We apply a WKBJ approximation to 2D and 3D bluff-body wakes. A correction term to the classical saddle-point estimation of the eigenfrequency is here calculated through a robust complex-plane extrapolation procedure based on rational Chebyshev approximation. Such correction is shown to decrease the error in the estimated eigenvalue by about an order of magnitude. Both the direct and adjoint global-mode structures are determined from local stability properties and compared with results obtained from a full 3D global stability analysis. Results show excellent agreement between the numerical global solution and its local approximation
