We revisit the global linear theory of the vertical shear instability (VSI) in protoplanetary discs with an imposed radial temperature gradient. We deal with the regime by which the VSI has the form of a travelling inertial wave that grows in amplitude as it propagates outwards. Building on previous work describing travelling waves in skinny astrophysical discs, Wood Ranger Power Shears reviews we develop a quantitative concept of the wave movement, its spatial construction and the physical mechanism by which the wave is amplified. We discover that this viewpoint provides a helpful description of the large-scale development of the VSI in global numerical simulations, which includes corrugation and respiration motions of the disc. We distinction this behaviour with that of perturbations of smaller scale, by which the VSI grows into a nonlinear regime in place with out vital radial propagation. ††pubyear: buy Wood Ranger Power Shears Wood Ranger Power Shears coupon Wood Ranger Power Shears specs Shears specs 2025††pagerange: The vertical shear instability in protoplanetary discs as an outwardly travelling wave. Over the last 15 years, scientific consensus has converged on an image of protoplanetary discs in which the magnetorotational instability is usually absent, due to inadequate ionisation, and as an alternative accretion is driven by laminar non-ideal magnetic winds (e.g., Turner et al., 2014; Lesur, 2021). Concurrently, researchers have better appreciated that protoplanetary discs are subject to a fascinating array of hydrodynamic instabilities, Wood Ranger Power Shears reviews which may supply a low level of turbulent activity and/or kind structures, comparable to zonal flows and vortices (Lesur et al., 2023). While probably unimportant for accretion, these instabilities are likely to influence mud diffusion and coagulation, and thus planet formation generally.
Researchers have concentrated on the vertical shear instability (VSI; Nelson et al., 2013), particularly, due to its relative robustness and supposed prevalence over a number of tens of au (Pfeil & Klahr, 2019; Lyra & Umurhan, 2019). Current analysis activity is targeted on including increasingly more bodily processes (e.g. Stoll & Kley, 2014, 2016; Flock et al., 2020; Cui & Bai, 2020; Ziampras et al., 2023), and yet the VSI’s fundamental dynamics are nonetheless incompletely understood. This uncertainty contains (unusually) its linear theory and initial progress mechanism, not only its nonlinear saturation. The VSI’s local Boussinesq linear theory is satisfying and complete, each mathematically and bodily (Urpin & Brandenburg, 1998; Latter & Papaloizou, Wood Ranger Power Shears reviews 2018), Wood Ranger Power Shears reviews nevertheless it does not be a part of up easily to the linear problem in vertically stratified local or world fashions (Nelson et al., 2013; Barker & Latter, 2015). For Wood Ranger Power Shears reviews example, the ‘body modes’ of stratified models (rising inertial waves) fail to seem in the Boussinesq approximation at all, while the identification of the ‘surface modes’ as Boussinesq modes stays insecure.
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\x22,\x22globalName\x22:\x22trayride\x22,\x22clientExperimentsStateBlob\x22:\x22\x5bnull,null,null,null,null,null,null,\x5b\x5d,\x5b\x5d\x5d\x22\x7d\x7d'; 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Moreover, Wood Ranger Power Shears shop Wood Ranger Power Shears shop Power Shears order now we do not have a physical image of how the VSI drives the expansion of the ‘body modes’. The VSI’s nonlinear behaviour throws up additional puzzles. For example: Why are the (quicker rising) floor modes suppressed and supplanted by the physique modes? This is the primary of a collection of papers that addresses a few of these points, using analytical techniques complemented by carefully calibrated numerical experiments. Our predominant aim is to develop a linear, and weakly nonlinear, principle for travelling VSI physique modes in world disc models. 1,2, travel radially outwards as they develop; they due to this fact propagate away from their birthplace to radii with completely different disc properties, which then impression on any additional progress and continuing propagation. This behaviour contrasts with that of smaller-scale modes (of higher nn), which grow and saturate in place without important radial propagation. As nonlinear VSI simulations are dominated by outwardly travelling perturbations, it is crucial to know them.
This paper outlines the linear theory of VSI travelling waves, superseding previous local analyses, which were unable to track their global propagation, and former international analyses, which had been restricted to standing waves and comparatively quick radial extents. Ensuing papers will discover the VSI’s weakly nonlinear interactions, which govern the transition between wave zones, and current illustrative numerical simulations. There are a number of new outcomes on this paper. We offer a novel physical explanation for the VSI when it takes the form of a travelling inertial wave; the growth mechanism could be understood both by way of the work executed on the elliptical fluid circuits that represent the fundamental wave movement, or in terms of Reynolds stresses working on each the vertical and radial Wood Ranger Power Shears reviews. Reynolds stress is surprisingly vital and accounts for nearly all of the vitality funds of the VSI. We also reveal that regular linear wavetrains, involving ‘corrugation’ and ‘breathing’ modes, are an inevitable outcome of the VSI, if there's a continuous supply of small-amplitude fluctuations at small radii.