Non-modal instability of core-annular flow

The classical problem of the stability of Core-Annular Flow (CAF) in pipes is reconsidered from the point of view of the linear non-modal analysis. An accurate Chebyshev pseudospectral code in polar coordinates has been developed in order to separately discretize the two phases of the flow. Transient amplifications of the energy of three-dimensional perturbations are computed by taking into account the effects of viscosity and volume ratios between the two liquids, as well as of Reynolds number and surface tension parameter. A detailed investigation is conducted in wide regions of the parameters space and the occurrence of remarkable transient growths is found for asymptotically both stable and unstable configurations. Optimal perturbations (i.e. giving the maximum energy amplification) are determined and their structure during the unsteady evolution is analyzed. It is shown that in conditions in which axisymmetric modes are expected to constitute the most dangerous exponential disturbances, spiral perturbations can provide higher levels of transient energy amplification. Amplification levels and growth rates of modal and non-modal mechanisms are compared in order to analyze more in depth previous disagreements between experiments and modal theory.