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We consider local vortex identification in turbulent flows using the two kinematic parameter framework of Chakraborty, Balachandar & Adrian (2005) (hereafter referred to as CBA05). The inter-relationships between the various local criteria are summarized and the notion of ‘equivalent thresholds’ is applied to two canonical turbulent flows: sphere wake and channel flow. Remarkably similar vortex structures are extracted using the ‘equivalent thresholds’.

In isotropic turbulence, stagnation points form a fractal multiple-scale network in space such that their number density = − (/) where is a dimensionless constant, / is the inner to outer length-scale ratio and the fractal dimension is given by + 2/ = 3; is the dimensionality of the flow and is the exponent of the energy spectrum. On the other hand, the statistical persistence of stagnation points is defined in terms of the statistics of stagnation point velocities, and we show that, on average, stagnation points stop moving as the Reynolds number tends to infinity in the frame where the mean flow is zero.

A new approach to particle pair diffusion in self-similar turbulence is developed in terms of coherent structures, i.e. coherent vortices and streamlines associated with them. The well-known Richardson equation can be re-derived by a simple model proposed by this approach. The model and its implications are verified by the use of direct-numerical simulation of pair diffusion in the inverse energy cascade regime of two-dimensional turbulence.

Dynamical properties of passive particle pairs are investigated in two-dimensional free convection turbulence by direct numerical simulation. In terms of the exittime statistics, it is confirmed that the growth of relative separations () is consistent with the prediction of the Bolgiano-Obukhov scaling in the inertial range, 〈()〉 ∝ . Furthermore, by looking into the probability density function (PDF) of exit-time, motions of relative separations of particle pairs are classi- fied into two types: ballistic and diffusive motions, both of which satisfy the Bolgiano-Obukhov scaling. The probability density function of exit-time of diffusively separating motions is described by Richardson’s diffusion equation, and that of ballistically separating motions corresponds to the PDF of the Lagrangian velocity increment. Our results also indicate that the PDF of the Lagrangian velocity increment relates to that of the stretching rate of a relative separation in the dissipation range.

The purpose of this study is to elucidate the relation between a growth of twoparticle distance and the fine-scale structures of turbulence by the three-dimensional direct numerical simulation. It is shown that the Lagrangian bursts of particlepair occur in the straining stagnation region, whereΔ < 0 (here,Δ = (/3)+ (/2) with and being the 2nd and 3rd invariance of the velocity gradient tensor). The scaling law of 〈(Δ)〉~τ γ (Δ and τ are the increment of separation distance and the diffusion time, respectively) has been investigated. It is found that the relation γ = 6/ is useful, where is the power exponent of ≈−(/η) ( and η are the integral length scale and Kolmogorov microscale, respectively; is the number density of straining stagnation points; is a dimensionless number). It is also shown that the trajectories of particlepairs in the (,) space are useful to recognize the fine-scale structure bearing the Lagrangian burst of particle-pair.

We consider a simple model of transport of a passive scalar around a coherent vortex at distances much larger than its size but much smaller than the distance to its nearest neighbours. The vortex is approximated by a point vortex with circulation Γ, the strain rate has harmonic time-dependence, and the principal axes rotate with constant angular velocity.

Pressure fluctuation is measured by using a condenser microphone and piezoresistive transducer. In order to confirm the experimental accuracy, measured data are compared with direct numerical simulation. This basic test encourages us to study small-scale statistics from the standpoint of Kolmogorov universal scaling. The power-law exponent and proportional constant of normalized pressure spectrum are discussed. The clear power law with scaling exponent –7/3 is confirmed in the range of λ ≥ 600. These Reynolds numbers are much larger than those in velocity fluctuation for achieving the Kolmogorov scaling. The spectral constant is not universal but depends on Reynolds number.

Resolution requirements of direct numerical simulation (DNS) for passive scalar advected by homogeneous turbulence are numerically investigated. We examine the effects of dissipation intermittency on the small-scale statistics by performing DNSs with various spatial resolutions at the fixed Reynolds number λ ≃ 180.

A new similarity theory is proposed for decaying two-dimensional Navier–Stokes turbulence, including the viscous range, which encompasses all Reynolds numbers and various degrees of hyperviscosity. In the high Reynolds number limit where the energy is invariant, the theory predicts the enstrophy decay law ~ −, where is time and is the degree of hyperviscosity ( = 1 is the usual Laplacian viscosity). This is at variance with the vortex scaling theory of Carnevale . (1991). However it is consistent with previously published numerical simulations using the usual viscosity. That enstrophy decay in the high Reynolds number limit may depend on the degree of hyperviscosity suggests that the inviscid limit is singular. Indeed, our similarity theory based on the inviscid equations predicts an upscale energy flux for all wavenumbers, in violation of basic physical constraints. This may be part of the reason for the failure of Batchelor’s (1969) decay law ~ , ~ −.

This paper presents a new grid-free type of redistribution model for turbulent flow analysis, in which each vortex particle is redistributed into some elements in accordance with its stretching rate. The model is applied to an inclined collision of two vortex rings. Energy spectra are analyzed and compared with existing DNS data and results of experiments by Saddoughi & Veeravalli (1994). The energy cascade and dissipation process are reasonably simulated. In addition, the LES model proposed by Kiya & Izawa (1999) is applied to the proposed redistribution model. The results show that the analyzed energy spectra are in close agreement with the existing DNS data up to high wave number region.