The onset of penetrative convection in an inclined porous layer

Giuseppe Arnone, Giulio Cantini, Florinda Capone, Mauro Carnevale

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In the present article, a model for penetrative convection in a fluid-saturated inclined porous medium is analyzed. Penetrative convection occurs when an unstably stratified fluid moves into a stably stratified region. In this study, it will be shown that the inclination of the layer plays a relevant role for the penetrative thermal convection of a fluid-saturated porous medium. The results reported in the literature for the limiting case of horizontal layer are recovered and the numerical results for the linear instability, obtained via the Chebyshev-τ method, show that the most destabilizing perturbations are the longitudinal and, as expected, the transverse ones destabilize only up to a certain critical inclination angle of the layer. Moreover, in the numerical analysis of the three-dimensional perturbations, we show that the longitudinal perturbations are the most destabilizing not only with respect to the transverse but also with respect to any general perturbation. We also give nonlinear stability results for the longitudinal perturbations via the weighted energy method.

Original languageEnglish
Article number124532
JournalInternational Journal of Heat and Mass Transfer
Early online date3 Aug 2023
Publication statusPublished - 1 Dec 2023

Bibliographical note

Funding Information:
This paper has been performed under the auspices of the National Group of Mathematical Physics (GNFM-INdAM). G. Arnone would like to thank Progetto Giovani GNFM 2023: “Modelli per la propagazione termica governati dalla legge di Darcy frazionaria”, CUP_E53C22001930001. The authors want to thank Simon Vella for his expertise in helping them to present the 3D numerical simulations with high-quality images and Jacopo Gianfrani for his helpful suggestions. The authors kindly thank the anonymous Referees, whose suggestions and comments led to significant improvements in the manuscript.


  • Chebyshev-tau method
  • Inclined layer
  • Instability analysis
  • Nonlinear stability
  • Penetrative convection
  • Porous media

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanical Engineering
  • Fluid Flow and Transfer Processes


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