An improved measure of strain state probability in turbulent flows

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Abstract
Probability density functions (PDFs) of the strain-rate tensor eigenvalues are examined. It is found that the accepted normalization used to bound the intermediate eigenvalue between ±1 leads to a PDF that must vanish at the end points for a non-singular distribution of strain states. This purely kinematic constraint has led previous investigators to conclude incorrectly that locally axisymmetric deformations do not exist in turbulent flows. An alternative normalization is presented that does not bias the probability distribution near the axisymmetric limits. This alternative normalization is shown to lead to the expected flat PDF in a Gaussian velocity field and to a PDF that indicates the presence of axisymmetric strain states in a turbulent field. Extension of the new measure to compressible flow is discussed. Several earlier results concerning the likelihood of various strain states and the correlation of these with elevated kinetic energy dissipation rate are reinterpreted in terms of the new normalization. Most importantly, it is found that regions of axisymmetric expansion play a much more dominant role in the turbulent dissipation process than was previously believed.