We have solved two-dimensional eigenvalue problem for the stability analysis of axisymmetric boundary layer. The spectrum of the eigenvalues shows that the flow is temporally stable for a given eigenmode at particular Reynolds number. The associated eigenvector gives the two-dimensional spatial structure of the disturbance velocity. The 2d structure of the streamwise disturbance velocity disturbances is attached herewith. If the magnitudes of the disturbances increases in the streamwise direction then can we say it is unstable?

which terminology one should use.

1. Spatially unstable

2. convectively unstable ..however, it is local stability concept.

How one can explain this phenomenon in term of global stability analysis.