STATISTICAL COEFFICIENTS IN THE EQUATION FOR THE JOINT 
PROBABILITY DENSITY OF A SCALAR AND ITS GRADIENT

V. A. Babenko, Yu. V. Zhukova,
V. A. Sosinovich,* and J. Hierro

UDC 532.517.4

The characteristic scales, dispersions, and dissipation 
rates of isotropic, degenerate, turbulent velocity and scalar fields 
as well as several third-order moments for these fields have been 
determined and compared to those obtained by direct numerical simulation. 
These quantities determined as a time function were used to close 
the equation for the joint probability density of a scalar and its 
gradient, obtained by the authors earlier. The coefficients of this 
equation calculated using two models developed by the authors are 
in good agreement with those determined by direct numerical simulation.

A. V. Luikov Heat and Mass Transfer Institute, National 
Academy of Sciences of Belarus, 15 P. Brovka Str., Minsk, 220072, 
Belarus. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 77, 
No. 2, pp. 65-74, March-April, 2004. Original article submitted 
July 25, 2003.