Turbulent and Nonturbulent Vortices

  • Donald Greenspan
Part of the Modeling and Simulation in Science, Engineering & Technology book series (MSSET)


Since turbulence is the most commonly observed form of fluid behavior, interest has been exceptional in the modeling of related phenomena. Beginning with G. I. Taylor’s seminal paper (Taylor (1921)), one school of study (Favre (1964)) has emphasized the statistical approach. A second major school of thought, following fundamental papers of Landau (1944), Hopf (1984), Lorenz (1963), and Ruelle and Takens (1971) uses Galerkin approximations to simplify the Navier-Stokes equations and bifurcation theory to analyze the resulting ordinary differential system (Barenblatt, Looss and Joseph (1983)). A more recent, computer-oriented approach is to solve the full Navier-Stokes equations numerically, assuming, of course, that these equations represent turbulent flow in some average sense (Markatos (1986)). In addition, there exists a variety of no less interesting, but less studied, approaches, as, for example, the thermodynamic model of Malkus (1960).


Velocity Field Instantaneous Velocity Fluid Particle Vortex Motion Galerkin Approximation 
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Copyright information

© Birkhäuser Boston 1997

Authors and Affiliations

  • Donald Greenspan
    • 1
  1. 1.Department of MathematicsUniversity of Texas at ArlingtonArlingtonUSA

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