This report develops and studies a new family of Navier–Stokes equation regularizations: Leray–Tikhonov regularizations with time relaxation models. This new family of turbulence models is based on a modification (consistent with the large scales) of Tikhonov–Lavrentiev regularization. With this approach, we obtain an approximation of the unfiltered solution by one filtering step. We introduce the modified Tikhonov deconvolution operator and study its mathematical properties. We also perform rigorous numerical analysis of a computationally attractive algorithm for this family of models and present numerical experiments using it