This thesis presents a study on turbulence generated by space-filling fractal square grids using Particle Image Velocimetry (PIV) as the experimental technique in a water tunnel. The main focus of the present work is on the turbulent structure of the velocity gradient tensor. The need for such a study arises due to the discovery of a new scaling for the turbulent energy dissipation related, though not exclusively, to flows generated by such grids.

At the centreline, turbulence generated by space-filling fractal square grids is composed by a production region, where turbulence intensity increases, followed by a decay one. Therefore, one of the main novelties presented here is the spatial evolution of turbulence structures as opposed to the vast majority of work done in a fixed spatial location. The locations in the production and decay regions were chosen carefully to have similar Reynolds numbers based on the Taylor microscale, turbulence intensity and strain level. Nevertheless, it is shown that the distribution of vortex stretching/compressing, eigenvalues of the strain rate tensor and the alignments of vorticity with eigenvectors of the strain rate tensor are different between these two locations. In addition it is found that the Kolmogorov's -5/3 exponent for the turbulent energy spectrum or its physical space counterpart 2/3 scaling for the second order structure function are already seen in the production region where one would not expect that Kolmogorov's assumptions would hold.

The production region is studied in more detail by estimating the terms in the non-homogeneous Kármán-Howarth-Monin equation. Scale-by-scale energy transfers show the presence of an inverse cascade along an attractive axis, which is at a small angle with the streamwise direction and a forward cascade in the transverse direction.