Periodic porous structures manufactured using 3D-printing are candidates for intensified process devices. Detailed measurements of the velocity field are required to characterise the turbulent mixing generated by flow through the channel network. We used time-resolved single-shot spiral magnetic resonance velocity (MRV) imaging to noninvasively record snapshots of the velocity field for water flowing through a Schwarz Diamond monolith. The time-resolved velocity data lend themselves to more detailed analysis than is possible with conventional time-averaged MR methods. The turbulent energy spectra measured with MRV confirmed that the pore network places an upper size limit on the eddies that could exist in the flow. The -5/3 power-law scaling from Kolmorogov theory was only attained at a Reynolds number around 2000, indicative of a higher transition point to a fully turbulent regime than is usually reported for random porous media. The local Reynolds stress tensor showed considerable anisotropy within the network, which affects mass transport to the channel surfaces. The time-resolved MRV method offers valuable insights into turbulence in porous media that can inform the design and operation of novel geometries.