Is there a limit for the solution of Navier Stokes equation?

[robert80]

Dear all

I have 1 simple question. If the solution of Navier Stokes equation exists, its limits for infimum length, time and velocity would be the Kolmogorov Microscale equations, am I correct?

Thanks,

Robert

 

[Cantstandit]

I am not so sure about that. I think Kolmogorov Microscale apply to turbulence and eddies only. Below that scale you could have flow, but it would be laminar. I think its limits would be certain lengths below which the assumption of continuity is not satisfied (i.e. like 1000 times molecule size). That would be my guess.

 

[Daiquiri]

As said above, Kolmogorov theory deals with turbulent flows at "sufficiently" high Reynolds numbers, whilst N-S equations can give either laminar-flow solutions or turbulent-flow solutions, depending on initial and boundary conditions.

Think of a free uniform rectilinear flow, for example. If you don't introduce an artificial initial instability to generate a turbulence, the solution of N-S will give a uniform rectilinear and laminar flow at all length scales.

But generally speaking, if the resulting flow is turbulent (because you've decided to make it turbulent) then DNS solution should reflect Kolmogorov's hypothesis as the length scale goes to zero. It will, of course, depend on the numerical accuracy of the solution.

 

[Andy Resnick]

Dear all

I have 1 simple question. If the solution of Navier Stokes equation exists, its limits for infimum length, time and velocity would be the Kolmogorov Microscale equations, am I correct?

Thanks,

Robert

Can you provide some sort of reference for the Kolmogorov microscale equation? The reference I found:

http://www.google.com/url?sa=t&sour...sg=AFQjCNHoGK-uadD_2HuQGaqLCVA2u7EtjQ&cad=rja

indicates the equation relates to energy, not momentum- the NS equation is a momentum equation.

 

[Daiquiri]

The reference I found
...
indicates the equation relates to energy, not momentum- the NS equation is a momentum equation.

That is correct. You can find a very good and easy-to-read short essay about Kolmogorov theory here (PowerPoint file): http://www.bakker.org/dartmouth06/engs150/09-kolm.ppt

 

[robert80]

Ok thank you for all the help, this links are preety useful.