On a New Definition of the Reynolds Number from the Interplay of Macroscopic and Microscopic Phenomenology

  • B. E. J. Bodmann
  • M. T. Vilhena
  • J. R. Zabadal
  • D. Beck


Turbulence is a behavior seen in many fluid flows, which is conjectured to be driven by the inertia to viscosity force ratio, i.e. the Reynolds number. Even though research in turbulence has existed for more than a century there is still no consensus as how to elaborate a self-consistent and genuine theory, which describes the dynamics of a transition from a laminar to a turbulent regime or vice versa, and the geometric flow structure of turbulent phenomena. So far, it is believed that the Navier–Stokes equations model turbulence in an adequate way. However the existence of general solutions in three plus one space–time dimensions is still an open question (Cao, Titi 2007), (Cao, Titi 2008), (Constantin 2001), (Constantin et al. 2007), (Fefferman 2006).


Reynolds Number Thermal Velocity Pressure Tensor Boltzmann Transport Equation Friction Pressure 
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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • B. E. J. Bodmann
    • 1
  • M. T. Vilhena
    • 1
  • J. R. Zabadal
    • 1
  • D. Beck
    • 1
  1. 1.Universidade Federal do Rio Grande do SulPorto AlegreBrazil

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