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Sunwen April 27, 1999 13:20

instability analysis
Hi, all

where can I find a software for instabilty analysis of a top-hat jet? I am doing LES of plume. I want to find a most unstable mode of instabilty.



Patrick Godon April 29, 1999 10:26

Re: instability analysis
Hi THere,

I know there has been some analytical work done on the unstable modes in jets, but I am not sure exactly what you are looking for. Are you interested in the instability of the bow shock region, or just the jet itself pushing behind it? Are you looking at a high density jet in a low density medium or rather the opposite. What is the speed of the jet (in unit of the Mach number of the ambient medium)? If you give me more details I can try to find the exact reference (if it is related to your problem).

Cheers, Patrick.

Sunwen April 29, 1999 12:04

Re: instability analysis
Hi, Patrick,

Thank you very much for your reply.

I am interested in the instability of jet itself pushing behind it at low Mach number and with low density jet at high density medium. The density ratio is 2, because the air of high temperature 600K is injected vertically into the sorrounding air with 300K. Therefore the buoyancy effect is strong. The inflow velocity is 0.98m/s and the jet diameter is 0.0635m. And the tangential top-hat profile is used at the inflow. I don't know if other forms such as parabolic profile also have the most unstable mode of instability.

Many thanks again.



Patrick Godon April 29, 1999 13:45

Re: instability analysis
I see that what you called jet is some smoke coming out of an exhaust pipe or chimney, just due to the boyancy forces. I had in mind something more like a jet where matter is injected at a high speed into a medium and where no buoyancy and gravity act in the direction of the 'jet'. I am not sure how relevant is the instability analysis I saw on purely hydrodynamical jets to the instability of cigarette smoke (initially the flow is 'smooth' and at higher altitude it is wavy and after that it breaks into clumps and it is unstable), but there is for sure some similarities (some of the basic instabilities are the same). I will check the reference on the stability of hydro (supersonic I think) jets and get back to you later. PG.

Sunwen April 30, 1999 06:10

Re: instability analysis
Dear Patrick,

I am sorry I haven't explained to you very clearly.

My concern is a jet with both momentum and buoyancy. Initially it performs like a jet and then the buoyancy dominates the flow. I think the instability analysis for the purely hydrodynamical jets might be very useful for the buoyant jet case. I just want to test which kind of initial conditions can lead to the most unstable mode of instability. From my experience the helical mode gives a much larger spreading than the axisymmetric one. I don't know much about the mechanism. It seems the instability analysis is quite useful for the numerical modelling especially for the initial conditions.

I am doing large-eddy simulation of buoyant jet (not pure plume) with very low Mach number (subsonic not supersonic).

Thanks a lot for your great help.

All the best,


Patrick Godon April 30, 1999 09:09

Re: instability analysis
Ok, I guess the same instabilities do appear in both kind of jets (whether it is purely hydro or buoyant). The first instability is the Kelvin-Helmholtz instability due to the shear between the jet and the medium. The other instability is due to resonance (of sound waves) in the 'cavity' formed by the jet itself surounded by the medium. There are therefore two kind of modes and these are interacting. For example some of the fast growing resonance mode can more easily trigger and induce given modes of the K-H kind, etc.. Since the problem is really 3D, of course non-axisymmetric modes can grow too, like the helical ones you mentioned. Because of the different jet speeds (sub or super sonic) the overall results might be different but in principle it looks like it is the same mechanism. I will get back to you when I have the exact reference.

Cheers, PG.

Patrick Godon May 6, 1999 14:52

Re: instability analysis

I checked the reference and found out that the supersonic case is indeed different from the subsonic one. In the subsonic case only the KH instability takes place (surface modes), while in the supersonic case the resonance instability is also found. The reference I wanted to give you is irrelevant because it treats only the resonance instability (where 'body' modes grow). I am not aware of any analytical work in which non-axisymmetric modes have been studied (since it is a 3D problem, it is quite complex). You might want to try and have a look at Brown and Roshko, 1974, J. Fluid Mech., vol. 284, p. 171 concerning the stability of subsonic jets. As you mentioned in your first message, a hydrocode would be adequate to check the most unstable modes. PG.

Patrick Godon May 7, 1999 13:47

The reference is Brown and Roshko, 1974, J Fluid Mech, vol. 64, p. 775 (and not vol.284, 171). Sorry for that. The paper is mainly experimental, so I am not sure how much it will help. PG.

Sunwen May 9, 1999 06:30


Thanks for your Journal information. I will find the paper again to see if it helps.

If you know where I can find the very simple code for analyzing the instability, please tell me. Even it is two dimensional or supersonic or pure hydrodynamic, it can also be of great benificial. I know little about the numerical procedure for this analysis.

All the best,


Patrick Godon May 10, 1999 15:26

K-H (shear) instability in Jets

The basic Kelvin-Helmholtz instability (also known sometimes as the shear instability) originates in the region of the shear between the jet and the outer ambient medium. Due to the viscosity, the transition region where (inside the jet) the speed is high to where (outside the jet, the ambient medium) the speed is zero has a finite width (say d). The most unstable mode of the KH instability is usually of length 2*pi*d . This is for 2D simple flow (see Ong and Roderick, Planet.Space Sci. vol.20, p.1-10, 1972). In the case of the jet, the instability is 3D in the cylindrical envelop around the jet.

The reference to a 2D and 3D free software is on its way to you. Cheers, Patrick.

Patrick Godon May 17, 1999 08:47

Re: reference
For the reference,

I sent you and I am sending you again a personnal email to . Let me know if you get it.

Cheers, PG.

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