Optimal large eddy simulation (OLES) is an approach to LES sub-grid modeling that requires multi-point correlation data as input. Until now, this has been obtained by analyzing DNS statistics. In the finite-volume OLES formulation studied here, under the assumption of small-scale homogeneity and isotropy, these correlations can be theoretically determined from Kolmogorov inertial-range theory, small-scale isotropy, along with the quasi-normal approximation. These models are expressed as generalized quadratic and linear finite volume operators that represent the convective momentum flux. These finite volume operators have been analyzed to determine their characteristics as numerical approximation operators and as models of small-scale effects. In addition, the dependence of the model operators on the anisotropy of the grid and on the size of the stencils is analyzed to develop idealized general operators that can be used on general grids. The finite volume turbulence operators developed here will be applicable in a wide range of LES problems. / text