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We explore the origin of phase-space substructures revealed by the secondGaia data release in the disc of the Milky Way, such as the ridges in the$V_{\phi}$-$r$ plane, the undulations in the $V_{\phi}$-$r$-$V_r$ space and thestreams in the $V_{\phi}$-$V_r$ plane. We use a collisionless N-body simulationwith co-spatial thin and thick discs, along with orbit integration, to studythe orbital structure close to the Outer Lindblad Resonance (OLR) of the bar.We find that a prominent, long-lived ridge is formed in the $V_{\phi}$-$r$plane due to the OLR which translates to streams in the $V_{\phi}$-$V_r$ planeand examine which closed periodic and trapped librating orbits are responsiblefor these features. We find that orbits which carry out small librations aroundthe $x_1(1)$ family are preferentially found at negative $V_r$, giving rise toa `horn'-like feature, while orbits with larger libration amplitudes, trappedaround the $x_1(2)$ and $x_1(1)$ families, constitute the positive $V_r$substructure, i.e. the Hercules-like feature. This changing libration amplitudeof orbits will translate to a changing ratio of thin/thick disc stars, whichcould have implications on the metallicity distribution in this plane. We findthat a scenario in which the Sun is placed close to the OLR gives rise to astrong asymmetry in $V_r$ in the $V_{\phi}$-$V_r$ plane (i.e. Hercules vs. `thehorn') and subsequently to undulations in the $V_{\phi}$-$r$-$V_r$ space. Wealso explore a scenario in which the Sun is placed closer to the bar corotationand find that the bar perturbation $alone$ cannot give rise to the thesefeatures.

On the ridges, undulations & streams in Gaia DR2: Linking the topography of phase-space to the orbital structure of an N-body bar