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Laminar flows through pipes driven at steady, pulsatile or oscillatory ratesundergo a sub-critical transition to turbulence. We carry out an extensivelinear non-modal stability analysis of these flows and show that forsufficiently high pulsation amplitudes the stream-wise vortices of the classiclift-up mechanism are outperformed by helical disturbances exhibiting anOrr-like mechanism. In oscillatory flow, the energy amplification dependssolely on the Reynolds number based on the Stokes-layer thickness and forsufficiently high oscillation frequency and Reynolds number, axisymmetricdisturbances dominate. In the high-frequency limit, these axisymmetricdisturbances are exactly similar to those recently identified by Biau (2016)for oscillatory flow over a flat plate. In all regimes of pulsatile andoscillatory pipe flow, the optimal helical and axisymmetric disturbances aretriggered in the deceleration phase and reach their peaks in typically lessthan a period. Their maximum energy gain scales exponentially with Reynoldsnumber of the oscillatory flow component. Our numerical computations unveil aplausible mechanism for the turbulence observed experimentally in pulsatile andoscillatory pipe flow.

Non-modal transient growth of disturbances in pulsatile and oscillatory pipe flow