Hydrodynamic stability- Rayleigh equation - Couette flow

In summary, the conversation is about formulating the stability problem in the incompressible inviscid limit and finding the dispersion relation in the Couette flow regime. The speaker mentions using the Rayleigh equation and asks for any references or ideas. The other person suggests searching for "couette flow stability" and mentions the book "Chandrasekhar." The first speaker asks for more specifics and the other person provides a link to the book.
  • #1
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TL;DR Summary
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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  • #2
If you google ”couette flow stability” plenty of references come up.
 
  • #3
Should I assume you've already explored references like Chandrasekhar?
 
  • #4
boneh3ad said:
Should I assume you've already explored references like Chandrasekhar?
No, can you be more specific?
 
  • #6
Much Appreciated!
 

1. What is hydrodynamic stability?

Hydrodynamic stability is the study of the stability of fluid flows. It involves understanding how small disturbances in a fluid flow can either grow and become turbulent, or dissipate and maintain a laminar flow.

2. What is the Rayleigh equation?

The Rayleigh equation is a mathematical equation that describes the growth or decay of disturbances in a fluid flow. It takes into account the effects of viscosity, inertia, and surface tension on the stability of the flow.

3. How is the Rayleigh equation used in hydrodynamic stability analysis?

The Rayleigh equation is used to determine the critical conditions at which a flow becomes unstable and transitions from a laminar to a turbulent state. It is also used to predict the growth rate of disturbances in a flow and to understand the mechanisms behind flow instability.

4. What is Couette flow?

Couette flow is a type of fluid flow between two parallel plates, where one plate is stationary and the other is moving at a constant velocity. It is a simple and commonly used model for studying fluid dynamics and stability.

5. How does the Rayleigh equation apply to Couette flow?

The Rayleigh equation can be applied to Couette flow to analyze the stability of the flow. By solving the Rayleigh equation for Couette flow, we can determine the critical conditions at which the flow becomes unstable and transitions to a turbulent state.

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