Clumping in the inner winds of hot, massive stars from hydrodynamical   line-driven instability simulations
  We investigate the effects of stellar limb-darkening and photospheric perturbations for the onset of wind structure arising from the strong, intrinsic line-deshadowing instability (LDI) of a line-driven stellar wind. A linear perturbation analysis shows that including limb-darkening reduces the stabilizing effect of the diffuse radiation, leading to a net instability growth rate even at the wind base. Numerical radiation-hydrodynamics simulations of the non-linear evolution of this instability then show that, in comparison with previous models assuming a uniformly bright star without base perturbations, wind structure now develops much closer ($r \la 1.1 R_\star$) to the photosphere. This is in much better agreement with observations of O-type stars, which typically indicate the presence of strong clumping quite near the wind base. 
Jon O. Sundqvist, Stanley P. Owocki
astro-ph.SR