# Can 'shock waves' occur in viscous fluid flows?

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 February 14, 2006, 09:26 Re: Concept & idea consolidation #101 Tom Guest   Posts: n/a diaw: I'm trying to understand why, in the pipe case, the solutions are isolated. This can certainly be said for traditional development of say gravity waves, where the perturbation is introduced, 3 sets of equations are developed - one for bulk flow, one for deviatoric & the final - for the non-linear linkages. The approach then makes simplifying assumptions which essentially reduce the non-linear linkage equation to zero - leaving two independent solutions operating in the same space - or drops the bulk solution completely - as in the case of gravity waves. This is a standard property of nonlinear equations - solutions can exist which are not bifurcations from a common "base state". You really need to read about what was done to obtain these solutions and not look at a "popular" account which does not tell you all the facts. You probably also need some some understanding of nonlinear stability theory/bifurcation analysis to appreciate what the results actually mean. There are some nice colour pictures of these solutions in Wedin, H. & Kerswell, R.R. ``Exact coherent structures in pipe flow: travelling wave solutions'' J. Fluid Mech. 508, 333-371, 2004. diaw: Granted, I am certainly referring to transient wave-forms in the context of a transient wave-field. given a consistent boundary disturbance, would there be no possibility of non-linear 'normal modes' forming? I think that perhaps the difference in viewpoints may be one of considering a reasonably consistent source of input 'noise' as a boundary-condition, or of flow-generated noise/perturbations. I would love to know if sound measurements of the onset of instability have been conducted - I'm sure they have. Does flow in a pipe make a noise? In some cases, it certainly can. Most experimental fluid experiments use sound waves to excite the flow and induce transition. Turbulence does produce noise - just go outside on a windy day. There is a considerable amount of work on this - numerous papers by Lighthill, Crighton and Howe (Howe's also written a book vortex sound). To study this type of problems you must abandon the incompressible assumption and work with a fuller set of equations since the solenoidal condition filters all acoustic waves from the equations. There is no such thing as a nonlinear normal mode (by definition!) and even if there was there is no need to invoke it to describe the problem - the linear "branch cut" argument in the complex plane gives the solution for small amplitude disturbances (just as in the gravity wave case). diaw: What happens when we 'pull' flow out of a pipe - by setting a slight suction on the outlet boundary? (This one can be rather fun to observe, although some solvers will definitely not want to oblige.) In an incompressible fluid cavitation occurs (you are taking out more fluid than you are putting in) and the solution to the problem (as posed with noslip bcs) has failed to exist - hence the solvers that fail are the ones that are correct! For the solution to make sense you need to augment the statement of the problem with suitably altered boundary conditions. diaw:What would a pressure-wave look like in a pipe? As I've already stated there is no pressure wave in the incompressible limit.

 February 16, 2006, 05:32 Re: Wave-solutions & div(v) re-visited #104 Tom Guest   Posts: n/a "Can I respectfully ask advice on suitable Journals to consider when publishing my research findings?" If you really believe you have something new and interesting to say about the equations of motion then you should consider either the Journal of fluid mechanics, Proceedings of the Royal society of London A, European Journal of Mechanics B/fluids, physics of fluids or possibly Theroetical and computational fluid dynamics. However I would suggest that, if you submit to one of these journals, you prepare yourself for some harsh critism/rejection (JFM rejects around 55% of submitted papers as policy!). It is always worth the extra effort to publish in a respected journal though.

 February 16, 2006, 06:44 Re: Wave-solutions & div(v) re-visited #105 diaw (Des Aubery) Guest   Posts: n/a Tom: "Can I respectfully ask advice on suitable Journals to consider when publishing my research findings?" If you really believe you have something new and interesting to say about the equations of motion then you should consider either the Journal of fluid mechanics, Proceedings of the Royal society of London A, European Journal of Mechanics B/fluids, physics of fluids or possibly Theroetical and computational fluid dynamics. However I would suggest that, if you submit to one of these journals, you prepare yourself for some harsh critism/rejection (JFM rejects around 55% of submitted papers as policy!). It is always worth the extra effort to publish in a respected journal though. diaw: Thanks so much Tom, for the Journal list. Those are indeed very well respected Institutions. I would certainly expect some very harsh criticism/rejection - this would most certainly be in order. I believe that this would be well worth the effort. In some ways, your gentle wise comments during the course of this debate have been preparing my mental resolve. At each point, it has sent me more & more deeply into the books to try & explain what I have seen. This has forced me to go back to basics in some areas & explain my case more thoroughly. No doubt, the review team of some of these Journals will put my research through the distilling fires - but, so, let it be. Once again, thank you so much for your debate & wisdom. It has been suncerely appreciated. Des Aubery...

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