On the competition of anti-lift-up mechanism and Reynolds stress mechanism in Spiral Poiseuille flow

This work is devoted to the studies of optimal perturbation and its transient growth characteristics in Spiral Poiseuille flow (SPF). The Poiseuille number P, representing the dimensionless axial pressure gradient, is varied from 0 to 20,000. The results show that for the axisymmetric case, with the increase of axial shear, the peaks of the amplitudes of azimuthal and radial velocities are both shifted towards the inner cylinder, and a second peak appears near the outer cylinder for both velocity components. Viewing the time evolution of azimuthal shear contribution J(V) and axial shear contribution J(W) to the kinetic energy growth of the optimal perturbation, while P is large enough (P = 10, 000, 20,000), the Reynolds stress mechanism in the meridional plane (r, z) is dominant for the transient growth behavior in SPF relative to anti-lift-up mechanism, which is dominant in the absence of axial flow for co-rotating Taylor-Couette flow with wide gap. For the oblique mode with azimuthal wave number m = 10, which becomes the optimal azimuthal mode over a wide range of azimuthal wave number (m = 0-10) when P is large enough, the peaks of the amplitudes of azimuthal and radial velocities are both shifted towards the outer cylinder, opposite to the axisymmetric case.