Re: Generalized Math. Form of Turbulence
 

It's surprising that no one has insisted on using relativistic quantum mechanics! : )

Re: Generalized Math. Form of Turbulence
 

Thanks Tom. The onset of transition in Rayleigh Benard convection is the one I'm most familiar with. Ed Lorenz examined this type of system to derive his butterfly effect 'theorem' (meteorologist -> non-linear dynamics!).

I hadn't quite appreciated the differences in considering transitional issues in closed systems vs. open systems.

Such bifurcation reminds me of that observed in the Logistics equation. The rate of period doubling I think is pretty constant in such systems and was found by Feignenbaum to be 3.5699.... (Feignenbaum's delta). Apparently "This number has been measured in experiments with chicken hearts, electronic circuits, lasers, chemical reactions, and liquids in their approach to a turbulent state, as well as the bouncing ball system" (from http://www.drchaos.net/drchaos/Book/node44.html). I think it was Taylor-Couette flow (fluid between counter rotating cylinders, one inside another I think?) that was the experiment which exhibited the said rate of bifurcation.

Point is, does any of this help engineers in their prediction of when turbulence might onset??

Re: Generalized Math. Form of Turbulence
 

It depends upon your problem. In a boundary layer the answer is no - some features of such flows can be described, at least in the very early stages of transition, using high Reynolds number (matched) asymptotic expansions but we are still a long way from having a clear theory of what's going on (and the equations are nothing like the canonical equations of bifurcation theory - you usually end up with integro-partial differential equations).

In other problems, such as the Shilnikov case in the Taylor-Couette experiment, then the answer is maybe. The transition to a chaotic flow in the Taylor-Couette experiment (turbulence occurs at higher Taylor numbers than the chaotic behaviour) agrees quite well with theory as I recall (Tom Mullin's group did a lot of work on this in the late eighties/early nineties?)

Re: turbulence and chaos
 

Interesting enough for Fluent to apply their marketing wizardry:

http://www.fluent.com/about/news/pr/pr5.htm

Re: the problem is....
 

"... Nomad.

Until you are able to come up with the Nomad Equations that define the fluid flow exactly .... "

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You copy-yes-men, you indirectly admit that your have been using wrong equations. I had told Nomad equations to your professors 2 decades ago - BUT their brains were/are so thick that they were unable to understand and they continued to stay as a yes-men / copy-men to get their PhD titles from their old masters.

Now, I'm not here to try to them / you more about Nomad exact equations. Just tell me again that you still admit YOU DO NOT KNOW whether N-S equations represent the flows or not. Yes, you do not know, you are not sure - but still playing your modelling games blindly in your dark room.

"... Looking forward to seeing your work published in a journal ..."

Journals? LOL - All misinformation with politic biased literatures. If you don't kiss their as* of their editors, a top science study can't be published because they do not understand and they are biased. If you kiss their as* of those editors, then your worthless papers can be published as featured papers. Come'n you can cheat people out of the field - but can't cheat such people like this Nomad.

Re: Generalized Math. Form of Turbulence
 

"... It's surprising that no one has insisted on using relativistic quantum mechanics! : ) ..."

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Relativistic fluid dynamic equations. Should have been used much more decades ago - Then, today's fluid dynamic (in theoretical, dns, cfd, experimental, etc) fields would be completely in another direction today. But those old scholar! masters of fluid dynamics IGNORED / NEGLECTED "relativistic effects" in the fluid flows. because they were TOO deterministic minds. Fluid dynamic scholers were the most believers of Karma!

Re: the problem is....
 

You talking like claiming that "CFD is a REAL world application UNLIKE theoretical mathematics of fluid flow"...

Pardon me! If CFD is a real world application, then you're transforming the objects/functions of unreal/dream world to the real world by using CFD? You're dreaming somethings and I see your transformations to the daylight.

As I told in my previous posts, whichever direction (east, west, north, south) you go when doing somethings in this life, you'll do somethings useful. In all directions, you'll obtain some useful applications. But this doesn't mean you're on the correct way. To understand the correct way, look at your behind, look at the residuals you remained behind you. Them these residuals show you're on the wrong way. Before application, think twice. Don't help Mercedes factory if it's not yours... Pity you if you help them.

Re: the problem is....
 

Sounds like someone's a little bitter about not getting through the peer review process....

Re: Generalized Math. Form of Turbulence
 

Here is what you might be looking for, Nomad. Jackiw, Roman (2002), Lectures on Fluid Dynamics.

Mathematical description of any physical phenomenon makes certain assumptions. Validity of these models are greatly limited by our understanding of the physical process and/or by the over-simplification due to assumptions. N-S equations produce meaningful results so long as the assumptions used to describe a newtonian fluid are valid. Proof of existence and uniqueness of these equations in 3-D is open problem indicating that we have derived a mathematical model that could be ill-posed problem partly because of such a simple constitutive assumption for the fluid in turbulent flows

Turbulence defined by salient features of non-linear, dissipative, random/chaotic/stochastic systems has given some insights into the actual "fluid turbulence" phenomenon. Clearly, the order within chaos, makes the mathematical tools inapplicable at times.

MT

Re: the problem is....
 

Well, now I'm curious... Can you post a link to your work? Thanks,

Re: the problem is....
 

I was wondering what your background, scientifically, is Nomad? Also, I wonder if you are a silly 1st year undergrad, because you sure sound like on. Its a bummer to come across people who live in la-la land, as you clearly do. As I read somewhere, Scientists want the correct answer, Engineers want the best answer NOW. CFD is an amalgamation of these two approaches.

Re: the problem is....
 

I've been following this conversation with a lot of interest. The only conclusion I have so far is that "Nomad" is someone that is often referred to as "troll" in newsgroups.

Re: the problem is....
 

A disgruntled grad school dropout, maybe?

Troll - a definition
 

Troll - n. An individual who regularly posts specious arguments, flames or personal attacks to a newsgroup, discussion list, or in email for no other purpose than to annoy someone or disrupt a discussion. Trolls are recognizable by the fact that they have no real interest in learning about the topic at hand - they simply want to utter flame bait. Like the ugly creatures they are named after, they exhibit no redeeming characteristics, and as such, they are recognized as a lower form of life on the net, as in, "Oh, ignore him, he's just a troll."

Re: the problem is....
 

"..Well, now I'm curious... Can you post a link to your work? Thanks,.."

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I'm sorry - I don't give. I've never linked my works to errorous completely wrong works in the journals. Science fields long time ago has been a field like "deafs play - blinds dance" mind field. I'd be ashamed of if I had published my any work in any current journal/conference/seminar/etc.

Re: Troll ? - Then, you intelligent people... you
 

can win an argument/debate against a simple troll.

don't go off topic - stay on topic - and lets see what you know and you don't know. Prove my points wrong.. if you are able to.

Einstein-like scientists are only very very few in millions of so called scientists like you and your master professors. So, you people speaking like that off-topic are a big majority here.

Re: the problem is....
 

No - just someone enjoying how much of a fuss his goofy statements have drummed up on this site. This being his goal, I assume, he's done a pretty good job! :) Congrats, Nomad. Just quit while you're ahead.

Re: the problem is....
 

It would be enlightening for all of us if given access to your work. Letting others know your view in specific terms would be quite good. I understand this is the way science progresses.

Re: Troll ? - Then, you intelligent people... you
 

we dont have to prove your points wrong! More importantly you have to prove your points right. seeing as you wont give any more detail than you speculation then it would be impossible to make an sensible comment about your point. So I dont see the point of your conversation.