A numerical investigation on the effect of the inflow conditions on the self-similar region of a round jet

In this paper we consider the direct numerical simulation (DNS) of a spatially developing free round jet at low Reynolds numbers. Simulation of a spatially evolving flow such as the jet requires boundary conditions, which allow entrainment into the turbulent flow across the lateral boundaries of the computational domain. The boundary conditions which satisfy this requirement are so-called traction free boundary conditions. After showing that these boundary conditions lead to a correct behavior of the velocity near the lateral boundary of the jet, we will consider the DNS of the jet flow at a Reynolds number of ${\text{2.4×10}}^3$ and compare the results with experimental data obtained by Hussein et al. [J. Fluid Mech. 258, 31 (1994)] and by Panchapakesan and Lumley [J. Fluid Mech. 246, 197 (1993)]. The results of our numerical simulations agree very well with the experimental data. Next we use the DNS to investigate the influence of the shape of the velocity profile at the jet orifice on the self-similarity scaling for the far-field velocity and shear stress profile. Evidence is presented in support of the suggestion by George [Advances in Turbulence (Springer, New York, 1989)] that the details of self-similarity depend on the initial conditions. This fact implies that there may exist no universally valid similarity scaling for the free jet.