Characterization of the dynamical behavior of the compressible "poor man's navier-stokes equations"

J. P. Strodtbeck, J. M. McDonough, P. D. Hislop

Research output: Contribution to journalReview articlepeer-review

1 Scopus citations


The compressible "poor man's NavierStokes equations" (PMNS equations) are a discrete dynamical system derived from a Galerkin expansion of the compressible NavierStokes equations. Complete details of the derivation are presented, with attention given to the differences from the original, incompressible case. A thorough numerical investigation of the bifurcation behavior is given in the form of regime maps characterizing the different kinds of dynamical behavior, bifurcation sequences, power spectral density analysis, time series and phase portraits. As in the case of previously studied incompressible PMNS equations, the full range of dynamical behavior associated with physical turbulence is exhibited by the system of coupled maps. The conclusion is drawn that this system can be viable as a source of temporal fluctuations in synthetic-velocity subgrid-scale models for large-eddy simulation.

Original languageEnglish
Article number1230004
JournalInternational Journal of Bifurcation and Chaos
Issue number1
StatePublished - Jan 2012


  • Bifurcation
  • discrete dynamical systems
  • turbulence
  • turbulence modeling

ASJC Scopus subject areas

  • Modeling and Simulation
  • Engineering (miscellaneous)
  • General
  • Applied Mathematics


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