title: Convection Scaling Laws
section: Introduction
head: Overview
  o Part of <font color=red>The Quest</font>, to show
    - Astrophysics indepedent of diffusion coefficients
      - Magnetic dissipation independent of eta
      - Dynamo properties independent of eta and nu
      - Convection independent of nu and kappa
  o Classical Polytropes
    - Radiative polytropic indices
    o Problems and Constraints
      - Large radiative fluxes
      - Large range of temperatures
  o Convection Dominated Polytropes
    - Energy diffusion ~ entropy gradient
    - Much better test benches
    - Allow clean tests of, e.g.,
      - Prandtl number dependence
      - Time dependent MLT
  o Conclusions
    - Evidence for Prandtl number independence
    - Overall scaling ~ Mixing Length Theory
      - Because of overturning / mass conservation

head: The Quest
<br>
text: From the ironic point of view, this is just a self-cleansing 
process among theoreticians.  Most astrophysicist just take the
final outcome for granted, and go about doing more
productive things!
end:
<p><br>
box: <font color=red>The Quest</font>: To show that / demonstrate why / large
scale, turbulent phenomena in Astrophysics are, in general, independent
of details of the microphysics, such as coefficients of
viscosity, thermal and electrical conductivity. 
end:
<br><br>
text: There are of course interesting exceptions, where things
clearly depend on collision cross sections and the like:
end:
  o Non-LTE radiative transfer
  o Almost collisionless plasmas
    - Particle acceleration
    - Non-thermal emission

head: Boiling Stars
  o A long tradition of Reynolds and Rayleigh number worshipping
    - Astrophysics turbulence has <font color=red>so</font> high Reynolds numbers
    - Stellar convection has <font color=red>so</font> low Prandtl numbers
  o Often used in applications for super-computer time
    - And not in the sense "let's show it does not matter"
<p>
box: If it really was the case that it mattered, then by the shear size of
the dimensionless numbers we could all pack and go home, and those
supercomputer applications should be turned down from the start.
end:
<p>
  o Simple polytropic models have been used traditionally
    - Suitable for parameter studies(?)