Non-axisymmetric instabilities in discs with imposed zonal flows

Abstract

We conduct a linear stability calculation of an ideal Keplerian flow on which a sinusoidal zonal flow is imposed. The analysis uses the shearing sheet model and is carried out both in isothermal and adiabatic conditions, with and without self-gravity (SG). In the non-SG regime a structure in the potential vorticity (PV) leads to a non-axisymmetric Kelvin-Helmholtz (KH) instability; in the short-wavelength limit its growth rate agrees with the incompressible calculation by Lithwick (2007), which only considers perturbations elongated in the streamwise direction. The instability's strength is analysed as a function of the structure's properties, and zonal flows are found to be stable if their wavelength is $\gtrsim 8H$, where $H$ is the disc's scale height, regardless of the value of the adiabatic index $\gamma$. The non-axisymmetric KH instability can operate in Rayleigh-stable conditions, and it therefore represents the limiting factor to the structure's properties. Introducing SG triggers a second non-axisymmetric instability, which is found to be located around a PV maximum, while the KH instability is linked to a PV minimum, as expected. In the adiabatic regime, the same gravitational instability is detected even when the structure is present only in the entropy (not in the PV) and the instability spreads to weaker SG conditions as the entropy structure's amplitude is increased. This eventually yields a non-axisymmetric instability in the non-SG regime, albeit of weak strength, localised around an entropy maximum.

arXiv comment12 pages, 16 figures // v2: corrected mistakes in adiabatic terms in Eq. 24-26. These changes impacted only on Figs. 11-13, which were also updated

References in corpus (21)

• Rapid planetesimal formation in turbulent circumstellar discs
• Coagulation, fragmentation and radial motion of solid particles in protoplanetary disks
• Dust coagulation in protoplanetary disks: a rapid depletion of small grains
• Rossby Wave Instability of Keplerian Accretion Disks
• Planetesimal Formation by Gravitational Instability
• Zonal Flows and Long-Lived Axisymmetric Pressure Bumps in Magnetorotational Turbulence
• Planetesimal formation around the snow line in MRI-driven turbulent protoplanetary disks
• On the relevance of subcritical hydrodynamic turbulence to accretion disk transport
• Magnetic self-organisation in Hall-dominated magnetorotational turbulence
• Magnetic Flux Concentration and Zonal Flows in Magnetorotational Instability Turbulence
• Emergent Mesoscale Phenomena in Magnetized Accretion Disc Turbulence
• Hydrodynamic stability of rotationally supported flows: Linear and nonlinear 2D shearing box results
• On the accumulation of solid bodies in global turbulent protoplanetary disc models
• The excitation of spiral density waves through turbulent fluctuations in accretion discs I: WKBJ theory
• Vortices in Thin, Compressible, Unmagnetized Disks
• The effect of self-gravity on vortex instabilities in disc-planet interactions
• Dust Distribution in Gas Disks. A Model for the Ring Around HR 4796A
• Rossby Wave Instability with Self-Gravity
• Nonlinear Evolution of Hydrodynamical Shear Flows in Two Dimensions
• Formation, Survival, and Destruction of Vortices in Accretion Disks
• Modification of Angular Velocity by Inhomogeneous MRI Growth in Protoplanetary Disks

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