On corrugation mode radial wavelengths of the vertical shear instability

ABSTRACT The vertical shear instability (VSI) is a promising mechanism to drive turbulence in protoplanetary discs. Numerical simulations in the literature demonstrate that the VSI non-linear saturation is predominated by the linear corrugation modes. These modes possess vertical wavelengths crucially longer than radial wavelengths. This paper aims to investigate the natural radial wavelength of corrugation modes upon VSI saturation, by a series of numerical simulations conducted in Athena++ at different grid resolutions, disc aspect ratios, and viscosity parametrized by ν. We find a sign of convergence emerges at 64 cells per gas scale height for fiducial simulations, below which a continuous reduction of wavelengths with grid resolution is observed. Synthetic ALMA molecular line observations of ^12 CO (2-1) are performed to inspect the observability of the corrugation modes feature, which is significantly diminished with a resolution of 32 cells per scale height or above. Flared and viscous discs exhibiting longer saturation wavelengths may mitigate the observational difficulty.