Up until recently direct numerical simulation (DNS) studies involving round turbulent jets have focused on first and second order statistics and vortical behavior near the source of the jet. The third order statistics necessary to compute the turbulent kinetic energy and Reynolds stress transport equations have been examined using LES studies. However, further examination with DNS is important as, on the subgrid scale, LES uses models for Reynolds stress. In this study a DNS of a turbulent free jet with a Reynolds number equal to ReJ = 2000 is computed using a second order accurate, time splitting finite volume scheme. First, second, and third order statistics are compared with previous experimental and numerical studies. All terms of the turbulent kinetic energy balance are calculated directly. The results are compared to experimental studies such as those of Hussein et al. [“Velocity measurements in a high-Reynolds-number, momentum-conserving, axisymmetric, turbulent jet,” J. Fluid Mech. 258, 31–75 (1994)], Panchapakesan and Lumley [“Turbulence measurements in axisymmetric jets of air and helium. Part 1. Air jet,” J. Fluid Mech. 246, 197–233 (1993)], and others. The assumptions made by the various experimental studies in order to solve the dissipation and pressure diffusion terms are discussed and examined using the data from the current study. The Reynolds stress transport equations are also calculated and discussed. Vortical structures are visualized by the λci method and discussed along with entrainment of ambient fluid into the jet. The one dimensional energy spectra in the azimuthal direction are calculated directly and are also discussed.

Plumes occur in many natural and industrial settings, such as chimney smoke, volcanic eruptions and deep water oil spills. A plume function, $\unicode[STIX]{x1D6E4}$, is used to characterize plumes and jets. The far-field behaviour of these flows has been studied in great detail while the near-field behaviour has not quite received the same attention. We examine near-field phenomena such as radial constriction, termed necking, and vortex structure formations with new high resolution direct numerical simulations. Four lazy plumes with increasing values of the source plume parameter, $\unicode[STIX]{x1D6E4}_{0}$, are simulated. We study the evolution of entrainment and the plume function. The original assumptions, that Reynolds stresses dominate viscous shear stresses, do not hold for lazy plumes in the near field. Due to this, a deviation from self-similarity occurs initially and is corrected by a large entrainment coefficient caused by vortex stretching and compression. After correcting for the virtual origin, comparison between theory and simulations shows a monotonic decay of $\unicode[STIX]{x1D6E4}$ towards pure plume behaviour. The entrainment coefficient asymptotes to a widely accepted constant value for plumes.

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In this study, direct numerical simulations of a turbulent free jet (Re = 2000), a lazy plume ( √ Gr = 2000), and a forced plume (Re = 1684, Ri = 0.025) are compared. The evolution of the various fluxes and the so-called source parameter, , are examined as a function of distance from the source. The first-, second-, and third-order statistics of the flows are calculated and discussed. The radial profiles of such statistics, as well as that of the turbulent kinetic energy balance and other second-order transport equations are examined at two axial distances, one axial distance before the flows have adjusted to their similarity solution, and the other beyond the similarity adjustment length scale. Vortical structures are visualised and discussed along with entrainment. The source term was not found to monotonically decrease with axial distance from the source as predicted by past researchers. While the mean flow and turbulent velocity statistics of the simulated lazy and forced plumes took on similar behaviour far from the sources turbulent statistics which involve buoyancy did not.