The saturation of the VSI in protoplanetary discs via parametric instability

Abstract

ABSTRACT The vertical shear instability (VSI) is a robust and potentially important phenomenon in irradiated protoplanetary discs (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 idealized 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. We argue that it is challenging to capture parametric instability in global simulations unless the radial resolution is very fine, possibly ∼300 grid cells per scale height in radius; thus the VSI is likely far more disordered and incoherent than current global simulations suggest.