a fluid or in a fluid-saturated porous medium. Anomalous diffusion is mathematically modelled via a diffusion equation with a time-dependent mass diffusivity. In this study, the stationary and parallel buoyant flow in a vertical porous layer saturated by a fluid is investigated. The implications of the anomalous diffusion model for the proof that such a flow is always linearly stable are analysed.
ER -