Non-linear stability of a perturbed Orr-Sommerfeld solution for the wake of a stationary cylinder at low Reynolds numbers

O. Shoshani, O. Gottlieb

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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 languageEnglish
Pages (from-to)176-182
Number of pages7
JournalInternational Journal of Non-Linear Mechanics
Volume57
DOIs
StatePublished - 4 Sep 2013
Externally publishedYes

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

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