  Recent experimental observations (Kuehnen et al., 2018) have shown that
flattening a turbulent streamwise velocity profile in pipe flow destabilises
the turbulence so that the flow relaminarises. We show that a similar
phenomenon exists for laminar pipe flow profiles in the sense that the
nonlinear stability of the laminar state is enhanced as the profile becomes
more flattened. Significant drag reduction is also observed for the turbulent
flow when triggered by sufficiently large disturbances. The flattening is
produced by an artificial body force designed to mimick a baffle used in the
experiments of Kuehnen et al. (2018) and the nonlinear stability measured by
the size of the energy of the initial perturbations needed to trigger
transition. In order to make the latter computation more efficient, we examine
how indicative the minimal seed for transition is in measuring transition
thresholds. We first show that the minimal seed is relatively robust to base
profile changes and spectral filtering. We then compare the (unforced)
transition behaviour of the minimal seed with several forms of randomised
initial conditions in the range of Reynolds numbers Re=2400 to 10000 and find
that the energy of the minimal seed after the Orr and oblique phases of its
evolution is close to that of a localised random disturbance. In this sense,
the minimal seed at the end of the oblique phase can be regarded as a good
proxy for typical disturbances (here taken to be the localised random ones) and
is thus used as initial condition in the simulations with the body force. The
enhanced nonlinear stability and drag reduction predicted in the present study
are an encouraging first step in modelling the experiments of Kuehnen et al.
and should motivate future developments to fully exploit the benefits of this
promising direction for flow control.
