Global stability analysis of the flow behind an axisymmetric blunt based body

A three-dimensional global mode linear analysis of the flow behind an axisymmetric blunt-based body is numerically investigated. The two-dimensional steady base flow is obtained from time-dependent simulations based on a finite-element spatial discretization and a Lagrange-Galerkin temporal discretization. The generalized eigenvalue problem is solved by use of the Implicitly Restarted Arnoldi method. We show that a helical (m=1) non-oscillating mode, whose eigenmode is mainly located in the recirculating area, becomes unstable at a critical Reynolds number Re=295, and that a helical oscillating mode, whose eigenmode exhibits the spatially periodic downstream structure characteristic of the oscillatory wake instability, becomes unstable at a supercritical Reynolds number Re=409 with a frequency fD/U$_{\infty }$=0.14. As a step to address the relevance of the second bifurcation, we then consider the non-linear saturation amplitude of the non-oscillating mode by solving the amplitude equation associated with the first bifurcation.