The present manuscript investigates the influence of velocity, vorticity and temperature in a hydrogen combustor operating under Moderate or Low Intense oxygen Dilution conditions, focusing on the \(NO\) formation. The study was conducted on a database obtained from Large Eddy Simulations and an approach based on Proper Orthogonal Decomposition was used to study the most relevant coherent structures. It was shown that the dominant structures are primarily associated with air (oxidizer) and hydrogen (fuel) inlet jets and the vortex region that forms at the outlet. Modal decomposition of these specific areas identifies vortex wandering and pulsation modes. Whereas, the two jets exhibit a bending motion, tending to interact and coalesce within the vortex. Moreover, the temporal analysis of the POD coefficients shows a strong mutual connection between velocity, temperature and \(NO\) formation. It is also shown that vortex dynamics is closely related to jet modes and, consequently, strongly affects both heat transfer processes and \(NO\) formation.