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Benchmark solution for the stability of plane Couette flow with net throughflow
B M Shankar1, I S Shivakumara2
1Department of Mathematics, PES University, Bangalore, 560 085, India. bmshankar@pes.edu.
Scientific Reports
|May 26, 2021
Summary
Vertical throughflow destabilizes plane Couette flow (PCF), altering its stability based on flow magnitude. This study reveals throughflow
Area of Science:
- Fluid dynamics
- Hydrodynamic stability
Background:
- Plane Couette flow (PCF) is typically stable to small disturbances.
- Understanding stability in flows with throughflow is crucial for various engineering applications.
Purpose of the Study:
- To investigate the linear stability of incompressible viscous fluid flow between parallel plates with vertical throughflow.
- To determine the influence of throughflow magnitude and direction on PCF stability.
Main Methods:
- Linear stability analysis using the method of normal modes.
- Numerical solution of the stability equation via the Chebyshev collocation method.
Main Results:
- Vertical throughflow can destabilize PCF, with instability onset dependent on throughflow magnitude.
- Throughflow exhibits both stabilizing and destabilizing effects on the base flow.
- The direction of throughflow does not impact the fluid flow stability.
Conclusions:
- Vertical throughflow fundamentally alters the stability characteristics of plane Couette flow.
- Critical Reynolds number for instability is dependent on throughflow parameters.
- Comparative analysis with plane Poiseuille flow highlights distinct stability behaviors.
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