CFD Online Logo CFD Online URL
www.cfd-online.com
[Sponsors]
Home > Forums > Main CFD Forum

Orr Sommerfeld equation

Register Blogs Members List Search Today's Posts Mark Forums Read

Reply
 
LinkBack Thread Tools Display Modes
Old   March 18, 2012, 02:12
Default Orr Sommerfeld equation
  #1
New Member
 
Aniket Sachdeva
Join Date: Mar 2012
Posts: 22
Rep Power: 5
thegodfather is on a distinguished road
My question is very fundamental.
why, at all do we need to have a separate equation that predicts the growth or decay of perturbations in a steady base flow..? If at all, there are any perturbations in the flow, why can't the resultant motion of fluid be predicted using the usual Navier Stokes equations??
thegodfather is offline   Reply With Quote

Old   March 18, 2012, 05:27
Default
  #2
Senior Member
 
truffaldino's Avatar
 
Join Date: Jan 2011
Posts: 238
Blog Entries: 5
Rep Power: 8
truffaldino is on a distinguished road
Because Navier-Stokes equation is too complicated to be solved analytically. This is the main problem of all fluid dynamics. That is why we still know almost nothing exact about turbulence.
truffaldino is offline   Reply With Quote

Old   March 18, 2012, 07:43
Default
  #3
New Member
 
Aniket Sachdeva
Join Date: Mar 2012
Posts: 22
Rep Power: 5
thegodfather is on a distinguished road
thanks a lot for replying... but as far as i know, even Orr - Sommerfeld equation is a fourth order linear differential equation which cannot be solved analytically for most cases, and various numerical methods have to be resorted to solve it... In that case would it not be better to bear with a little more complexity in terms of better numerical methods and solve the full N-S equations?
thegodfather is offline   Reply With Quote

Old   March 18, 2012, 07:57
Default
  #4
Senior Member
 
truffaldino's Avatar
 
Join Date: Jan 2011
Posts: 238
Blog Entries: 5
Rep Power: 8
truffaldino is on a distinguished road
As you said Orr-Sommerfeld is a linear system, while Navier-Stokes is nonlinear and shows chaotic behavior (turbulence) which is difficult analyse even numerically (DNS is done on supercomputers).

In the case of Orr-Somerfeld you have a possibility of qualitative analysys of transition to turbulence. You can see how perturbations amplify etc.
truffaldino is offline   Reply With Quote

Old   March 18, 2012, 08:04
Default
  #5
New Member
 
Aniket Sachdeva
Join Date: Mar 2012
Posts: 22
Rep Power: 5
thegodfather is on a distinguished road
thanks.. that was really helpful..
thegodfather is offline   Reply With Quote

Reply

Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are On
Pingbacks are On
Refbacks are On


Similar Threads
Thread Thread Starter Forum Replies Last Post
Calculation of the Governing Equations Mihail CFX 7 September 7, 2014 06:27
Constant velocity of the material Sas CFX 15 July 13, 2010 08:56
mass flow in is not equal to mass flow out saii CFX 2 September 18, 2009 08:07
Orr Sommerfeld on Airfoils Mojtaba Main CFD Forum 0 October 1, 2008 15:40
Orr Sommerfeld equation Mojtaba Ahmadi Main CFD Forum 2 September 9, 2008 05:00


All times are GMT -4. The time now is 00:41.