The saturation of the VSI in protoplanetary disks via parametric instability

Abstract

The vertical shear instability (VSI) is a robust and potentially important phenomenon in irradiated protoplanetary disks (PPDs), yet the mechanism by which it saturates remains poorly understood. Global simulations suggest that the non-linear evolution of the VSI is dominated by radially propagating inertial wavetrains (called `body modes'), but these are known to be susceptible to a parametric instability. In this paper, we propose that the global VSI saturates via this secondary instability, which initiates a redistribution of energy from the large scales to smaller-scale inertial waves, and finally into a turbulent cascade. We present an analytic theory of the instability in a simple idealised model that captures the main physical and mathematical details of the problem. In addition, we conduct numerical simulations with the SNOOPY code to consolidate the theory. Once the parametric instability prevails, the VSI is likely far more disordered and incoherent than current global simulations suggest. We also argue that it is challenging to capture parametric instability in global simulations unless the radial resolution is very fine, possibly $\sim 300$ grid cells per scale height in radius.

10 pages, 2 figures, submitted to MNRAS

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Cited by in corpus (12)

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• The effects of nonlinearities on tidal flows in the convective envelopes of rotating stars and planets in exoplanetary systems
• Two saturated states of the vertical shear instability in protoplanetary disks with vertically varying cooling times
• Vertical shear instability in two-moment radiation-hydrodynamical simulations of irradiated protoplanetary disks II. Secondary instabilities and stability regions
• Hydrodynamic turbulence in disks with embedded planets
• A high resolution simulation of protoplanetary disk turbulence driven by the vertical shear instability
• Rossby wave instability in weakly ionized protoplanetary disks. II. radial B-fields
• Hydrodynamical simulations of the vertical shear instability with dynamic dust and cooling rates in protoplanetary disks
• The stability of propagating plane inertial waves in rotating fluids