  The mechanism of angular momentum transport in accretion discs has long been
debated. Although the magnetorotational instability appears to be a promising
process, poorly ionized regions of accretion discs may not undergo this
instability. In this letter, we revisit the possibility of transporting angular
momentum by turbulent thermal convection. Using high-resolution spectral
methods, we show that strongly turbulent convection can drive outward angular
momentum transport at a rate that is, under certain conditions, compatible with
observations of discs. We find however that the angular momentum transport is
always much weaker than the vertical heat transport. These results indicate
that convection might be another way to explain global disc evolution, provided
that a sufficiently unstable vertical temperature profile can be maintained.
