Hydrodynamic stability- Rayleigh equation - Couette flow

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SUMMARY

The discussion focuses on formulating the stability problem in the incompressible inviscid limit for Couette flow, specifically addressing the dispersion relation using the Rayleigh equation. Participants emphasize the need for clarity in the application of the Rayleigh equation in scenarios where both plates are in motion, contrasting it with the standard case of one static plate. References to Chandrasekhar's work on Couette flow stability are suggested as foundational material for further understanding. The conversation highlights the importance of specific literature in tackling complex fluid dynamics problems.

PREREQUISITES
  • Understanding of Couette flow dynamics
  • Familiarity with the Rayleigh equation
  • Knowledge of dispersion relations in fluid mechanics
  • Basic principles of incompressible inviscid flow
NEXT STEPS
  • Study the Rayleigh equation in the context of fluid stability analysis
  • Explore Chandrasekhar's contributions to Couette flow stability
  • Research dispersion relations specific to fluid dynamics
  • Investigate the effects of plate motion on stability in fluid systems
USEFUL FOR

Fluid dynamics researchers, graduate students in mechanical engineering, and professionals studying stability in fluid flow systems will benefit from this discussion.

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TL;DR
Folks,
I'm trying to formulate the stability problem in the incompressible inviscid limit and find the dispersion relation in the Couette flow regime. As shown, the 2 infinite plates move one against the other, unlike the "standard" case where one plate is static and the second moves. I'm trying to use the Rayleigh equation but I'm not sure how to do this.

Any references or ideas are welcome :)
Folks,
I'm trying to formulate the stability problem in the incompressible inviscid limit and find the dispersion relation in the Couette flow regime. As shown, the 2 infinite plates move one against the other, unlike the "standard" case where one plate is static and the second moves. I'm trying to use the Rayleigh equation but I'm not sure how to do this.
Any references or ideas are welcome :)

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If you google ”couette flow stability” plenty of references come up.
 
Should I assume you've already explored references like Chandrasekhar?
 
boneh3ad said:
Should I assume you've already explored references like Chandrasekhar?
No, can you be more specific?
 
Much Appreciated!
 

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