Flow-thermodynamics interactions in decaying anisotropic compressible turbulence with imposed temperature fluctuations
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abstract
The fundamental nature of the non-linear flow-thermodynamics interactions in a compressible turbulent flow with imposed temperature fluctuations is investigated. Direct numerical simulations (DNS) of decaying anisotropic compressible turbulence (turbulent Mach number 0.06-0.6) with imposed temperature fluctuations are performed to examine: (i) interactions between solenoidal and dilatational kinetic energy; (ii) partition between dilatational kinetic energy and thermodynamic potential energy; and (iii) redistribution of solenoidal and dilatational kinetic energy among the various Reynolds stress components. It is found that solenoidal kinetic energy levels and return-to-isotropy are weakly dependent on Mach number but independent of imposed temperature fluctuations in the parameter range studied. The dilatational kinetic energy generated is proportional to the square of the pressure fluctuations associated with the initial solenoidal and temperature fluctuations and thus a strong function of Mach number and heat release intensity. The energy exchange between dilatational kinetic and potential energy is driven by a strong proclivity toward equipartition. Consequently, the dynamics of pressure-dilatation (pd), which is the mechanism of this energy exchange between dilatational and potential energies, is dictated entirely by the requirement to impose energy equipartition. Based on the results, we provide a physical picture of the solenoidal-dilatational-potential energy interactions and the action of pressure-dilatation. The identification of the fundamental precepts underlying the various interactions is of great utility for turbulence closure model development. Copyright Springer-Verlag 2011.
