Streak breakdown instability in pipe Poiseuille flow

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Abstract
This work is devoted to the study of the stability of Hagen–Poiseuille flow or pipe flow. The analysis is focused on the streak breakdown process by which two-dimensional streamwise-independent finite amplitude perturbations transiently modulate the basic flow leading to a profile that contains saddle points and is linearly unstable with respect to very small streamwise-dependent perturbations. This mechanism is one possible route of transition to turbulence in subcritical shear flows. The exploration is carried out for initial disturbances of different finite amplitudes and axial and azimuthal periodicity. This study covers a wide range of Reynolds numbers and the double threshold curve obtained for transition is consistent with experimental observations.