Perturbation growth in vortices with axial flow

Aim of the present paper is to perform a linear temporal stability analysis of the trailing line vortex model named q-vortex. Both exponential and non-modal instabilities are inquired with a local approach, for swirl numbers q near the limit of Gaussian jet. In the range of axial and azimuthal wavenumbers in which both instabilities are present, the competition between the two linear mechanisms is analyzed, focusing the attention on a particular swirl value of typical aeronautic interest in order to extract the dominant effects which lead to vortex breakdown at realistic finite times. These instabilities are studied numerically using an accurate Chebyshev collocation spectral method; the computation of the optimal perturbations has been obtained by means of two different techniques: “matrix exponentiation” and “direct-adjoint simulation”. Maps of the transient growth peaks up to Re=10^5 for the parameters space here inquired are obtained. Furthermore, the competition between the weak viscous exponential growths and the non-modal ones is analysed, over a certain range of Re numbers.