A simple model is presented of the formation of the spiral the (z,v_z) phase plane of solar-neighbourhood stars that was recently discovered in Gaia data. The key is that the frequency Omega_z at which stars oscillate vertically depends on angular momentum about the z axis in addition to the amplitude of the stars vertical oscillations. Spirals should form in both <v_phi> and <v_R> whenever a massive substructure, such as the Sgr dwarf galaxy, passes through the Galactic plane. The model yields similar spirals to those observed in both <v_phi> and <v_R>. The primary driver is the component of the tidal force that lies in the plane. We investigate the longevity of the spirals and the mass of the substructure, but the approximations inherent in the model make quantitative results unreliable. The work relies heavily on a self-consistent, multi-component model of our Galaxy produced by the AGAMA package for f(J) modelling.
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