The statistics of the organized vortical structure in turbulent mixing layers

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Abstract
The statistics of the large scale vortex structure in turbulent mixing layers have been investigated theoretically. It is shown that similarity in the fully developed flow results in a common description of the Eulerian and Lagrangian statistics. In the Eulerian frame of reference, a conservation equation is derived and solved to show that the distribution of vortex circulation is lognormal. It is also shown that the standard deviation normalized by the mean value of the distribution depends only on the amalgamation mechanism. The value for pairing is in good agreement with experimental measurements. These results are used to calculate the life span and survival probabilities of the vortices in the Lagrangian frame of reference. These distributions are in good agreement with direct measurements of the life span probability and with space‐time correlation measurements, respectively. Some implications of these results on the dynamics of the large scale vortices in the fully developed turbulent flow are discussed.