The Reynolds stresses alone are not sufficient to characterize complex turbulent flows adequately. Complementary information, contained in the structure dimensionality tensor, must also be included in one-point turbulence models. This work uses hypothetical turbulent eddies to bring awareness of turbulence structure into the turbulence model. Averaging over a large ensemble of eddies produces a set of one-point statistics, representative of the eddy field, and a set of equations of state relating the Reynolds stresses and the structure dimensionality to the eddy statistics. An algebraic model for the eddy statistics is constructed in terms of the local mean deformation and two turbulent scales; the turbulent kinetic energy and the large-scale enstrophy. The algebraic model is further sensitized to the presence of walls by a blocking scheme, which ensures proper asymptotic behavior for the Reynolds stresses in the vicinity of walls. Contrary to existing ad-hoc definitions of a second scale equation, the large-scale enstrophy equation has a fundamental background; it is derived from the large-scale vorticity equation. Its terms represent large-scale processes, and their exact form provides valuable guidance when making choices for their closure, and when matching their asymptotic behavior in the vicinity of walls. The algebraic model produces physically realistic Reynolds stresses and structure tensors for different combinations of mean strain and mean rotation, with and without frame rotation. The complete model, with evolution equations for the turbulent scales and algebraic equations for the turbulence structure, was successfully implemented. The full model was found to produce excellent results for a set of channel flows in fixed frames and in spanwise-rotating frames of reference.