Multimodal analysis for the stability of vortices with axial flow

The problem of transient behavior of perturbations in the linear stability analysis of vortex columns with axial flow is considered. We use the Batchelor vortex as the base flow and the analysis is carried out by focusing on a region of the parameters space in which both weak viscous exponential instabilities and transient growths of perturbations are present. The competition between the two linear effects is analyzed in a certain range of axial and azimuthal wavenumbers. The numerical discretization has been performed by employing an accurate Chebyshev collocation spectral method. The computations of the growth function evolution and of the optimal perturbations have been conducted by implementing two different strategies, the matrix exponentiation and the direct-adjoint techniques, and a comparison in terms of computational cost and accuracy is presented. Furthermore, some aspects of the competition between viscous instabilities and transient effects, in a swirl numbers range in which are both present, are discussed