We discuss the motion and structure of the magnetopause/boundary layer observed by Cluster in response to a joint tangential discontinuity/vortex sheet (TD/VS) observed by the Advanced Composition Explorer spacecraft on 7 December 2000. The observations are then supplemented by theory. Sharp polarity reversals in the east‐west components of the field and flow By and Vy occurred at the discontinuity. These rotations were followed by a period of strongly northward interplanetary magnetic field (IMF). These two factors elicited a two‐stage response at the magnetopause, as observed by Cluster situated in the boundary layer at the duskside terminator. First, the magnetopause suffered a large deformation from its equilibrium position, with large‐amplitude oscillations of ∼3‐min period being set up. These are argued to be mainly the result of tangential stresses associated with ΔVy the contribution of dynamic pressure changes being small in comparison. This strengthens recent evidence of the importance to magnetospheric dynamics of changes in azimuthal solar wind flow. The TD/VS impact caused a global response seen by ground magnetometers in a magnetic local time range spanning at least 12 h. The response monitored on ground magnetometers is similar to that brought about by magnetopause motions driven by dynamic pressure changes. Second, Cluster recorded higher‐frequency waves (∼79 s). Two clear phases could be distinguished from the spectral power density, which decreased by a factor of ∼3 in the second phase. Applying compressible linearized MHD theory, we show that these waves are generated by the Kelvin‐Helmholtz (KH) instability. Varying the local magnetic shear at the Cluster locale, as suggested by the temporal profile of the IMF clock angle, we find that locally stability was reinstated, so that the reduced power in the second phase is argued to be due residual KH activity arriving from locations farther to the dayside.