is specified together with the local length scale, 
.
Smirnov et al.[16] further modified Kraichnan's [15] method to allow anisotropic turbulent velocity fluctuations to be specified. In this case, the local Reynolds stress tensor, is specified together with the local length scale, .
Before applying the spectrum of random numbers, the local Reynolds stress tensor is rotated into its principal coordinates, to obtain a diagonal tensor 
. The wave number sequence, 
, is modified as follows:
| (145) |
where 
, 
and 
are the components of the 
vector and 
, 
and 
are the diagonal components of 
.
The spectrum is then applied as follows to obtain an intermediate field of velocity fluctuations:
| (146) |
where 
, 
, 
, 
, 
, 
and 
are defined as with the isotropic field.
This intermediate field, termed 
is then scaled as follows:
| (147) |
where 
, 
and 
are the components of 
.
Finally, the field of velocity fluctuations, 
, is obtained by rotating 
from the principal coordinates of 
back into flow field's coordinates.