Would you like to make 1,000,000 dollars?

Explain Turbulence, and it is as easy at that!

The understanding the Navier–Stokes equations is considered to be the first step for understanding the elusive phenomenon of turbulence, the Clay Mathematics Institute offered a US$1,000,000 prize in May 2000, not to whomever constructs a theory of turbulence, but (more modestly) to the first person providing a hint on the phenomenon of turbulence. In that spirit of ideas, the Clay Institute set a concrete mathematical problem

"Prove or give a counter-example of the following statement:
In three space dimensions and time, given an initial velocity field, there exists a vector velocity and a scalar pressure field, which are both smooth and globally defined, that solve the Navier–Stokes equations."

All theory's should be sent into Clay Institute.



Obviously, you are welcome to try and do that, but here is the real reason I made this thread.


How crazy is it that we don't understand Turbulence already? Sometimes I think we forget how much is still unknown in this World.....





Ps. the answer isn't PI

flow regime characterized by chaotic and stochastic property changes. This includes low momentum diffusion, high momentum convection, and rapid variation of pressure and velocity in space and time. Nobel Laureate Richard Feynman described turbulence as "the most important unsolved problem of classical physics."[1] Flow in which the kinetic energy dies out due to the action of fluid molecular viscosity is called laminar flow. While there is no theorem relating Reynolds number (Re) to turbulence, flows at Reynolds numbers larger than 5000 are typically (but not necessarily) turbulent, while those at low Reynolds numbers usually remain laminar. In pipe flow, for example, turbulence can first be sustained if the Reynolds number is larger than a critical value of about 2040[2]; moreover, the turbulence is generally interspersed with laminar flow until a larger Reynolds number of about 3000. In turbulent flow, unsteady vortices appear on many scales and interact with each other. Drag due to boundary layer skin friction increases. The structure and location of boundary layer separation often changes, sometimes resulting in a reduction of overall drag. Although laminar-turbulent transition is not governed by Reynolds number, the same transition occurs if the size of the object is gradually increased, or the viscosity of the fluid is decreased, or if the density of the fluid is increased. PAY ME

reply to post by shortyboy


Nice Try. lol


Next time you should Site your source =P

that Still didn't prove it though.

reply to post by truthinfact


Could you provide a link to the action ?

oh.. I would think NASA and the Air force have mastered turbulance

Jesus did it, check will do.

Well this has always been my understanding of what causes turbulence. I guess it is wrong then. hmmm....

What causes turbulence?
Turbulence is the up-and-down air currents that help to mix the air in the troposphere. It is usually mentioned in the context of airplane flights, where these air currents can feel like "bumps in the road" while flying. Turbulence can occur in the lowest part of the troposphere during the daytime when heating of the sun causes convective mixing of the air. Once the airplane rises above this turbulent "boundary layer", the air becomes smoother. But other processes can also cause these up- and down-drafts. One example is convective clouds. If an airplane must fly through a thunderstorm, these updrafts and downdrafts can be very strong. There is also "clear air turbulence", which can also become very strong. This usually occurs near jet streams, where rapidly changing wind speeds with height can combine with an unstable air layer to cause "waves" of up and down motion in this air layer.

www.weatherquestions.com...

I really have no idea as to the answer to the question but I know its not asking what turbulence is, it wants you to prove or disprove the statement "In three space dimensions and time, given an initial velocity field, there exists a vector velocity and a scalar pressure field, which are both smooth and globally defined, that solve the Navier–Stokes equations."

Id look to figuring out what the Navier-Strokea Equations are first, and define velocity field, vector velocity, and scalar pressure field. Then if youre smart enough maybe you can figure it out from there goodluck lol. If you do figure it out I would publish your work or something before sending it in an envelope to someone who may give you 1 million dollars or steal your idea.

We understand what turbulence is, not how or why it happens

reply to post by shortyboy


You dont want to give credit to the site you pulled that from, nearly verbatim?

Plagerism

This is a mathematical problem asking for mathematical proof that solutions alway exist or dont exist for the Navier Stokes equation when applied in 3 dimensions.

This is a challenge for mathematicians not experts in fluid mechanics. Unfortunately

Science does understand fluid flow but as it is chaotic is is very difficult to model with 100% accuracy just like the weather which is of course a chaotic, turbulent system.

reply to post by truthinfact


Maybe an airplane is like a jetski. If the jetski could go underwater or fly at a low enough altitude there would be no turbulence. But when its in the middle right on the water its gonna go with the waves. Maybe air acts the same way with different levels, and if a plane is caught in between two levels it can't just slice through one level smoothly it will contact both and jump in between the two causing the bouncing. I doubt the different atmosphere levels are 100% smooth. This is just a guess though cause I don't know the science behind air or turbulence.

The answer to this problem is worth more than one million dollars. [Insert picture of Dr Evil]

...but seeing as I'm a poor beggar, I will submit my solution anyway. Even if only to prove the challenge wrong. To...

"Before consideration, a proposed solution must be published in [color=gold] a refereed mathematics publication of worldwide repute (or such other form as the SAB shall determine qualifies), and it must also have general acceptance in the mathematics community two years after."

... that is, not publicly on the internet.

I mean applying Newton's second law to fluid mechanics in the first place ... just what were they thinking.


David Grouchy

reply to post by truthinfact


Turbulance= Chaos.

Fractally speaking.

I'll take a cheque thanks.

Originally posted by atlasastro

Turbulance= Chaos.

Fractally speaking.

I'll take a cheque thanks.

In the first five minutes of this video he dispells each item stated above.

It's also a decent refresher for anyone working on the challenge.


David Grouchy

Disorder is a neccessary factor in turbulence, it is not howerver sufficient.

Something with strange attractors. If I am not mistaken there are different ones in chaotic systems (deterministic looping systems). Or am I mixing up stuff?