Turbulent pressure from 3D convection...
I have simulated convection near the surface of the sun, using the
code by Åke Nordlund and
Bob Stein and incoorporating
realistic
equation of state and opacities. The simulation is performed on a
100x100x82 point grid, and it has run for a couple of solar hours,
to allow it to relax.
The turbulent pressure contributes 
to
the vertical
momentum balance. Assuming that the density fluctuations are small,
most of the behavoir of the turbulent pressure can be derived from
looking at 
.
A normal 1D stellar model don't give any information on velocity
fields and density fluctuations except a density which can be
interpreted as 
and a convective velocity which
might be something like 
, the horisontally averaged
vertical speed.
This is just a sensible suggestion for a correspondance between 3D
and 1D models and there might be better choises.
Assuming no density fluctuations,
so that the problem now is reduced to finding a relation between
and 
.
Figure 1:
This figure depicts the distribution of vertical velocities as a
function of depth measured in mega-meters. The x-axis is the
velocity in km/s and the z-axis shows the fraction of the plasma
moving with that velocity at any given depth. z=0.0 marks the
height where 
and positive depths are inward, as positive
velocities are inward. This figure is a sum of 12 timesteps covering
6 minutes, and it is quite representative for the behaviour,
although it changes somewhat with time. It is certainly not a
pathological case.
Figure 2: The upper solid curve shows the ratio between a mean of squared
velocities and a square of mean speeds. In MLT this ratio is not only
assumed constant, but is also set to unity. The lower solid curve, depicts
the correlation between the velocity field and the density fluctuations.
Below z=.3 Mm this correlation is slightly larger than unity as large
densities are associated with cool downdrafts moving at greater speeds
than the warmer upwelling plasma. The dashed curve is the ratio between
the actual 
and the 1D version, using
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Last updated
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by: trampedach@pa.msu.edu.