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Turbulence usually makes the onset of dust gravitational instability of an astrophysical disk harder in three complementary ways. It increases the dust random velocity dispersion, raising $c$ and the Toomre parameter; it stirs dust vertically, reducing the self-gravity enhancement of a razor-thin disk; and it mixes density enhancements through turbulent diffusion. The last effect is particularly important for a slowly growing secular gravitational instability, which can be erased before it amplifies appreciably.

A simple diffusion model adds $D{\nabla }^2\sigma$ to the dust continuity equation, giving a damping scale of order $D{k}^2$. Growth then has to compete with mixing as well as pressure and rotational support. In the long-wavelength weak-drag regime where ${\omega }^2\simeq {\Omega }^2$, the indicative competition iswith further pressure and finite-thickness corrections. This is a model-dependent long-wave estimate, not a substitution into the original cubic without changing its continuity equation. In an infinite domain, diffusion proportional to $k^2$ need not remove growth proportional to $|k|$ at every arbitrarily long wavelength; in a finite disk, the remaining wavelengths and their growth times may be inadequate. The conclusion is therefore a higher practical collapse threshold and slower growth, rather than guaranteed stability for all turbulent flows.

Turbulence can also concentrate dust through coherent structures or pressure maxima, increasing local surface density and encouraging collapse. Its net quantitative effect requires a model for stirring, diffusion, thickness and concentration. The deterministic fixed gas flow used in the preceding parts does not specify those statistics. This competition is turbulent mixing of a secularly unstable dust layer.