  Two conditional averages for the increment Delta(x,x+r) = T(x)-T(x+r) of the
scalar field are estimated for DNS data: H(Delta)=<nabla^2
Delta(x,x+r)|Delta(x,x+r)> and G(Delta)=<|nabla Delta(x,x+r)|^2| Delta(x,x+r)>.
The probability density function P(Delta) for Delta(x,x+r) is also calculated.
If Delta, P(Delta), H(Delta), and G(Delta) are expressed as theta, P(theta),
h(theta), and g(theta) in a dimensionless form, the data analysis has revealed
interesting simple relationships between them. These relations may be helpful
to construct a turbulence model.
