AN IMPROVED MEASURE OF STRAIN STATE PROBABILITY IN TURBULENT FLOWS

Probability density functions (PDFs) of the strain-rate tensor eigenva lues are examined. It is found that the accepted normalization used to bound the intermediate eigenvalue between +/-1 leads to a PDF that mu st vanish at the end points for a non-singular distribution of strain states. This purely kinematic constraint has led previous investigator s to conclude incorrectly that locally axisymmetric deformations do no t 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 expecte d flat PDF in a Gaussian velocity field and to a PDF that indicates th e presence of axisymmetric strain states in a turbulent field. Extensi on of the new measure to compressible flow is discussed. Several earli er 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 domi nant role in the turbulent dissipation process than was previously bel ieved.