  The standard thin accretion disc model predicts that discs around stellar
mass black holes become radiation pressure dominated and thermally unstable
once their luminosity exceeds L>0.02 L_Edd. Observationally, discs in the
high/soft state of X-ray binaries show little variability in the range 0.01
L_Edd < L < 0.5 L_Edd, implying that these discs in nature are in fact quite
stable. In an attempt to reconcile this conflict, we investigate one-zone disc
models including turbulent and convective modes of vertical energy transport.
We find both mixing mechanisms to have a stabilizing effect, leading to an
increase in the L threshold up to which the disc is thermally stable. In the
case of stellar mass black hole systems, convection alone leads to only a minor
increase in this threshold, up to ~5 per cent of Eddington. However turbulent
mixing has a much greater effect -- the threshold rises up to ~20 per cent
Eddington under reasonable assumptions. In optimistic models with
superefficient turbulent mixing, we even find solutions that are completely
thermally stable for all accretion rates. Similar results are obtained for
supermassive black holes, except that all critical accretion rates are a factor
~10 lower in Eddington ratio.
