Please let me know the liteature available on above topic.

Hi there,

It is not clear from the question exactly what kind of flow and duct are involved in the problem.

Are you interested in the flow escaping from a vertical duct (like the smoke coming out of chemney)? Then basically what you have is a kind of jet. Do you have buoyancy effects too? The jet by itself is unstable to a shearing (Kelvin-Helmholtz) instability on its surface boundary with the ambient flow, which eventually can lead to turbulence. Then you first will have a wavy-like pattern. If the buoyance effects are also taken into account then you will have in addition a Rayleigh-Taylor instability that makes the flow go upwards (really like a smoke).

Or are you rather interested in the flow inside the duct itself? and instability due to the boundaries of the duct and (again) the buoyancy ?

If you could be more specific, that would help to understand exactly what is the flow problem.

PG.