Linear analysis of the cylinder wake mean flow

PACS. 47.20.Ft – Instability of shear flows (e.g., Kelvin-Helmholtz). PACS. 47.20.Ky – Nonlinearity, bifurcation, and symmetry breaking. Abstract. – A highly accurate 2D linear stability analysis is performed on the mean flow of laminar vortex shedding from a circular cylinder for Reynolds numbers between 46 and 180. Consistent with past studies of mean profiles, the analysis shows that the eigenfrequency of the mean flow tracks almost exactly the Strouhal number of vortex shedding. The linear growth rate reveals that the wake mean flow is a marginally stable state over the whole range of Reynolds numbers for stable 2D vortex shedding. This is contrasted with 2D stability analysis about the unstable steady base flow. The relevance to nonlinear saturation and frequency selection are discussed. Introduction. – Fluid flow past a circular cylinder has long been a prototype for bluff-body wake flows. The flow configuration is governed by a single non-dimensional parameter, the Reynolds number Re = U∞d/ν, where ν is the kinematic viscosity of the fluid which is moving with free-stream speed U ∞ and d is the cylinder diameter. For values of Re below a critical value Rec 46, the flow is asymptotically steady and two-dimensional. (See fig. 1(a)