This paper presents results from the first fully three-dimensional direct numerical simulations of initially turbulent wakes with net momentum in unstratified and density stratified fluids. The initial conditions contain a super-position of an initially axisymmetric mean streamwise velocity profile plus a spectrally specified fluctuation velocity field with initially incoherent phases to model initial turbulence. To provide evidence in favor of their validity, we compare results from these simulations with previous measurements behind towed bodies in wind tunnels and towing tanks, and also compare with theories of turbulent wakes. Comparisons with laboratory flow experiments provide agreement, both with statistical quantities and vortex structures and evolution. We subsequently investigate open questions by analysis of the fully three-dimensional flow. Coherent vortices in stratified wakes have their origins in the vortex geometry of the mean wake flow, and do not require stratification or coherent seeding in the initial velocity fluctuations. We conclude that the simulations provide a trustworthy and valuable complement to wake research, and that the vortex structures result from a combination of the necessity that vortices form loops and diffusion of vorticity to smooth the loops into rings.

Equilibrium similarity considerations are applied to the axisymmetric turbulent wake, without the arbitrary assumptions of earlier theoretical studies. Two solutions for the turbulent flow are found: one for infinite local Reynolds number which grows spatially as x1/3; and another for small local Reynolds number which grows as x1/2. Both solutions can be dependent on the upstream conditions. Also, the local Reynolds number diminishes with increasing downstream distance, so that even when the initial Reynolds number is large, the flow evolves downstream from one state to the other. Most of the available experimental data are at too low an initial Reynolds number and/or are measured too near the wake generator to provide evidence for the x1/3 solution. New results, however, from a laboratory experiment on a disk wake and direct numerical simulations (DNS) are in excellent agreement with this solution, once the flow has had large enough downstream distance to evolve. Beyond this the ratio of turbulence intensity to centerline velocity deficit is constant, until the flow unlocks itself from this behavior when the local Reynolds number goes below about 500 and the viscous terms become important. When this happens the turbulence intensity ratio falls slowly until the x1/2 region is reached. No experimental data are available far enough downstream to provide unambiguous evidence for the x1/2 solution. The prediction that the flow should evolve into such a state, however, is confirmed by recent DNS results which reach the x1/2 solution at about 200 000 momentum thicknesses downstream. After this the turbulence intensity ratio is again constant, until box-size affects the calculation and the energy decays exponentially.

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