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Large-scale, dust-trapping vortices may account for observations ofasymmetric protoplanetary discs. Disc vortices are also potential sites foraccelerated planetesimal formation by concentrating dust grains. However, in 3Ddiscs vortices are subject to destructive `elliptic instabilities', whichreduces their viability as dust traps. The survival of vortices in 3D accretiondiscs is thus an important issue to address. In this work, we perform shearingbox simulations to show that disc self-gravity enhances the survival of 3Dvortices, even when self-gravity is weak in the classic sense (e.g. with aToomre $Q\simeq5$). We find a 3D, self-gravitating vortex can grow on seculartimescales in spite of the elliptic instability. The vortex aspect-ratiodecreases as it strengthens, which feeds the elliptic instability. The resultis a 3D vortex with a turbulent core that persists for $\sim 10^{3}$ orbits. Wefind when gravitational and hydrodynamic stresses become comparable, the vortexmay undergo episodic bursts, which we interpret as interaction between ellipticand gravitational instabilities. We estimate the distribution of dust particlesin self-gravitating, turbulent vortices. Our results suggest large-scalevortices in protoplanetary discs are more easily observed at large radii.

Vortex survival in 3D self-gravitating accretion discs