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Recent studies have revealed an oscillating asymmetry in the verticalstructure of the Milky Way's disc. Here we analyze 16 high-resolution, fullycosmological simulations of the evolution of individual Milky Way-sizedgalaxies, carried out with the MHD code AREPO. At redshift zero, about $70\%$of our galactic discs show strong vertical patterns, with amplitudes that canexceed 2 kpc. Half of these are typical `integral sign' warps. The rest areoscillations similar to those observed in the Milky Way. Such structures arethus expected to be common. The associated mean vertical motions can be aslarge as 30~km/s. Cold disc gas typically follows the vertical patterns seen inthe stars. These perturbations have a variety of causes: close encounters withsatellites, distant flybys of massive objects, accretion of misaligned cold gasfrom halo infall or from mergers. Tidally induced vertical patterns can beidentified in both young and old stellar populations, whereas those originatingfrom cold gas accretion are seen mainly in the younger populations. Galaxieswith regular or at most weakly perturbed discs are usually, but not always,free from recent interactions with massive companions, although we have onecase where an equilibrium compact disc reforms after a merger.

Warps and waves in the stellar discs of the Auriga cosmological simulations