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

In summary, the conversation is discussing the relationship between the Navier Stokes equation and the Kolmogorov Microscale equations. There is some disagreement about whether the Kolmogorov theory applies to all scales or just turbulence, and one person provides a reference that suggests it only applies to energy, not momentum. Another person recommends a PowerPoint presentation for more information on Kolmogorov theory.
  • #1
robert80
66
0
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
 
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  • #2
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.
 
  • #3
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.
 
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  • #4
robert80 said:
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.
 
  • #5
Andy Resnick said:
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
 
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  • #6
Ok thank you for all the help, this links are preety useful.
 

1. What is fluid dynamics?

Fluid dynamics is the study of how fluids (liquids and gases) behave and interact with their surroundings. It involves understanding the motion, forces, and energy of fluids in various situations.

2. What are some real-world applications of fluid dynamics?

Fluid dynamics has many practical applications, such as in designing aircraft and cars, predicting weather patterns, and understanding blood flow in the human body. It is also used in industries such as aerospace, automotive, and energy production.

3. How is fluid dynamics different from fluid mechanics?

Fluid dynamics focuses on the behavior of fluids as a whole, while fluid mechanics focuses on the forces within fluids and how they affect the motion of objects within the fluid. Fluid mechanics is a subset of fluid dynamics.

4. What are some important principles in fluid dynamics?

Some key principles in fluid dynamics include conservation of mass, conservation of energy, and Newton's laws of motion. Bernoulli's principle and the Navier-Stokes equations are also fundamental in understanding fluid behavior.

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