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Lagrangian statistics of fluid-particle velocity and acceleration conditioned on fluctuations of dissipation, enstrophy and pseudo-dissipation representing different characteristics of local relative motion are extracted from a direct numerical simulation database of stationary (forced) homogeneous isotropic turbulence. The grid resolution in the simulations is up to 20483, and the Taylor-scale Reynolds number ranges from about 40 to 650, where characteristics of small-scale intermittency in the Eulerian flow field are well developed. A key joint statistic of the conditioning variables is the dissipation-enstrophy cross-correlation, which is asymmetric, but becomes less so at high Reynolds number. Conditional velocity autocorrelations are consistent with rapid changes in the velocity of fluid particles moving in regions of large velocity gradients. Examination of statistics conditioned upon enstrophy, especially in a local coordinate frame moving with the vorticity vector, and of the centripetal acceleration suggests the presence of vortex-trapping effects which persist for several Kolmogorov time scales. Further results on acceleration statistics and joint velocity-acceleration autocorrelations are also presented to help characterize in detail the properties of a joint stochastic process of velocity, acceleration and the pseudo-dissipation. Together with recent work on Eulerian conditional acceleration and Reynolds-number dependence of basic Lagrangian quantities, the present results are directly useful for the development of a new stochastic model formulated to account for intermittency and Reynolds-number effects as described in detail in a companion paper. [ABSTRACT FROM AUTHOR]

The modelling of fluid-particle acceleration in homogeneous isotropic turbulence in terms of stochastic models for the Lagrangian velocity, acceleration and a dissipation rate variable is considered. The basis for the Reynolds model (A. M. Reynolds, Phys. Rev. Lett.vol. 91, 2003, 084503) is reviewed and examined by reference to direct numerical simulations (DNS) of isotropic turbulence at Taylor-scale Reynolds number (R?) up to about 650. In particular, we show DNS data that support stochastic modelling of the logarithm of pseudo-dissipation as an Ornstein?Uhlenbeck process and reveal non-Gaussianity of the acceleration conditioned on fluctuations of the pseudo-dissipation rate. The DNS data are used to construct a new stochastic model that is exactly consistent with Gaussian velocity and conditionally cubic-Gaussian acceleration statistics. This model captures the effects of small-scale intermittency on acceleration and the conditional dependence of acceleration on pseudo-dissipation (which differs from that predicted by the refined Kolmogorov hypotheses). Non-Gaussianity of the conditionally standardized acceleration probability density function (PDF) is accounted for in terms of model nonlinearity. The large-time behaviour of the new model is that of a velocity-dissipation model that can be matched with DNS data for conditional second-order Lagrangian velocity structure functions. As a result, the diffusion coefficient for the new model incorporates two-time information and its Reynolds-number dependence as observed in DNS. The resulting model predictions for conditional and unconditional velocity autocorrelations and time scales are shown to be in very good agreement with DNS. [ABSTRACT FROM AUTHOR]

We examine available data from experiment and recent numerical simulations to explore the supposition that the scalar dissipation rate in turbulence becomes independent of the fluid viscosity when the viscosity is small and of scalar diffusivity when the diffusivity is small. The data are interpreted in the context of semi-empirical spectral theory of Obukhov and Corrsin when the Schmidt number, $\hbox{\it Sc}$, is below unity, and of Batchelor's theory when $\hbox{\it Sc}$ is above unity. Practical limits in terms of the Taylor-microscale Reynolds number, $R_\lambda$, as well as $\hbox{\it Sc}$, are deduced for scalar dissipation to become sensibly independent of molecular properties. In particular, we show that such an asymptotic state is reached if $R_\lambda \hbox{\it Sc}^{1/2}\,{\gg}\,1$ for $\hbox{\it Sc} \,{<}\, 1$, and if $\ln(\hbox{\it Sc})/R_\lambda\,{\ll}\,1$ for $\hbox{\it Sc} \,{>}\,1$. [ABSTRACT FROM AUTHOR]

We explore very fine scales of scalar dissipation in turbulent mixing, below Kolmogorov and around Batchelor scales, by performing direct numerical simulations at much finer grid resolution than was usually adopted in the past. We consider the resolution in terms of a local fluctuating Batchelor scale and study the effects on the tails of the probability density function and multifractal properties of the scalar dissipation. The origin and importance of these very fine-scale fluctuations are discussed. One conclusion is that they are unlikely to be related to the most intense dissipation events. [ABSTRACT FROM AUTHOR]

A new model for Lagrangian particle-pair separation in turbulent flows is developed and compared with data from direct numerical simulations (DNS) of isotropic turbulence. The model formulation emphasizes (i) non-Gaussian behaviour in Eulerian and Lagrangian statistics, (ii) the occurrence of large separation velocities, (iii) the role of straining and streaming flow structure as recognized in kinematic simulations of turbulence, and (iv) the role of conditionally averaged accelerations in stochastic modelling of turbulent relative dispersion. Previous stochastic models of relative dispersion have produced unrealistic behaviour, particularly in the dissipation subrange where viscous effects are important, which have led to questions on the adequacy of stochastic modelling. However, this failure can now be recognized as inadequate detail in formulation, which is explained and rectified in this paper. The model is quasi-one-dimensional in nature, and is focused on the statistics of particle-pair separation distance and its rate of change, referred to as the separation speed. Detailed comparisons are presented at several Reynolds numbers using the DNS database reported in a companion paper (Part 1). Up to fourth-order moments for these quantities are examined, as well as the separation-distance probability density function, which is discussed in the context of recent claims of Richardson scaling in the literature. The model is able to account for the spatial representation of straining regions as well as incompressibility of the flow, and is shown to reproduce strong non-Gaussianity and intermittency in the Lagrangian separation statistics observed in DNS. Comparisons with recent physical experiments are also remarkably consistent. This work demonstrates that stochastic models when properly formulated are effective and efficient representations of the dispersion process and this general class of models therefore possess great utility for calculations of both one-particle and two-particle dispersion. The techniques developed in this paper will facilitate such general model development. [ABSTRACT FROM AUTHOR]

The relative dispersion of fluid particle pairs in isotropic turbulence is studied using direct numerical simulation, in greater detail and covering a wider Reynolds number range than previously reported. A primary motivation is to provide an important resource for stochastic modelling incorporating information on Reynolds-number dependence. Detailed results are obtained for particle-pair initial separations from less than one Kolmogorov length scale to larger than one integral length scale, and for Taylor-scale Reynolds numbers from about 38 to 230. Attention is given to several sources of uncertainty, including sample size requirements, value of the one-particle Lagrangian Kolmogorov constant, and the temporal variability of space-averaged quantities in statistically stationary turbulence. Relative dispersion is analysed in terms of the evolution of the magnitude and angular orientation of the two-particle separation vector. Early-time statistics are consistent with the Eulerian spatial structure of the flow, whereas the large-time behaviour is consistent with particle pairs far apart moving independently. However, at intermediate times of order several Kolmogorov time scales, and especially for small initial separation and higher Reynolds numbers, both the separation distance and its rate of change (called the separation speed) are highly intermittent, with flatness factors much higher than those of Eulerian velocity differences in space. This strong intermittency is a consequence of relative dispersion being affected by a wide range of length scales in the turbulent flow as some particle pairs drift relatively far apart. Numerical evidence shows that substantial dispersion occurs in the plane orthogonal to the initial separation vector, which implies that the orientation of this vector has, especially for small initial separation, only limited importance. [ABSTRACT FROM AUTHOR]