| (142) |
Following the approach of Kraichnan [15], and modified by Smirnov et al.[16] to account for inhomogeneity, a divergence-free flow field of synthetic, isotropic turbulent velocity fluctuations may be specified as follows:
|
| (142) |
where 
is the specified turbulence intensity, 
is the local velocity magnitude and:
| (143) |
is a sequence of 
three-dimensional Cartesian vectors, each component of which is a normally distributed random number with mean 0 and standard deviation 0.5. 
and 
are sequences of 
three-dimensional Cartesian vectors, each component of which is a normally distributed random number with mean 0 and standard deviation 1. 
is a sequence of 
normally distributed random numbers with mean 0 and standard deviation 1.
and 
represent the wave-number vectors and frequencies of a model turbulence spectrum defined by:
| (144) |
is a specified local length scale of the turbulence. 
is a local time scale of the turbulence, and is irrelevant for the purposes of specified initial turbulence fields where it is assumed that 
. For the specification of inflow turbulence, the convective time scale 
is used.
The default value for 
in STAR-CCM+ is 100. Using a larger number will increase the resolution of the spectrum, but will incur additional computational cost.