Stabilising effect of generic anomalous diffusion independent of the Rayleigh number

TL;DR

This paper explores how generic anomalous diffusion influences the stability of fluid convection in porous media, revealing that certain diffusion models can extend stability beyond classical thresholds and affect transient dynamics.

Contribution

It introduces a comprehensive mathematical framework for analyzing the stabilizing effects of various anomalous diffusion models on convection in porous media.

Findings

Anomalous diffusion can extend the stability threshold beyond classical limits.

Different memory functions significantly influence transient disturbance growth.

Transient perturbations may grow temporarily before decaying, depending on diffusion type.

Abstract

This work investigates the influence of a generic anomalous diffusion model on mass convection in a fluid-saturated porous medium, focusing on superdiffusive regimes. A mathematical model is developed, and tability analyses - both linear and nonlinear - are performed. Results demonstrate that the specific form of the time function describing anomalous diffusion significantly affects system stability, allowing stability to persist beyond the classical Rayleigh-B\'enard neutral threshold. Furthermore, transient perturbation growth is observed under certain conditions, followed by eventual decay. The paper systematically examines various memory functions, including power-law, exponential, and logarithmic forms, highlighting their impact on the dynamics of disturbances. The findings underscore the importance of anomalous diffusion in modulating stability and provide new insights into the transient behaviours induced by non-Fickian mass transport.