Non-modal instability of annular Poiseuille–Couette flow

Abstract 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.