Convection in solar-type stars
Solar-type stars are characterized by an outer convecting zone where heat
is transported by fluid motions resulting from the Rayleigh-Bénard instability.
The convection in these stars appears because of surface cooling: the surface
material cools too rapidly to be reheated by the radiative conductivity
of the fluid; the fluid at the surface is too cold and sinks till a depth
where the conductivity is high enough to smear out the "superadiabatic
gradient" thus built up by the cooling. This critical depth where the convective
zone ends is given by the famous Schwarzschild criterium. For our sun this
place is 200000 km below the surface.
Because of the size
of the stars the fluid motions are characterized by very high Reynolds
numbers which means that the flows are turbulent. This turbulence is the
basic difficulty which astrophysicist must face to model solar-type
stars. Making progress is very hard because we have no general theory of
turbulence at hand. One way in this jungle is to do direct simulations
of these flows (using Reynolds number around 1000), understand the important
properties of these flows and then extrapolate to the real sun where the
Reynolds number is 10^12. Then we may test our results and conjectures
on some observables like the differential rotation or the magnetic activity
of the sun.
More on direct simulations:
Nordlund A., Brandenburg A., Jennings R., Rieutord M., Ruokolainen J.,
Stein R. and Tuominen I. (1992), "Dynamo action in stratified convection
with overshoot", Astrophysical Journal vol. 392, pp.~647--652.
Rieutord M., Brandenburg A., Mangeney A. and Drossart P. (1994), "Reynolds
stresses and differential rotation in Boussinesq convection in a rotating
spherical shell", Astronomy and Astrophysics vol. 286, pp.~471--480.
Brandenburg A., Jennings R., Nordlund A., Rieutord M., Stein R. and Tuominen
I. (1996), "Magnetic structures in a dynamo simulation", Journal of Fluid
Mechanics vol. 306, pp.~325--357.
More on extrapolation:
Rieutord M. and Zahn J.-P. (1995), "Turbulent plumes in stellar convective
envelopes", Astronomy and Astrophysics vol. 296, pp.~127--138.
Bonin P. and Rieutord M. (1996), "The dynamics of turbulent plumes in a
stellar convective envelope", Astronomy and Astrophysics vol. 310 pp.~221--227.