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Stability of Bödewadt flow.

Sharon O Mackerrell1

  • 1School of Mathematics, University of Birmingham, Birmingham B15 2TT, UK. s.o.mackerrell@bham.ac.uk

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|August 18, 2005
PubMed
Summary

This study examines fluid flow stability over a stationary plane in a rotating fluid. Linear inviscid stability analysis accurately predicts spiral instabilities observed experimentally.

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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.

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