Optimal disturbances in swirling flows

The mechanism of optimal disturbances, which are composed of both growing and decaying modes, in swirling flows (with an axial velocity component) is explored. Two characterizing cases are considered: stationary disturbances in rotating pipe flow and temporal disturbances in a trailing vortex. It is found that in both cases the optimal transient growth amplification in short times or distances is much larger than the known exponential mode amplification., Unlike the flow in a nonrotating pipe, in which the amplification is based on the existence of a least stable pair of modes and the cancellation of their associated initial axial velocity components, when a rotation is added to the flow the optimal amplification mechanism is based on the cancellation, at the initial state, of the most unstable mode velocity components by many decaying modes. For the trailing vortex, the transient growth mechanism seems to be based on the contribution of the continuous spectrum, and the optimal transient growth is not significantly affected by the existence of swirl in the flow. Evidently, when the flow is unstable with respect to discrete exponential modes, decaying modes still may have a substantial contribution for the linear stability of the flow in short times or distances, assuming the existence of a particular initial disturbance.