Mixing-length theory, granulation, and the Schwarzschild criterion
The Schwarzschild criterion states convection occurs when ∇_rad > ∇_ad, where ∇ = d(lnT)/d(lnP). In the Sun, the convection zone extends from ~0.714 R_☉ to the surface. Granules (~1 Mm, 5–10 min lifetime) carry ~80% of the energy flux; supergranules span ~30 Mm. Mixing-length theory parameterizes the convective efficiency via α = ℓ/H_p where H_p is the pressure scale height.