A numerical model is implemented to describe fluid dynamic processes associated with mid-latitude small-scale (10 km) upper ocean fronts by using modified state of the art computational fluid dynamics tools. A periodic system was simulated using three different turbulent closures: 1) URANS-Reynolds Stress Model (RSM, seven equation turbulence model), 2) LES-Standard Smagorinsky (SS, algebraic model), and 3) LES-Modified Smagorinsky, introducing a correction for non-isotropic grids (MS). The results show the front developing instabilities and generating sub-mesoscale structures after four days of simulation. A strongly unstable shear flow is found to be confined within the mixed layer with a high Rossby number (Ro > 1) and high vertical velocity zones. The positive (negative) vertical velocity magnitude is found to be approximately O(10(-3)) m/s(O(10(-2)) m/s), one (two) order(s) of magnitude larger than the vertical velocity outside the sub-mesoscale structures, where the magnitude is stable at O(10(-4)) m/s. The latter value is consistent with previous numerical and experimental studies that use coarser grid sizes and therefore do not explicitly calculate the small scale structures. The nonlinear flow introduced by the sub-mesoscale dynamics within the mixed layer and the non-isotropic grid used in the calculations generates a disparity between the predicted horizontal wave-number spectra computed using the RSM model with respect to the linear eddy viscosity model SS. The MS approach improves SS predictions. This improvement is more significant below the mixed layer in the absence of flow nonlinearities. The horizontal spectra predicted with the RSM model fits a slope of 3 for large scale structures and a slope between 2 and -5/3 for turbulent structures smaller than 300 m. This work contributes to the investigation of the physical and methodological aspects for the detailed modelling and understanding of small scale structures in ocean turbulence.