On fragmentation of turbulent self-gravitating discs in the long cooling
  time regime
  It has recently been suggested that in the presence of driven turbulence
discs may be much less stable against gravitational collapse than their non
turbulent analogs, due to stochastic density fluctuations in turbulent flows.
This mode of fragmentation would be especially important for gas giant planet
formation. Here we argue, however, that stochastic density fluctuations due to
turbulence do not enhance gravitational instability and disc fragmentation in
the long cooling time limit appropriate for planet forming discs. These
fluctuations evolve adiabatically and dissipate away by decompression faster
than they could collapse. We investigate these issues numerically in 2D via
shearing box simulations with driven turbulence and also in 3D with a model of
instantaneously applied turbulent velocity kicks. In the former setting
turbulent driving leads to additional disc heating that tends to make discs
more, rather than less, stable to gravitational instability. In the latter
setting, the formation of high density regions due to convergent velocity kicks
is found to be quickly followed by decompression, as expected. We therefore
conclude that driven turbulence does not promote disc fragmentation in
protoplanetary discs and instead tends to make the discs more stable. We also
argue that sustaining supersonic turbulence is very difficult in discs that
cool slowly.
