# Radial Transport and Meridional Circulation in Accretion Disks

## TL;DR

This paper investigates how thermal stratification influences radial transport and meridional circulation patterns in 3D accretion disks, revealing conditions that lead to inward or outward flows relevant for astrophysical processes.

## Contribution

It demonstrates analytically and numerically that steeply increasing entropy and temperature with height can cause inward radial flow at all altitudes in accretion disks.

## Key findings

- Steep thermal gradients induce inward flow at all altitudes.
- Disks with typical conditions exhibit midplane outflow and upper inflow.
- Results inform simulation design for prescribed circulation patterns.

## Abstract

Radial transport of particles, elements and fluid driven by internal stresses in three-dimensional (3D) astrophysical accretion disks is an important phenomenon, potentially relevant for the outward dust transport in protoplanetary disks, origin of the refractory particles in comets, isotopic equilibration in the Earth-Moon system, etc. To gain better insight into these processes, we explore the dependence of meridional circulation in 3D disks with shear viscosity on their thermal stratification, and demonstrate strong effect of the latter on the radial flow. Previous locally isothermal studies have normally found a pattern of the radial outflow near the midplane, switching to inflow higher up. Here we show, both analytically and numerically, that a flow, which is inward at all altitudes, is possible in disks with entropy and temperature steeply increasing with height. Such thermodynamic conditions may be typical in the optically thin, viscously heated accretion disks. Disks in which these conditions do not hold should feature radial outflow near the midplane, as long as their internal stress is provided by the shear viscosity. Our results can also be used for designing hydrodynamical disk simulations with a prescribed pattern of the meridional circulation.