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thegodfather March 18, 2012 02:12

Orr Sommerfeld equation
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??

truffaldino March 18, 2012 05:27

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.

thegodfather March 18, 2012 07:43

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?

truffaldino March 18, 2012 07:57

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.

thegodfather March 18, 2012 08:04

thanks.. that was really helpful..

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