Diagnostic statistics for the assessment and characterization of complex turbulent ows

A simple parameterization scheme for a complex turbulent ow using nondimensional parameters coming from the Reynolds stress equations is given. De nitions and brief descriptions of the physical signi cance of several nondimensional parameters that are used to characterize turbulence from the viewpoint of single-point turbulence closures are given. These nondimensional parameters re ect measures of 1) the spectral band width of the turbulence, 2) deviations from the ideal Kolmogorov behavior, 3) the relative magnitude, orientation, and temporal duration of the deformation to which the turbulence is subjected, 4) one and two-point measures of the large and small scale anisotropy of the turbulence and 5) inhomogeneity. This is an attempt to create a more systematic methodology for the diagnosis and classi cation of turbulent ows as well as in the development, validation and application of turbulence model strategies. The parameters serve also to indicate the adequacy of various assumptions made in single-point turbulence models and in suggesting the appropriate turbulence strategy for a particular complex ow. The compilation will be of interest to experimentalists and to those involved in either computing turbulent ows or whose interests lies in verifying the adequacy of the phenomenological beliefs used in turbulence closures. 1This research was supported by the National Aeronautics and Space Administration under NASA Contract No. NAS1-19480 while the author was in residence at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA 23681-0001.