Effects of anisotropy on the transition to absolute instability in a porous medium heated from below

TL;DR

This paper investigates how anisotropic permeability in a heated porous medium affects the transition from modal to absolute instability, revealing that vertical permeability destabilizes while horizontal permeability stabilizes the flow.

Contribution

It provides an analytical analysis of the impact of anisotropic permeability on the onset of buoyancy-driven instabilities in porous media.

Findings

Vertical permeability increases instability.

Horizontal permeability decreases instability.

Anisotropy influences the transition to absolute instability.

Abstract

The emerging instability of a forced throughflow in a fluid saturated horizontal porous duct of rectangular cross section is investigated. The duct is heated from below by assuming the horizontal boundaries to be at different temperatures. Both the horizontal and the vertical boundaries are impermeable and the basic flow is parallel to such boundaries. The porous medium is anisotropic with different permeabilities in the vertical and horizontal directions. The effect of the anisotropy on the onset of the buoyancy driven modal instability and absolute instability is analysed. The parametric conditions leading to the instability of the basic flow are determined by employing an analytical dispersion relation. The different permeabilities in the vertical and horizontal directions come out to play opposite roles in the onset of modal instability and in the transition to absolute instability. It is shown that an increasing vertical permeability has a destabilising effect, while an increasing horizontal permeability has a stabilising effect.