TY - JOUR

T1 - A minimal model for vertical shear instability in protoplanetary accretion disks

AU - Yellin-Bergovoy, Ron

AU - Umurhan, Orkan M.

AU - Heifetz, Eyal

N1 - Publisher Copyright:
© 2021 Informa UK Limited, trading as Taylor & Francis Group.

PY - 2021

Y1 - 2021

N2 - The vertical shear instability is an axisymmetric effect suggested to drive turbulence in the magnetically inactive zones of protoplanetary accretion disks. Here we examine its physical mechanism in analytically tractable “minimal models” in three settings that include a uniform density fluid, a stratified atmosphere, and a shearing-box section of a protoplanetary disk. Each of these analyses show that the vertical shear instability's essence is similar to the slantwise convective symmetric instability in the mid-latitude Earth atmosphere, in the presence of vertical shear of the baroclinic jet stream, as well as mixing in the top layers of the Gulf Stream. We show that in order to obtain instability, the fluid parcels' slope should exceed the slope of the mean absolute momentum in the disk radial-vertical plane. We provide a detailed and mutually self-consistent physical explanation from three perspectives: in terms of angular momentum conservation, as a dynamical interplay between a fluid's radial and azimuthal vorticity components, and from an energy perspective involving a generalised Solberg-Høiland Rayleigh condition. Furthermore, we explain why anelastic dynamics yields oscillatory unstable modes and isolate the oscillation mechanism from the instability one.

AB - The vertical shear instability is an axisymmetric effect suggested to drive turbulence in the magnetically inactive zones of protoplanetary accretion disks. Here we examine its physical mechanism in analytically tractable “minimal models” in three settings that include a uniform density fluid, a stratified atmosphere, and a shearing-box section of a protoplanetary disk. Each of these analyses show that the vertical shear instability's essence is similar to the slantwise convective symmetric instability in the mid-latitude Earth atmosphere, in the presence of vertical shear of the baroclinic jet stream, as well as mixing in the top layers of the Gulf Stream. We show that in order to obtain instability, the fluid parcels' slope should exceed the slope of the mean absolute momentum in the disk radial-vertical plane. We provide a detailed and mutually self-consistent physical explanation from three perspectives: in terms of angular momentum conservation, as a dynamical interplay between a fluid's radial and azimuthal vorticity components, and from an energy perspective involving a generalised Solberg-Høiland Rayleigh condition. Furthermore, we explain why anelastic dynamics yields oscillatory unstable modes and isolate the oscillation mechanism from the instability one.

KW - Protoplanetary accretion disks

KW - dead zone

KW - shear instability

KW - slantwise convection

UR - http://www.scopus.com/inward/record.url?scp=85111856158&partnerID=8YFLogxK

U2 - 10.1080/03091929.2021.1941921

DO - 10.1080/03091929.2021.1941921

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AN - SCOPUS:85111856158

SN - 0309-1929

VL - 115

SP - 674

EP - 695

JO - Geophysical and Astrophysical Fluid Dynamics

JF - Geophysical and Astrophysical Fluid Dynamics

IS - 5-6

ER -