Non-dimensionalizing the N-S equations

  • Thread starter hanson
  • Start date
319
0
In non-dimensionalizing the N-S equations, are the choices of the characteristic variable important? I am currently reading the Stokes approximation to the N-S equation and find two versions of Stokes equations. They have used different scaling in their derivation and I find no clue in understanding the importance of scaling and am wondering if someone here can help me out.

Please kindly read the figure attached.

While the version 1 has characterise the time by U and L, version2 uses the kinemtic viscosity to scale the time. Are there any difference between these two approaches? I don't know what kind of difference will be produced and what effect would different choice of scales bring out. Could anyone explain clearly?

And are the two versions of Stokes equation the same? If not, what are the differences?

I find no clue in non-dimensionalization....
 

Attachments

Last edited:
19,030
3,714
In non-dimensionalizing the N-S equations, are the choices of the characteristic variable important? I am currently reading the Stokes approximation to the N-S equation and find two versions of Stokes equations. They have used different scaling in their derivation and I find no clue in understanding the importance of scaling and am wondering if someone here can help me out.

Please kindly read the figure attached.

While the version 1 has characterise the time by U and L, version2 uses the kinemtic viscosity to scale the time. Are there any difference between these two approaches? I don't know what kind of difference will be produced and what effect would different choice of scales bring out. Could anyone explain clearly?

And are the two versions of Stokes equation the same? If not, what are the differences?

I find no clue in non-dimensionalization....
The only real difference between these two approaches is in the definition of the dimensionless time. The second approach looks more appropriate for considering the transient case.
 

Want to reply to this thread?

"Non-dimensionalizing the N-S equations" You must log in or register to reply here.

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving

Hot Threads

Top