The ( ) ( axisymmetric ) gravitational instability of a razor thin particle layer occurs when the Toomre parameter Q _ { \mathrm { T } } \equiv c _ { \mathrm { p } } \Omega _ { 0 } / \pi G \Sigma _ { \mathrm { p } } < 1 ( c _ { \mathrm { p } } being the particle dispersion velocity ) . ( ) extended this analysis by adding the effect of gas drag upon particles and found that even when Q _ { \mathrm { T } } > 1 , sufficiently long waves were always unstable . ( ) carried out a detailed analysis and showed that the instability allows chondrule-sized ( \sim 1 mm ) particles to undergo radial clumping with reasonable growth times even in the presence of a moderate amount of turbulent stirring . The analysis of Youdin includes the role of turbulence in setting the thickness of the dust layer and in creating a turbulent particle pressure in the momentum equation . However , he ignores the effect of turbulent mass diffusivity on the disturbance wave . Here we show that including this effect reduces the growth-rate significantly , by an amount that depends on the level of turbulence , and reduces the maximum intensity of turbulence the instability can withstand by 1 to 3 orders of magnitude . The instability is viable only when turbulence is extremely weak and the solid to gas surface density of the particle layer is considerably enhanced over minimum-mass-nebula values . A simple mechanistic explanation of the instability shows how the azimuthal component of drag promotes instability while the radial component hinders it . A gravito-diffusive overstability is also possible but never realized in the nebula models .