On turbulence in fractal porous media

Research output: Contribution to journalArticlepeer-review


We examine three fundamental equations governing turbulence of an incompressible Newtonian fluid in a fractal porous medium: continuity, linear momentum balance and energy balance. We find that the Reynolds stress is modified when a local, rather than an integral, balance law is considered. The heat flux is modified from its classical form when either the integral or local form of the energy density balance law is studied, but the energy density is always unchanged. The modifications of Reynolds stress and heat flux are expressed directly in terms of the resolution length scale, the fractal dimension of mass distribution and the fractal dimension of a fractal's surface. When both fractal dimensions become integer (respectively 3 and 2), classical equations are recovered.

Original languageEnglish (US)
Pages (from-to)1111-1117
Number of pages7
JournalZeitschrift fur Angewandte Mathematik und Physik
Issue number6
StatePublished - Nov 2008


  • Averaging of perturbations
  • Balance laws
  • Energy density
  • Fractal media
  • Heat flux
  • Porous media
  • Reynolds stress
  • Turbulence

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Physics and Astronomy(all)


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