From visualizations and velocity measurements, we study the formation of new spiral patterns at the periphery of a rotor-stator cavity when an axial inward throughflow is superimposed. We determine the transition diagram for a given intermediate aspect ratio in the plane (${\hbox {\it Re}},V_z$), where ${\hbox {\it Re}}$ is the rotational Reynolds number and $V_z$ the axial velocity in the radial gap between the rotating disk and the shroud. Both techniques are used to characterize the frequency, the azimuthal wavenumber, the inclination angle of the spirals and to localize them axially and radially. We also show that this new instability is a crossflow instability due to the strong competition between rotation and throughflow.