Does the choice of the forcing term affect flow statistics in DNS of turbulent channel flow?

Abstract

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.