  We seek possible statistical consequences of the way a forcing term is added
to the Navier--Stokes equations in the Direct Numerical Simulation (DNS) of
incompressible channel flow. Simulations driven by constant flow rate, constant
pressure gradient and constant power input are used to build large databases,
and in particular to store the complete temporal trace of the wall-shear stress
for later analysis. As these approaches correspond to different dynamical
systems, it can in principle be envisaged that these differences are reflect by
certain statistics of the turbulent flow field. The instantaneous realizations
of the flow in the various simulations are obviously different, but, as
expected, the usual one-point, one-time statistics do not show any appreciable
difference. However, the PDF for the fluctuations of the streamwise component
of wall friction reveals that the simulation with constant flow rate presents
lower probabilities for extreme events of large positive friction. The low
probability value of such events explains their negligible contribution to the
commonly computed statistics; however, the very existence of a difference in
the PDF demonstrates that the forcing term is not entirely uninfluential. Other
statistics for wall-based quantities (the two components of friction and
pressure) are examined; in particular spatio-temporal autocorrelations show
small differences at large temporal separations, where unfortunately the
residual statistical uncertainty is still of the same order of the observed
difference. Hence we suggest that the specific choice of the forcing term does
not produce important statistical consequences, unless one is interested in the
strongest events of high wall friction, that are underestimated by a simulation
run at constant flow rate.
