How to Determine the Stability Condition in Couette Flow?

URIA
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Homework Statement
Hi all,
I would like to solve the attached .
Relevant Equations
Can someone help with the attached?
Dear All,
I tried to solve the attached question. it's about Couette flow, where the 2 plates move.
2023-01-13 110841.png

in fact, I have to find the stability condition. is someone familiar with this and can help?
many thanks,
uria
 
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Do you have a general idea on how to do the stability analysis? Basically it's expanding around the un-perturbed given solution and linearizing the NS equations.
 
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HI,
I assume I have to use the rayleigh equation because of the incompressible inviscid limit.
 

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