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The spatial distribution of intense structures in isotropic turbulence is studied from numerical and experimental data. Box-counting of the intense vorticity and strain rate sets gives evidence of a strong clustering at intermediate scales, from which a possible fractal dimension can be defined. Algebraically distributed free intervals between intense velocity derivative from experimental time series confirms this self-similar clustering at larger Reynolds numbers, but without further specifying its dimensionality.

A process for formation of the stretched spiral vortex was investigated using the DNS data of homogeneous turbulence. It was shown that vortex tube was generated not by a rolling up of single vortex sheet but through an interaction of dual sheets. Depending on the alignment of vorticity vectors on vortex tube and vortex sheets which emanate from vortex tube, three modes of configuration were shown to exist. Frequency of appearance of three modes and its implication for turbulence generation was discussed in isotropic and sheared flows.

Local topological and statistical measures of enstrophy and strain-rate structures are compared with global statistics to determine the effects of mean shear on the interactions between fluctuating vorticity and strain rate in DNS of transitioning isotropic to shear turbulence. “Structures” are extracted as concentrations of turbulence fluctuations, allowing quantitative with visual analysis. We find that mean shear adjusts the alignment of fluctuating vorticity and strain rate so as to (1) enhance global and local alignments between vorticity and the second eigenvector of fluctuating strain rate, (2) two-dimensionalize fluctuating strain rate, and (3) align the compressional components of fluctuating and mean strain rate. Shear causes amalgamation of structures and suppresses strain-rate structures between enstrophy structures. Shear enhances “passive” strain-rate fluctuations—strain rate kinematically induced by local vorticity concentrations with negligible enstrophy production—relative to “active,” or vorticity-generating, strain-rate fluctuations. Enstrophy structures separate into “active” and “passive” based on the second eigenvalue of fluctuating strain rate. The time evolution of a shearinduced hairpin enstrophy structure was analyzed. The structure originated in the initial isotropic state as a vortex sheet, evolved into a vortex tube during a transitional period, and developed into a well-defined horseshoe vortex in the shear-dominated state.

The interaction between a columnar vortex and external turbulence is investigated numerically. As columnar vortices, the Lamb-Oseen vortex and the -vortex are used. The columnar vortex is immersed in an initially isotropic homogeneous turbulence field, which itself is produced by a direct numerical simulation of decaying turbulence. Using visualization techniques, we investigate the formation of inhomogeneous fine turbulent eddies around the columnar vortex, vortex-core deformations and the dynamical evolution in the passive scalar field.

DNSs of turbulent channel flows with one rough wall and one smooth wall are presented to show how the vorticity field depends on the shape and orientation of the roughness elements. The passive scalar is also evaluated. The high correlation coefficients between vorticity and scalar gradients, in the wall layer, emphasize that in all cases flow visualizations can be used in a laboratory to have a qualitative picture of the modifications of the high- and low-speed streaks. Joint probability density function between vorticity and scalar gradients show how the bursting events affect the scalar distribution.

Models for the viscous and buffer layers over smooth walls are reviewed. It is shown that there is a family of numerically-exact nonlinear structures which account for about half of the energy production and dissipation in the wall layer. The other half can be modelled by the unsteady bursting of those structures. Many of the best-known characteristics of the wall layer, such as the lateral spacing among the streaks, are well predicted by these models. The limitations of minimal models are then discussed, and it is noted that a better approximation is to represent the velocity streaks as ‘semi-infinite’ wakes of the wall-normal velocity structures, both in the buffer and in the logarithmic layer. The consequences of this characterization on the causal relation between bursting structures are also briefly discussed.

Coherent fine scale eddies (CFSEs) play an important role in generating streak structures and Reynolds shear stress not only in the near-wall region but also in the logarithmic region. The diameter and maximum azimuthal velocity of the CFSEs in the near-wall, logarithmic and wake regions can be scaled by Kolmogorov length η and velocity . The most expected diameter and maximum azimuthal velocity of the CFSEs are about 10 η and 2.0 in the near-wall region ( < 40). In the logarithmic region (40 < < 200 ~ 300), they become about 8.5 η and 1.7, respectively. These features are independent of Reynolds number up to Reτ = 1270. Large-scale structure in turbulent channel flows is organized by the CFSEs in the logarithmic region, which contribute to the streamwise velocity deficit (i.e. low-momentum region). By visualizing spatial distributions of the CFSE axes, it is made clear that the probability that the CFSEs exist in lowmomentum regions is higher than that existing in high-momentum regions. The low-momentum regions of the logarithmic layer are composed of the CFSEs which have narrower diameter and stronger azimuthal velocity.

Direct numerical simulation of a turbulent channel flow in a periodic domain of relatively wide spanwise extent, but minimal streamwise length, is carried out at Reynolds number Reτ = 349. The large-scale structures previously observed in studies of turbulent channel flow using huge computational domains are also shown to exist even in the streamwise-minimal channel of the present work. In the system, it is also clearly observed how the large-scale structures and the nearwall structures affect each other. While the collective behaviour of near-wall structures enhances a large-scale structure, the resulting large-scale structure in turn activates the generation and drift of the latter. Hence near-wall and largescale structures interact in a co-supporting cycle.

We investigate unstable periodic motion embedded in isotropic turbulence with high symmetry. Several orbits of different period are continued from the regime of weak turbulence into developed turbulence. The orbits of short period diverge from the turbulent state as the Reynolds number increases but the orbit of longest period we analysed, about two to three eddy-turnover times, represents several average values of the turbulence well. In particular we measure the energy dissipation rate and the largest Lyapunov exponent as a function of the viscosity. At the largest micro-scale Reynolds number attained in the continuation we compare the energy spectra of periodic and turbulent motion. The results suggest that periodic motion of a sufficiently long period can represent turbulence in a statistical sense.

The most elementary structures of turbulence, i.e., vortex tubes, are studied using laboratory velocity data for boundary layers with Reynolds numbersReλ = 295– 1258. We conduct conditional averaging for enhancements of a small-scale velocity increment and obtain the typical velocity profile for vortex tubes. Their radii are of the order of the Kolmogorov length. Their circulation velocities are of the order of the root-mean-square velocity fluctuation. These properties are independent of the Reynolds number and are hence expected to be universal.