Pipe flow transition threshold following localized impulsive perturbations

A numerical study of the destabilizing effects of localized impulsive perturbations in pressure-driven Hagen-Poiseuille or pipe flow is presented. The numerics intend to ellucidate the intrinsic mechanisms of subcritical transition to turbulence in pipe flow by reproducing very recent experimental explorations carried out by Hof, Juel, and Mullin [Phys. Rev. Lett. 91, 244502 (2003)], concluding that the minimum amplitude of a perturbation required to cause transition scales as the inverse of the Reynolds number, i.e., O(Re−1). The numerical model simulates the experimental disturbance generator based on impulsive injection of fluid through six slits azimuthally equispaced on a perimeter around the pipe. This is accomplished by introducing a local time-dependent impulsive volume force term in the Navier-Stokes equations for the perturbation velocity field, fulfilling incompressibility constraints. A comprehensive exploration of the critical amplitudes that trigger transition as a function of the injection duration is carried out. It is concluded, in agreement with experiments, that injections lasting longer than Δtinj≃24 advective time units do not remarkably decrease the critical amplitude of transition. Threshold amplitudes for long enough injections are then computed within the range Re∊[2000,14125]. For Re≳4000 the numerical results agree with the experiments. However, for Re≲2800, neat transitions are very difficult to obtain, being impossible to provide an accurate value of the critical amplitude. The apparent disagreement with the sound regular slope of the experimental threshold is explained in terms of the differences between constant mass-flux versus pressure-driven pipe flows.