ABSTRACT
The radiative diffusivity coefficient, that characterizes the diffusion of temperature perturbations, is
K X=-,
where cp is the specific heat at constant pressure. The factor pCp, the thermal energy per unit mass and Kelvin, increases by about five orders of magnitude through the convection zone (in the surface layers Cp is enhanced by about one order of magnitude relative to an ideal gas). Thus, the rate at which temperature fluctuations are smoothed out by diffusion decreases by about three orders of magnitude from the top to the bottom of the convection zone. Near the bottom of the solar convection zone X is around 107 cm2 / s, so the Peclet number is
UL 104 1010 Pe= - ~ ~ 107
(4.8)
(4.9)
(4.10)
2.0 .' 2.0
1.8 1.8
1.6 1.6
1.2 '_.' 1.2
1.0 ~~~~~~~~~~~~~ 1.0 ~~~~~~~~~~~~~ 0.2 0.4 0.6 0.8 1.0 1.2 0.2 0.4 0.6 0.8 1.0 1.2
x x
f..t (4.11)
90 BRANDENBURG, NORDLUND AND STEIN
In ordinary Boussinesq convection the degree of instability is characterized by the Rayleigh number
vx (4.12)
vxcp (4.13)
In the inviscid limit, v --+ 0, stability is simply governed by the sign of 9 . V s. In astrophysics this is known as Schwarzschild's criterion,
ASTROPHYSICAL CONVECTION 91
ASTROPHYSICAL CONVECTION 93
Figure 4.4: Evolution of two downdrafts shown as vertical slices of the entropy. Dark means low entropy.
