Hi Giulio
in RANS the time average of the fluctuations is zero by definition, and so will its gradients.
In case you want to compute the time-average of the gradients of the product of fluctuations (for instance, the gradients of the components of the Reynolds stress), then, as differentiating and taking the mean commute, you could get the gradients of the time-average of the product of fluctuations as follows:
0. keep in mind that avg(fluct-u*fluct-u) = avg(u*u) - avg(u)*avg(u)
1. get in pyfr the time average of the the variable and its square, say u and u*u
2. either compute the gradients of the time-average solution in Paraview or export the solution with the gradients as mentioned in the previous post.
3. in Paraview, compute the (gradients of) the product of fluctuations as the difference between the (gradients of) time-average of u*u and the (gradients of) time-average u squared: avg(u*u) - avg(u)*avg(u)
best
Giorgio