Let us consider a blob of fluid in a thin Keplerian disc. If the fluid element is "squished" in the radial direction, it might collapse to a clump, or return to its unperturbed state. The time scale for returning to its original shape is the inverse of the epicyclic frequency. For simplicity, we will use the Keplerian angular velocity instead. The time scale for collapse is just the Jeans' time , where is the universal constant of gravitation, and is the density. The criterion for stability is therefore that the period is much shorter than the Jeans time

The volume density is just the surface density divided by the height . The height is determined by pressure balance with gravity

where is the distance from the centre of the disc, is the local speed of sound, and is the Keplerian velocity. Putting it all together yields that a blob is stable if