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Phys. Rev. E 79, 065302(R) (2009) [4 pages]

Three-dimensional poor man’s Navier-Stokes equation: A discrete dynamical system exhibiting k−5/3 inertial subrange energy scaling

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J. M. McDonough*
Departments of Mechanical Engineering and Mathematics, University of Kentucky, Lexington, Kentucky 40506-0503, USA

Received 8 September 2008; revised 2 April 2009; published 3 June 2009

Outline of the derivation and mathematical and physical interpretations are presented for a discrete dynamical system known as the “poor man’s Navier-Stokes equation.” Numerical studies demonstrate that velocity fields produced by this dynamical system are similar to those seen in laboratory experiments and in detailed simulations, and they lead to scaling for the turbulence kinetic energy spectrum in accord with Kolmogorov K41 theory.

© 2009 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevE.79.065302
DOI:
10.1103/PhysRevE.79.065302
PACS:
47.27.−i

*jmmcd@uku.edu; http://www.engr.uky.edu/~acfd

 
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