In a diurnal cycle, different manifestations of a planetary boundary layer are generated by thermal and mechanical forcing. A stable boundary layer occurs when the soil surface has a lower temperature than the air above. In this layer, wind shear is the main mechanism of turbulence generation. In the present study, a direct numerical simulation of an Ekman layer on a surface is presented to study the different turbulent patterns that occur during evolution from a neutral boundary layer to a weakly stable boundary layer. The preliminary study shows the appearance of turbulent structures near the surface, due to the imposition of a stratification.