We revisit the worldwide linear theory of the vertical shear instability (VSI) in protoplanetary discs with an imposed radial temperature gradient. We focus on the regime during which the VSI has the type of a travelling inertial wave that grows in amplitude because it propagates outwards. Building on previous work describing travelling waves in skinny astrophysical discs, we develop a quantitative idea of the wave movement, its spatial construction and the physical mechanism by which the wave is amplified. We find that this viewpoint gives a helpful description of the large-scale improvement of the VSI in international numerical simulations, which includes corrugation and respiration motions of the disc. We distinction this behaviour with that of perturbations of smaller scale, wherein the VSI grows right into a nonlinear regime in place without vital radial propagation. ††pubyear: 2025††pagerange: Wood Ranger shears The vertical shear instability in protoplanetary discs as an outwardly travelling wave. Over the past 15 years, scientific consensus has converged on an image of protoplanetary discs during which the magnetorotational instability is generally absent, because of insufficient ionisation, and instead accretion is pushed by laminar non-excellent magnetic winds (e.g., Turner et al., 2014
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The Vertical Shear Instability in Protoplanetary Discs as an Outwardly Travelling Wave. I. Linear Theory
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