An LES simulation of the turbulent mixing in a T-junction has been carried out with the spectral element code NEK5000. Numerical results have been compared with an available experiment. A large database of snapshots has then been collected and Proper Orthogonal Decomposition (POD), a powerful statistical tool, has been used to identify the most energetic modes of turbulence. Since POD was also performed on the experiment PIV data, a further means of verification and validation was available for the present case. The structure of the numerical POD modes offers additional insight into the physics of turbulence in T-junctions. The present work also presents a more general opportunity to make advection-diffusion computations with CFD codes less expensive when buoyancy effects are not present. One could in fact solve the Navier-Stokes equations to obtain the principal modes of turbulence and then use those modes to solve the advection-diffusion equation for the temperature or a general passive scalar on considerably longer time frames.