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09:58
Investigating the Three-dimensional Flow Separation Induced by a Model Vocal Fold Polyp
Published on: February 3, 2014
Nonparallel spatial stability of the boundary layer induced by Long's vortex on a solid plane perpendicular to its
1E.T.S. Ingenieros Industriales, Universidad de Málaga (Spain).
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 26, 2005
Summary
This study analyzes the stability of a vortex boundary layer, finding both inviscid and viscous instabilities. Nonaxisymmetric perturbations with azimuthal wave number n=4 are the last to stabilize as the vortex axis is approached.
Area of Science:
- Fluid Dynamics
- Aerodynamics
- Hydrodynamics
Background:
- Investigates the linear, viscous stability of a boundary layer generated by an unbounded vortex.
- Focuses on a vortex whose outer inviscid structure aligns with Long's vortex near the axis.
- Examines the self-similar structure of the viscous boundary layer formed by vortex-plane interaction.
Purpose of the Study:
- To analyze the spatial stability of the self-similar vortex boundary layer solution.
- To investigate axisymmetric and nonaxisymmetric perturbations propagating towards the axis of rotation.
- To retain viscous and nonparallel effects up to the first order in the inverse local Reynolds number.
Main Methods:
- Numerical solution of parabolic stability equations using a spectral collocation method.
- Variation of nondimensional frequency and radius to analyze stability characteristics.
- Characterization of critical Reynolds numbers and frequencies as functions of azimuthal wave number.
Main Results:
- Identified inviscid instability for axisymmetric perturbations far from the axis.
- Observed viscous instabilities for both axisymmetric and nonaxisymmetric perturbations at moderate Reynolds numbers.
- Determined that nonaxisymmetric, corotating perturbations (n=4) are the last to stabilize near the axis.
Conclusions:
- The vortex boundary layer exhibits complex stability behavior with both inviscid and viscous modes.
- Azimuthal wave number significantly influences the stability characteristics and critical parameters.
- Understanding these instabilities is crucial for predicting vortex dynamics in various flow scenarios.
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