The envelopes of stars near the Eddington limit are prone to various instabilities. A high Eddington factor in connection with the Fe opacity peak leads to convective instability, and a corresponding envelope inflation may induce pulsational instability. Here, we investigate the occurrence and consequences of both instabilities in models of Wolf-Rayet stars. We determine the convective velocities in the sub-surface convective zones to estimate the amplitude of the turbulent velocity at the base of the wind that potentially leads to the formation of small-scale wind structures, as observed in several WR stars. We also investigate the effect of mass loss on the pulsations of our models. We approximated solar metallicity WR stars by models of mass-losing helium stars, and we characterized the properties of convection in the envelope adopting the standard MLT. Our results show the occurrence of sub-surface convective regions in all studied models. Small surface velocity amplitudes are predicted for models with masses below 10Msun. For models with M>10Msun, the surface velocity amplitudes are of the order of 10km/s. Moreover we find the occurrence of pulsations for stars in the mass range 9-14Msun, while mass loss appears to stabilize the more massive WR stars. We confront our results with observationally derived line variabilities of 17 WN stars. The data suggest variability to occur for stars above 10Msun, which is increasing linearly with mass above this value, in agreement with our results. We further find some of our models to be unstable to radial pulsations, and predict local magnetic fields of the order of hundreds of Gauss in WR stars more massive than 10Msun. Our study relates the surface velocity fluctuations induced by sub-surface convection to the formation of clumping in the inner part of the wind. From this mechanism, we expect a stronger variability in more massive WR stars.
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