The shear-layer instability in the flow over a rotating disk with a free surface is investigated experimentally by flow visualizations for a large range of the flow control parameters: the aspect ratio G of the cavity, the rotationnal Reynolds number Re and the radius ratio s between the inner and outer radii of the rotating disk. This instability develops along the cylindrical shroud as sharp-cornered polygonal patterns characterized by the number of vortices m. This number m can be scaled by considering an Ekman number based on the water depth, which confirms that the shroud boundary layer is of Stewartson type. The appearance threshold of the first polygonal mode is constant by considering the mixed Reynolds number introduced by Niino and Misawa (1984) based on both the water depth at rest and the rotating disk radius. For large values of s, the instability patterns appear along the hub as small stationary cells.