We study the nonlinear evolution of the Rossby wave instability in thin disks using global 2D hydrodynamic simulations .
The detailed linear theory of this nonaxisymmetric instability was developed earlier by Lovelace et al .
and Li et al. , who found that the instability can be excited when there is an extremum in the radial profile of an entropy-modified version of potential vorticity .
The key questions we are addressing in this paper are : ( 1 ) What happens when the instability becomes nonlinear ?
Specifically , does it lead to vortex formation ?
( 2 ) What is the detailed behavior of a vortex ?
( 3 ) Can the instability sustain itself and can the vortex last a long time ?
Among various initial equilibria that we have examined , we generally find that there are three stages of the disk evolution : ( 1 ) The exponential growth of the initial small amplitude perturbations .
This is in excellent agreement with the linear theory ; ( 2 ) The production of large scale vortices and their interactions with the background flow , including shocks .
Significant accretion is observed due to these vortices .
( 3 ) The coupling of Rossby waves/vortices with global spiral waves , which facilitates further accretion throughout the whole disk .
Even after more than 20 revolutions at the radius of vortices , we find that the disk maintains a state that is populated with vortices , shocks , spiral waves/shocks , all of which transport angular momentum outwards .
We elucidate the physics at each stage and show that there is an efficient outward angular momentum transport in stages ( 2 ) and ( 3 ) over most parts of the disk , with an equivalent Shakura-Sunyaev angular momentum transport parameter \alpha in the range from 10 ^ { -4 } to 10 ^ { -2 } .
By carefully analyzing the flow structure around a vortex , we show why such vortices prove to be almost ideal “ units ” in transporting angular momentum outwards , namely by positively correlating the radial and azimuthal velocity components .
In converting the gravitational energy to the internal energy , we find some special cases in which entropy can remain the same while angular momentum is transported .
This is different from the classical \alpha disk model which results in the maximum dissipation ( or entropy production ) .
The dependence of the transport efficiency on various physical parameters are examined and effects of radiative cooling are briefly discussed as well .
We conclude that Rossby wave/vortex instability is an efficient , purely hydrodynamic mechanism for angular momentum transport in thin disks , and may find important applications in many astrophysical systems .