CHARACTERIZATION OF THE DYNAMICAL BEHAVIOR OF THE COMPRESSIBLE "POOR MAN'S NAVIER–STOKES EQUATIONS"

Abstract

The compressible "poor man's Navier–Stokes equations" (PMNS equations) are a discrete dynamical system derived from a Galerkin expansion of the compressible Navier–Stokes 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.