We present the global baroclinic instability as a
source for vigorous turbulence leading to angular momentum transport
in Keplerian accretion disks.
We show by analytical considerations and three-dimensional radiation
hydro
simulations that, in particular, protoplanetary disks have a radially
outward directed entropy gradient, which makes
them baroclinic.
Two-dimensional numerical simulations show that this baroclinic flow
is
unstable and produces turbulence. These findings are
tested for numerical effects by performing barotropic
simulations which show that imposed turbulence rapidly decays.
The turbulence in baroclinic disks draws energy from the background
shear, transports angular momentum outward and creates a radially
inward bound accretion of matter, thus forming a self consistent process.
Gravitational energy is transformed into turbulent kinetic energy,
which is then dissipated, as in the classical accretion paradigm.
We measure accretion rates of $\dot M= - 10^{-9}~{\rm to~}-10^{-7}~\mbox{M}_{\sun}~
\mbox{yr}^{-1}$
and viscosity parameters of $\alpha = 10^{-4} - 10^{-2}$, which
fit perfectly together and agree reasonably with observations.
The turbulence creates
pressure waves, Rossby waves, and vortices in the ($r-\phi$) plane
of the disk.
We demonstrate in a global simulation that these vortices tend
to form out of little background noise and to
be long-lasting features, which have already been suggested to lead
to
the formation of planets.
For more details have a look in Klahr and Bodenheimer
ApJ submitted:
Turbulence
in Accretion Disks: Vorticity Generation and Angular Momentum Transport
via the Global Baroclinic Instability
See also the paper Klahr 1999, proceedings of Two
Decades of Numerical Astrophysics
TRAMP:
New Insight into Thermal Convection in Protoplanetary Accretion Disks
This is a short movie on the velocity pattern in the r-phi plane of the disk. One sees the interaction of irregular waves, typical for geostrophic turbulence.
In order to show the growth of the instability we created a short
movie: This is the evolution of a non-axisymmetric flowpattern out of an
axisymmetric one! This is a 3D radiation hydro simulation using the TRAMP
code with shearing disk boundary conditions. Colours are densities, vectors
are velocities in the local rotation frame. Rmin = 4.4 AU, Rmax = 5.6 AU,
Height 15 degrees, azimuthal opening angel 90 degrees. This is an 17MB
mpeg!
Steady state turbulence in a 2D r-phi calculation: Density fluctuations
(colors)
and Rossby waves (velocities. vectors). We remove the vertical structure
and
radiation transport, but mimic the entropy gradient with a suited polytrop.
Steady state turbulence in a 2D r-phi calculation:
Density fluctuations (colors) and Rossby waves (velocities. vectors).
But this time we model the radiation transport with a vertical
disk atmosphere model. Thus it is no artificial polytrop!
Thanks Scott!
Our SEPLFCONSISTENT SIMULATION! This is a 3D Simulation with
radiation transport without any artificial heating. The only heat source
is
the dissipation in shocks! One clearly sees the baroclinic instability
form an eddy
which eventually drifts outward.
