  We show that the energy required by a turbulent flow to displace a given
amount of fluid through a straight duct in a given time interval can be reduced
by modulating in time the pumping power. The control strategy is hybrid: it is
passive, as it requires neither a control system nor control energy, but it
manipulates how pumping energy is delivered to the system (as in active
techniques) to increase the pumping efficiency. Our control employs a
temporally periodic pumping pattern, where a short and intense acceleration (in
which the pumping system is on) followed by a longer deceleration (in which the
pumping system is off) makes the flow alternately visit a quasi-laminar and a
turbulent state. The computational study is for a plane channel flow, and
employs direct numerical simulations, which present specific computational
challenges, for example the highly varying instantaneous value of the Reynolds
number, and the importance of discretisation effects. Particular care is
devoted to a meaningful definition of drag reduction in the present context.
The ability of the forcing to yield significant savings is demonstrated. Since
only a small portion of the parameter space is investigated, the best
performance of the control technique remains to be assessed.
