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arXiv · 2209.00872

Gill's problem in a sandwiched porous slab

Antonio Barletta·Michele Celli·Stefano Lazzari·Pedro Vayssière Brandão
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Abstract

The classical Gill's stability problem for the stationary and parallel buoyant flow in a vertical porous slab with impermeable and isothermal boundaries kept at different temperatures is reconsidered in a different perspective. A three-layer slab is studied instead of a homogeneous slab as in Gill's problem. The three layers have a symmetric configuration where the two external layers have a high thermal conductivity, while the core layer has a much lower conductivity. A simplified model is set up where the thermal conductivity ratio between the external layers and the internal core is assumed as infinite. It is shown that a flow instability in the sandwiched porous slab may arise with a sufficiently large Rayleigh number. It is also demonstrated that this instability coincides with that predicted in a previous analysis for a homogeneous porous layer with permeable boundaries, by considering the limiting case where the permeability of the external layers is much larger than that of the core layer.

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Antonio Barletta, Michele Celli, Stefano Lazzari, Pedro Vayssière Brandão. 2022-09-02. Gill's problem in a sandwiched porous slab. https://doi.org/10.1017/jfm.2022.919

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