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Modeling and Experimental Analysis of the Single-Shaft Coaxial Motor-Pump Assembly in Electrohydrostatic Actuators
Published on: June 13, 2022
Hydrodynamic stability without eigenvalues
Science (New York, N.Y.)
|July 30, 1993
Summary
Smooth fluid flows can become unstable and turbulent. Traditional methods poorly predict this, but pseudospectral analysis reveals linear mechanisms that amplify small perturbations, reconciling theory with experiments in fluid dynamics.
Area of Science:
- Fluid dynamics
- Mathematical physics
Background:
- Fluid flow transitions from smooth to turbulent at higher speeds.
- Traditional analysis using linearized equations and eigenvalues often shows poor agreement with experimental observations of hydrodynamic instability.
Purpose of the Study:
- To reconcile traditional linear analysis with experimental findings in hydrodynamic instability.
- To explain how linear mechanisms can amplify perturbations despite decaying eigenmodes.
Main Methods:
- Analysis of the "pseudospectra" of linearized flow equations.
- Investigating linear mechanisms responsible for hydrodynamic instability.
Main Results:
- Pseudospectral analysis indicates that small perturbations can be amplified by factors up to 10^5 via a linear mechanism.
- This amplification occurs even when all eigenmodes of the linearized problem decay monotonically.
Conclusions:
- Pseudospectra offer a reconciliation between traditional linear stability theory and experimental results in fluid dynamics.
- The presented methods are applicable to other mathematical problems involving nonorthogonal eigenfunctions.
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