Theoretical and Computational Fluid Dynamics

, Volume 7, Issue 5, pp 363–395 | Cite as

Chaos and direct numerical simulation in turbulence



We show that direct numerical simulation will yield turbulent flowfields which are strongly dependent upon computer hardware and software. A computed flow trajectory is apparently uncorrelated to the true solution of a flowfield if it is allowed to evolve over a long time, and hence is called a pseudo-orbit. This is due to the trajectory instability of chaotic turbulent flows. All is not lost, however; a long-time average of flow quantities can now be computed using a pseudo-orbit by invoking the shadowing lemma. For the inviscid flow, this time average tends to approach asymptotically the phase average as predicted by the classical ergodic theorem. Although the inviscid two-dimensional flow has no real physical importance, the existence of canonical (equilibrium) distribution permits us to examine the accuracy of time averaging based on the pseudo-orbit and its inherent limitations.


Mathematical Method Direct Numerical Simulation Inherent Limitation Phase Average Computer Hardware 
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Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Jon Lee
    • 1
  1. 1.Wright Laboratory (FIB)Wright-Patterson Air Force BaseUSA

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