Rotating flows represent a very interesting area for researchers and industry for their extensive use in industrial and domestic machinery and especially for their great energy potential, annular flows are an example that draws the attention of researchers in recent years. The best design and optimization of these devices require knowledge of thermal, mechanical and hydrodynamic characteristics of flows circulating in these devices. An example of hydrodynamic parameters is the speed of rotation of the moving walls. This work is to study numerically the influence of the rotating speed ratio Γ of the two moving cylinders on the mean and especially on the turbulent quantities of the turbulent flow in the annular space. The numerical simulation is based on one-point statistical modeling using a low Reynolds number second-order full stress transport closure (RSM model), simulation code is not a black box but a completely transparent code where we can intervene at any step of the calculation. We have varied Γ from -1.0 to 1.0 while maintaining always the external cylinder with same speed Ω. The results show that the turbulence structure, profiles of mean velocities and the nature of the boundary layers of the mobile walls depend enormously on the ratio of speeds. The level of turbulence measured by the kinetic energy of turbulence and the Reynolds stresses shows well that the ratio Γ is an interesting parameter to exploit turbulence in this kind of annular flows.