Linear and nonlinear evolution of isolated disturbances in a growing thermal boundary layer in porous media

Asma Selim, D Andrew S Rees

Research output: Chapter in Book/Report/Conference proceedingChapter

3 Citations (Scopus)

Abstract

We consider the onset and development of convection in a saturated porous half-space which is initially cold, but where the lower boundary has its temperature raised suddenly to a new uniform level. The resulting thermal boundary layer diffuses upwards and eventually becomes thermoconvectively unstable. Previous works by the present authors have considered in turn linearised theory, the nonlinear development of cells, and the destabilisation of such cells due to subharmonic disturbances. In all three papers it was assumed that the convection pattern is horizontally periodic. In the present paper we relax this restriction by considering how an isolated disturbance develops in time, and this is compared with the horizontally periodic flows. New cells are generated outboard of existing ones so that the convecting region spreads horizontally with time. The effective wavelengths are also found to increase with time, newer cells having larger wavelengths than older ones. We also consider the nonlinear development of these disturbances.
Original languageEnglish
Title of host publicationAIP Conference Proceedings on Porous Media and Its Applications in Science, Engineering and Industry
EditorsK Vafai
Place of PublicationMelville
PublisherAmerican Institute of Physics
Pages47-52
Number of pages6
Volume1254
ISBN (Print)9780735408036
DOIs
Publication statusPublished - 2010
Event3rd International Conference on Porous Media and its Applications in Science, Engineering and Industry - Montecatini, Italy
Duration: 20 Jun 201025 Jun 2010

Publication series

NameAIP Conference Proceedings
PublisherAmerican Institute of Physics

Conference

Conference3rd International Conference on Porous Media and its Applications in Science, Engineering and Industry
CountryItaly
CityMontecatini
Period20/06/1025/06/10

Keywords

  • nonlinear convection
  • unsteady boundary layer
  • linear instability
  • free convection
  • isolated disturbance
  • Porous media

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  • Cite this

    Selim, A., & Rees, D. A. S. (2010). Linear and nonlinear evolution of isolated disturbances in a growing thermal boundary layer in porous media. In K. Vafai (Ed.), AIP Conference Proceedings on Porous Media and Its Applications in Science, Engineering and Industry (Vol. 1254, pp. 47-52). (AIP Conference Proceedings). American Institute of Physics. https://doi.org/10.1063/1.3453837