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The physical mechanisms by which the Reynolds shear stress is produced from dynamically evolving vortical structures in the wall region of a direct numerical simulation of turbulent channel flow are explored. The complete set of quasistreamwise vortices are systematically located and tracked through the flow by the locus of the points of intersection of their centres of rotation with the (y , z) numerical grid planes. This approach assures positive identification of vortices of widely differing strengths, including those whose amplitude changes significantly in time. The process of vortex regeneration, and the means by which vortices grow, distort and interact over time are noted. Ensembles of particle paths arriving on fixed planes in the flow are used to represent the physical processes of displacement and acceleration transport (Bernard & Handler 1990a) from which the Reynolds stress is produced. By interweaving the most dynamically significant of the particle paths with the evolving vortical structures, the dynamical role of the vortices in producing Reynolds stress is exposed. This is found to include ejections of low-speed fluid particles by convecting structures and the acceleration and deceleration of fluid particles in the cores of vortices. Sweep dominated Reynolds stress close to the wall appears to be a manifestation of the regeneration process by which new vortices are created in the flow.

The assumption of self-preservation permits an analytical determination of the energy decay in isotropic turbulence. Batchelor (1948), who was the first to carry out a detailed study of this problem, based his analysis on the assumption that the Loitsianskii integral is a dynamic invariant – a widely accepted hypothesis that was later discovered to be invalid. Nonetheless, it appears that the self-preserving isotropic decay problem has never been reinvestigated in depth subsequent to this earlier work. In the present paper such an analysis is carried out, yielding a much more complete picture of self-preserving isotropic turbulence. It is proven rigorously that complete self-preserving isotropic turbulence admits two general types of asymptotic solutions: one where the turbulent kinetic energy K ∼ t−1 and one where K ∼ t−α with an exponent α > 1 that is determined explicitly by the initial conditions. By a fixed-point analysis and numerical integration of the exact one-point equations, it is demonstrated that the K ∼ t−1 power law decay is the asymptotically consistent high-Reynolds-number solution; the K ∼ t−α decay law is only achieved in the limit as t → ∞ and the turbulence Reynolds number Rt vanishes. Arguments are provided which indicate that a t−1 power law decay is the asymptotic state toward which a complete self-preserving isotropic turbulence is driven at high Reynolds numbers in order to resolve an O(R1½) imbalance between vortex stretching and viscous diffusion. Unlike in previous studies, the asymptotic approach to a complete self-preserving state is investigated which uncovers some surprising results.

The nature of the momentum transport processes responsible for the Reynolds shear stress is investigated using several ensembles of fluid particle paths obtained from a direct numerical simulation of turbulent channel flow. It is found that the Reynolds stress can be viewed as arising from two fundamentally different mechanisms. The more significant entails transport in the manner described by Prandtl in which momentum is carried unchanged from one point to another by the random displacement of fluid particles. One-point models, such as the gradient law are found to be inherently unsuitable for representing this process. However, a potentially useful non-local approximation to displacement transport, depending on the global distribution of the mean velocity gradient, may be developed as a natural consequence of its definition. A second important transport mechanism involves fluid particles experiencing systematic accelerations and decelerations. Close to the wall this results in a reduction in Reynolds stress due to the slowing of sweep-type motions. Further away Reynolds stress is produced in spiralling motions, where particles accelerate or decelerate while changing direction. Both transport mechanisms appear to be closely associated with the dynamics of vortical structures in the wall region.

The spatially developing, unforced, turbulent mixing layer is simulated via a grid-free vortex method. Vortex filaments composed of straight tubes are used as the computational element with new vortex tubes produced as the filaments stretch. A loop removal algorithm serves as a de facto subgrid model limiting growth in the number of elements to practical levels. The computations are high resolution and well resolve the mixing layer from its unforced inception as a laminar flow through transition to a self-similar turbulent state. Mean velocity statistics including growth rate and Reynolds stresses agree well with experimental values. The vortical composition of the transition region is found to develop in one or another of the modes that have been documented in previous experiments and computations: roller/rib vortices, the chain-link fence structure in a diamond shaped pattern, and somewhat oblique roller/rib configuration with partial pairing. Evidently, small perturbative effects that are intrinsic to the numerical scheme influence which transitional mode appears locally in the simulations. The computations offer a clear view of the downstream dissolution of the identifiable structure into turbulence in the late transition and the salient aspects of the process are noted. Nomenclature h = maximum vortex tube length L = downstream boundary l = similarity length scale N = number of vortex tubes R x = boundary layer Reynolds number s i = axial vector along the ith vortex tube U in = inlet velocity U p x; t = potential velocity U t , U b = velocities at top and bottom of shear layer x, y, z = streamwise, vertical, and spanwise coordinates x i = center of ith vortex tube x 1 i , x 2 i = beginning and end of ith vortex tube i = circulation of ith vortex tube " = vertical offset of downstream vortex sheet = similarity variable = momentum thickness = smoothing parameter = smoothing function

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