Stability of Bödewadt flow

Area of Science:

• Fluid dynamics
• Hydrodynamics
• Aerodynamics

Background:

• Investigates the stability of fluid flow over a stationary plane in a rotating fluid system.
• The foundational flow is an exact solution to the Navier-Stokes equations, enabling rigorous theoretical analysis.
• Focuses on the asymptotic behavior in the regime of large Reynolds numbers.

Purpose of the Study:

• To theoretically analyze the stability of a specific fluid flow configuration.
• To explain the origin of stationary spiral instabilities observed in experiments.
• To validate theoretical predictions against experimental and numerical data.

Main Methods:

• Employs an asymptotic investigation in the limit of large Reynolds numbers.
• Utilizes linear inviscid stability analysis to model flow disturbances.
• Compares theoretical predictions with existing experimental and numerical results.

Main Results:

• Demonstrates that linear inviscid stability analysis can describe stationary spiral instabilities.
• Provides a theoretical prediction for the wave angle of these disturbances.
• Achieves good agreement between predicted and observed wave angles.

Conclusions:

• Linear inviscid stability analysis is a suitable method for understanding spiral instabilities in this rotating fluid flow.
• The theoretical framework accurately captures key features of the observed flow behavior.
• Confirms the validity of the theoretical approach through comparison with empirical and computational data.