The instability modes that lead to turbulence between two concentric spheres, the inner one rotating while the outer is at rest, are investigated through visualization and using the electrodiffusion (ED) method. The wall velocity gradients are measured for the first time in a spherical shell by ED method. The exploration of the flow regimes is carried out for a dimensionless gap width View the MathML source of 0.107, an aspect ratio Γ=H/d over the interval (17–21) and a Taylor number in the range (22–1500). The influence of these parameters on the apparition of instabilities is elucidated. The evolution of the flow patterns is visualized and also quantified by the wall velocity gradients and their fluctuations. Using the fast Fourier transform, the time series of velocity gradient obtained by the ED method permitted analysis and identification of the fundamental frequencies and their evolution associated with each flow state.