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Topological Classification and Identification of Small-Scale Turbulence Structure

  • J. C. Vassilicos
Part of the International Centre for Mechanical Sciences book series (CISM, volume 353)

Abstract

We seek ways to characterise and identify small-scale turbulence structure without ad hoc preconceived ideas of what a turbulent eddy, for example, should be, or what properties it should have. The turbulence field is a complex web of chaotic, random and ordered phenomena, and a numerical high Reynolds number solution of the Navier-Stokes equation cannot provide much insight into the kinematics and dynamics of the turbulence by itself. Direct Numerical Simulation (DNS) of turbulent flows generates large data sets, and gives us the satisfaction of having transformed a cryptic partial differential equation into a large set of inarticulate numbers. The problem of characterisation and identification of small-scale turbulence structure is a problem of transforming this inarticulate set of numbers into meaningful qualitative and quantitative statements about the kinematics and dynamics of the turbulence. In these lectures we introduce a recent attempt to characterise and identify topological and geometrical features of the turbulence based on a classification of turbulence singularities which follows as a consequence of Kolmogorov’s 1941 similarity theory of small-scale turbulence. A classification, characterisation and identification of turbulence singularities is important because this is where the highest velocity gradients are to be found in the turbulence.

Keywords

Direct Numerical Simulation Hausdorff Dimension Vortex Tube Vortex Sheet Koch Curve 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Wien 1996

Authors and Affiliations

  • J. C. Vassilicos
    • 1
  1. 1.DAMTPCambridgeUK

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