Hydrodynamic turbulence in disks with embedded planets

¹ Institut für Astronomie und Astrophysik, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany
e-mail: alexandros.ziampras@uni-tuebingen.de
² Astronomy Unit, School of Physical and Chemical Sciences, Queen Mary University of London, London E1 4NS, UK
e-mail: r.p.nelson@qmul.ac.uk

Received: 28 October 2022
Accepted: 17 December 2022

Abstract

The vertical shear instability (VSI) is a source of hydrodynamic turbulence that can drive vigorous vertical mixing and moderate levels of accretion in protoplanetary disks, and it could be observable in the near future. With high-resolution three-dimensional numerical hydrodynamics simulations, we modeled the behavior of the VSI in protoplanetary disks with and without embedded planets. We then measured its accretion and mixing capabilities by comparing the full Reynolds stress, which includes the contribution of nonaxisymmetric features, such as spiral arms and vortices, to the Reynolds stress due to the azimuthally averaged velocity field, which can be attributed to good approximation to the VSI. We verified that the VSI can contribute to the accretion stress and showed that, depending on disk conditions, an embedded planet can coexist with or suppress VSI turbulent stress. Specifically, the presence of spiral shocks launched by a planet or planet-generated vortices can interfere with the VSI near the planet’s vicinity, with the instability recovering at large enough distances from the planet or vortex. Our results suggest that observations of VSI signatures are unlikely in disks that contain massive, nonaxisymmetric features.