Summary
We present an, account of the linear instability of Darcy-Boussinesq convection in a uniform, unstably stratified porous layer at arbitrary inclinations α from the horizontal. A full numerical solution of the linearized disturbance equations is given and the detailed graphical results used to motivate various asymptotic analyses. A careful study shows that at large Rayleigh numbers two-dimensional instability can only arise when α≤31.30°. However it is also demonstrated that the maximum inclination below which this instability may be possible is the slightly greater value of 31.49° which corresponds to a critical Rayleigh number of 104.30.
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Rees, D.A.S., Bassom, A.P. The onset of Darcy-Bénard convection in an inclined layer heated from below. Acta Mechanica 144, 103–118 (2000). https://doi.org/10.1007/BF01181831
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DOI: https://doi.org/10.1007/BF01181831