Abstract
We derive and investigate the non-linear stability of a perturbed Orr-Sommerfeld solution for the wake of a stationary cylinder at low Reynolds numbers assuming locally parallel flow at a distance greater than 10 diameters downstream. A weakly non-linear asymptotic temporal multiple-scale analysis yields a Stuart-Landau oscillator for the slow time evolution equation of the disturbance which in turn enables a consistent estimation of parameters based on physical measurements. For a streamwise location of 12 diameters behind the cylinder we find: (i) an excellent agreement between the asymptotically computed Strouhal number of this analysis and measurements from several experimental studies; (ii) the spatial variation of the fundamental and second harmonic of the disturbance in this study agree with experimental observations; (iii) the weakly non-linear analysis does not change the location of the critical layer throughout the range of two-dimensional laminar vortex shedding (47<R<190) and hence verify the proposed asymptotic model-based estimation procedure for the reduced-order analysis.
Original language | English |
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Pages (from-to) | 176-182 |
Number of pages | 7 |
Journal | International Journal of Non-Linear Mechanics |
Volume | 57 |
DOIs | |
State | Published - 4 Sep 2013 |
Externally published | Yes |
Keywords
- Asymptotic model-based parameter estimation
- Cylinder wake
- Non-linear stability
- Perturbed Orr-Sommerfeld equation
- Stuart-Landau oscillator
ASJC Scopus subject areas
- Mechanics of Materials
- Mechanical Engineering
- Applied Mathematics