The comparison in this section, is between Pro50z and Pro50 from Tab. 1, with Pro50z having a z-scale similar to sol32 and Pro50 having a z-scale similar to sol100 as depicted in Fig. 1.
Figure 4: The turbulent- to total pressure ratio. Pink curves are for Pro50z
and black curves for Pro50 with the optimized z-scale.
I show both the total horizontal average (solid) as well as the
average in the upflow (dashed) and the downflow (dotted).
From Fig. 4 we see that turbulent- to total pressure ratio
actually decreases with better resolution in the photosphere -- rather
counterintuitive. If we correct for the differences in 
the
difference decreases somewhat, to 1% (cf. Tab. 1).
Figure 5: The superadiabatic gradient 
. Pink curves are for
Pro50z and black curves for Pro50 with the optimized z-scale.
I show both the total horizontal average (solid) as well as the
average in the upflow (dashed) and the downflow (dotted).
This decrease of 
can be explained by looking at the
superadiabatic gradient in Fig. 5, which shows that
increase with vertical resolution. The very sharp temperature
gradient, in particular in the upflow, needs a very dense vertical grid, in
order to get resolved, whereas the velocity field has less sharp features
(cf. Figs. 6 and 7) and is therefore less
demanding with respect to vertical resolution. The introduction of the
temperature optimized z-grid, is also accompanied by an optimized
and differentiable grid for the radiative transfer, which might help in
steepening the temperature gradient.
Figure 6: The vertical RMS velocity 
. Pink curves are for
Pro50z and black curves for Pro50 with the optimized z-scale.
I show both the total horizontal average (solid) as well as the
average in the upflow (dashed) and the downflow (dotted).
The larger means that the convective transport of energy gets
more efficient, and therefore that the same flux can be achieved with lower
velocities, which is clearly reflected in the vertical velocities in
Fig. 6.
The horizontal velocities also decrease as the vertical velocities decrease because they just serve to maintain the density gradient by deflecting matter from the upflow sideways into the downflows (overturning).
Figure 7: The horizontal RMS velocity 
. Pink curves are for
Pro50z and black curves for Pro50 with the optimized z-scale.
I show both the total horizontal average (solid) as well as the
average in the upflow (dashed) and the downflow (dotted).
The conclusion of this Section must be that the transport properties of the
simulation changes with the distribution of vertical grid-points, because the
sharp temperature gradient in the photosphere needs a good resolution. This
is also reflected in the decrease in as the resolution in the
photosphere increase. This decrease is too small though, to account for the
decrease in velocities, which must still be ascribed to the increased efficiency
of the convection, as discussed above.
We also see from Figs. 4-7 that the lower resolution in the deeper parts of Pro50 as compared to Pro50z, does not affect the structure significantly in this region, indicating that this redistribution of grid-points is closer to optimal.
Last updated [an error occurred while processing this directive] by: trampedach@pa.msu.edu.