Empirical estimation : Turbulent flows
The turbulent flows exhibit a chaotic behavior, this way their study is performed by the statistical tools. One of the powerful tool is the structure function analysis, which characterizes the statistics of the field. Due to the intermittent nature of these fields, the scaling exponent function can be described by the UM parameters. For velocity turbulence,
is the density flux
, with
, the parameter values
obtained by dimensional analysis, give a third order moment of the velocity structure function
.
The UM parameters can be estimated using the above formulations, and we it has been found
and
. The above figure (a) shows the comparison of the empirical structure function for velocity field and the one obtained using different models. Concerning the temperature field, the corresponding flux is a mix of the velocity flux and the temperature variance. The UM parameters obtained for the temperature field are
and
