Convection in stellar envelopes: a changing paradigm
  Progress in the theory of stellar convection over the past decade is reviewed. The similarities and differences between convection in stellar envelopes and laboratory convection at high Rayleigh numbers are discussed. Direct numerical simulation of the solar surface layers, with no other input than atomic physics, the equations of hydrodynamics and radiative transfer is now capable of reproducing the observed heat flux, convection velocities, granulation patterns and line profiles with remarkably accuracy. These results show that convection in stellar envelopes is an essentially non-local process, being driven by cooling at the surface. This differs distinctly from the traditional view of stellar convection in terms of local concepts such as cascades of eddies in a mean superadiabatic gradient. The consequences this has for our physical picture of processes in the convective envelope are illustrated with the problems of sunspot heat flux blocking, the eruption of magnetic flux from the base of the convection zone, and the Lithium depletion problem. 
H.C. Spruit (MPI for Astrophysics)