Absolute and convective instability of a cylinder wake

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Abstract
Local linear stability theory is used to investigate the stability characteristics of a circular cylinder wake at values of the Reynolds number, Re, up to 45. Both the Orr–Sommerfeld and Rayleigh analyses for complex frequency and wavenumber are applied to computed basic, steady wake profiles. These velocity profiles are Navier–Stokes solutions of a uniform, incompressible viscous flow around a cylinder, which we obtain by a spectral method. The distributions of convective and absolute instabilities in the near wake behind the cylinder are determined for different Reynolds numbers and locations. The study shows that an absolutely unstable region begins to form at Re of about 20, and grows with increasing Re. Hence the onset of global response of instability, which is known to occur at Re of about 40, must be characterized by a critical length of an absolutely unstable region. A criterion to determine the critical Reynolds number Rec and the preferred frequency, from local linear stability analysis, is proposed. The predicted values of Rec and frequency for global response agree well with the prediction of nonparallel stability analysis and experimental results.