Non-modal instability of annular Poiseuille-Couette flow

A non-modal stability analysis is presented for annular Poiseuille-Couette flow (APCF) which serves to complement existing linear and nonlinear stability studies. Modal linear stability analyses indicate a stabilizing trend for increasing inner cylinder velocity V, though this is at odds with experimental studies of transition such as Shands et al. (1980) who find that increasing V is destabilizing. Using the maximum achievable energy growth available at a given parameter regime as a measure of the non-modal stability of the flow, we also find that APCF is destabilized with increasing inner cylinder velocity V. Thus we conjecture that the transition mechanism in APCF is akin to that of the canonical subcritical shear flows, where linear instability of the base flow is not relevant.