Interactions between Turbulence and Zonal Flows as Self-regulating Saturation Processes in Astrophysical Accretion Disks*

The angular momentum transport mechanism in accretion disks is crucial for understanding their behavior. However, the saturation processes in a hydrodynamics disk remains uncertain. The Taylor Identity, which explains non-linear momentum transport from small-scale turbulence to large-scale zonal flow (ZF), presents a potential explanation for the turbulence saturation level. In this study, we derive the Taylor Identity for a compressible disk fluid in the presence of Rossby wave instability (RWI) associated with a pressure and density bump, analytically calculate the momentum transport, and elucidate the turbulence level in the saturation state.

To investigate the physics behind the turbulence level in a saturation state, we propose a self-regulation model. We conduct a 2D compressible hydrodynamic simulation of astrophysical disks containing a pressure bump, exploring momentum/energy transport between turbulence intensity, zonal flow, and free energy evolution during the disk saturation. Our findings indicate that: (1) the evolution of RWI leads to zonal flow generation; (2) the dynamics between turbulence intensity and zonal flow regulates the nonlinear stage; (3) the self-binding pressure bump mechanism dominates the oscillation frequency. These results strongly suggest that the dynamics of turbulence interacting with the zonal governs the nonlinear saturation state in accretion disks.

Future studies will focus on the self-regulated mechanism and its role in magnetized accretion disk, particularly the interaction with magnetorotational instability.