Rapid distortion theory for homogeneous compressed turbulence with application to modelling

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Abstract
Compressible rapid distortion theory is used to examine pressure fluctuations and the pressure–dilatation correlation in a field of turbulence subjected to rapid homogeneous compression. It is shown how a one-dimensional compression produces large solenoidal pressure fluctuations. As the dimensionality of the compression increases, the magnitude of these fluctuations decreases — it vanishes for a spherically symmetric compression. By contrast the dilatational, or acoustic, pressure fluctuations depend mainly on the net volumetric compression, and are relatively insensitive to the dimensionality of the compression. These same comments apply to the pressure–dilatation correlation. The pressure–dilatation correlation appears in the compressible turbulent kinetic energy equation and is significant in rapidly evolving flows; Reynolds stress closure models require that it be represented. The continuity equation provides a relation between pressure dilatation and the rate of change of pressure fluctuation variance. This relation is the basis for our RDT analysis. That analysis leads to a proposal for modelling the rapid contribution to pressure dilatation.