http://arxiv.org/abs/nlin.CD/0501049

Hi, I found one paper above. The guy claims their theory is new and is better than others.

Can anybody comment the theory feasible or not?

Thanks Tom

At a quick glance (I'll read it properly if it gets published in JFM) I'd say it's save to ignore this (if you're interested in energy ideas for the instability of parallel flows look up Arnold's theorem).

The same persons written a paper on the Rayleigh criterion for the Orr-Sommerfeld equation which is obviously wrong!

If you're interested in theoretical work on transition to turbulence look at the book by Drazin & Reid and various papers in JFM in the eighties-nineties (i.e. papers by Goldstein, Smith, Hall and Wu and various coworkers).

Thanks for your help. I have read the books you mentioned. But, the mechanism of transition in a pipe flow is still not clear.

Linear thoery obtains Re_c is infinite, while experiments showed Re_c=2000. Thus, that predicted using linear thoeory is not the one corresponding to turbulent transition.

How to explain this?

Thanks. Tom

At present there is no explaination, you might as well ask the questions why do flows become turbulent and what is turbulence?. In the case of pipe flow it is believed, as I recall there was some analysis of this, that there is a bifurcation point at infinite Reynolds number (which is necessarily subcritical) which gives rise to a second nonlinear solution to the equations at finite Re. Provided the initial perturbation/disturbance to the base flow is large enough the solution will jump to this other branch (or attracting set); i.e. linear stability requires infinitessimal perturbations which does not guarantee stability to finite amplitude (nonlinear) disturbances.

Hope this helps,

Tom.

P.S. before he died Philip Drazin wrote a more elementary introduction to stability theory which may be worth looking at.

Tom, this is a different problem, please help me find what i need to know. i am just a high school grad. i have no knowledge of physics. this is my delima. i am building a unit to rapidly heat water. the set up i am looking for would be similar to a pressure washer, which has coils inside that is heated and is put under pressure to clean. what i need is to take half inch steel pipe, coil it. put it inside of an insulated heater, using 100,000 btu's to bring my water temp. to 200 degrees, at a flow rate of 10 gallons per min. with my limited knowledge, i have no idea at all as to how to compute this so that i can figure how many feet of coils i must have, in order to obtain this. i think this is computable, but like i said, i dont know how or where to go to find out.please remember to put this in lehmans terms for me if possible. thank you Mark Rayl