How to Determine the Stability Condition in Couette Flow?

Click For Summary
SUMMARY

The discussion focuses on determining the stability condition in Couette flow, specifically when two plates are in motion. The user, Uria, seeks assistance with stability analysis, indicating the need to expand around the unperturbed solution and linearize the Navier-Stokes (NS) equations. The Rayleigh equation is identified as a key tool for this analysis due to the incompressible inviscid limit. This approach is essential for understanding the dynamics of fluid flow between moving plates.

PREREQUISITES
  • Understanding of Couette flow dynamics
  • Familiarity with Navier-Stokes equations
  • Knowledge of stability analysis techniques
  • Experience with the Rayleigh equation in fluid mechanics
NEXT STEPS
  • Research linearization techniques for Navier-Stokes equations
  • Study the application of the Rayleigh equation in fluid stability analysis
  • Explore numerical methods for simulating Couette flow
  • Investigate the effects of viscosity on stability conditions in fluid dynamics
USEFUL FOR

This discussion is beneficial for fluid mechanics researchers, graduate students studying stability analysis, and engineers working on applications involving Couette flow and fluid dynamics.

URIA
Messages
5
Reaction score
0
New poster has been reminded to show their work on schoolwork problems
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
 
Physics news on Phys.org
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.
 
Reply
  • Like
Likes   Reactions: Chestermiller
HI,
I assume I have to use the rayleigh equation because of the incompressible inviscid limit.
 

Similar threads

Graduate Hydrodynamic stability- Rayleigh equation - Couette flow
  • · Replies 5 ·
Replies
5
Views
2K
Why is solid density used in this thermodynamics problem?
  • · Replies 5 ·
Replies
5
Views
2K
Slip Conditions for flow between Parallel Plates
  • · Replies 9 ·
Replies
9
Views
3K
Doublet flow in Fluid Dynamics between two spheres or cylinders
  • · Replies 0 ·
Replies
0
Views
2K
What is happening in this fluid dynamics problem and how can we approach it?
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad How does friction in a pipe occur, with the "no slip condition" ?
  • · Replies 25 ·
Replies
25
Views
2K
Q: Fluid drainage along the outside of an inclined cylinder
  • · Replies 5 ·
Replies
5
Views
1K
Fluid Dynamics - Flow through a pipe
  • · Replies 4 ·
Replies
4
Views
7K
Where can I study this type of problem? (fluid dynamics)
  • · Replies 1 ·
Replies
1
Views
1K
Separation of Particles in a fluid flow?
  • · Replies 5 ·
Replies
5
Views
2K