A dimensional-decomposition approach, decomposing 3D into 3×1D for turbulent (reacting) flows are motivated, discussed and investigated. In the three-dimensional Linear Eddy Model (LEM3D), three orthogonally intersecting arrays of 1D domains are coupled to capture the 3D characteristics of fluid flows. The currently used recouplings for LEM3D are enlightened and thoroughly discussed. A study of the flame front of a freely propagating laminar premixed flame shows that the flame stabilizes at the upstream face of the initial solution when both the advective and auxiliary recouplings are activated. Furthermore, results from LEM3D simulations of a vitiated co-flow burner are re-visited providing a more detailed discussion of the noted early mixing and reaction of the hydrogen fuel of the burner. The main conclusion of the present work is that the auxiliary coupling based on rotations of the 3D control volumes introduces very large gradients in the near-field geometry of jets, leading to a significant amount of artificial diffusion and locally increased burning rates. This implies that applications of LEM3D should be restricted to sub-regions where high-resolution treatment of scalar mixing and reaction is of particular interest. © 2020, The Author(s).