Until recently the concern of the traditional theory of the atmospheric stable boundary layer (SBL) was, almost without exception, the nocturnal SBL developing after sunset on the background of a neutral or slightly stable residual layer. In the nocturnal SBLs the nature of turbulence is basically local. Its lower portion is well described by the classical Monin–Obukhov surface-layer similarity theory. Things are different in long-lived SBLs situated immediately below the stably stratified free flow. Here, the surface-layer turbulence is affected by the free-flow Brunt–Väisälä frequency, N. The surface layer represents approximately one-tenth of the SBL, so that it is separated from the free atmosphere by the upper nine-tenths of the SBL comprising hundreds of metres. Traditional concepts fail to explain such distant links. Zilitinkevich and Calanca extended the traditional Monin–Obukhov similarity theory by including N in the surface-layer scaling, and provided experimental evidence in support of this extension. In the present paper, physical mechanisms responsible for non-local features of the long-lived SBL turbulence are identified as: radiation of internal waves from the SBL upper boundary to the free atmosphere, and the internal-wave transport of the squared fluctuations of velocity and potential temperature. The third-order wave-induced fluxes are included in an advanced turbulence-closure model to correct the wind and temperature profiles in the surface layer. The model explains why developed turbulence in the surface layer can exist at much larger Richardson numbers than the classical theory predicts. Results from the new model are in good agreement with the extended similarity theory and experimental data. Copyright © 2002 Royal Meteorological Society.