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The analysis of the importance of the forces that act over an ensemble of particles in a turbulent field has been carried out by using direct numerical simulation for a wide range of density ratios (2.65<ρ<2650). It has been observed that, compared to the Stokes drag, the added mass is always negligible, the pressure drag is relevant for density ratios O(1), and the Basset force is appreciable for the whole range investigated. However, the effect of these forces on the particle dispersion is about 1% for ρ∼1 as well as for large density ratios.

In this study, the effects of small-scale velocity fluctuations on the motion of tracer particles is investigated by releasing particles in a turbulent channel flow at Reτ=175, and following their motion in time. Two types of numerical experiments were carried out: first, the Eulerian velocity field was evaluated by the direct numerical simulation (DNS) and the particles were advanced in time using the resolved and several filtered velocity fields to study the effect of the subgrid-scale velocity fluctuations on particle motion without the influence of modeling errors. In the second stage, the particle-motion study was performed using independent DNS and large-eddy simulations (LES), thus including the effect of interpolation and subgrid-scale stress modeling errors on the dispersion statistics. At this Reynolds number the small scales were found to have a limited effect on the statistics examined (one-particle dispersion, one-particle velocity autocorrelation, Lagrangian integral time scale, turbulent diffusivity, and two-particles rms dispersion). Only when a significant percentage of the energy was removed from the velocity field some differences were observed between filtered and unfiltered data (especially near the wall). It was found that when the dynamic eddy-viscosity model was employed, modeling errors did not affect the results as much as the filtering itself; the use of the Smagorinsky model, on the other hand, gave inaccurate results. Additional computations for finite-inertia particles have shown that these results represent a conservative estimate, in the sense that actual particles with inertia are less sensitive than the tracer particles examined in the first part of the investigation, and that LES provides improved results when particles with inertia are used.

The aim of this paper is to analyze the statistical properties of solute concentration in natural aquifers as sampled in observation wells, having a small diameter in comparison with the characteristic size of the heterogeneity in hydraulic properties. The analysis, in Langragian framework, takes advantage of the ''reverse formulation'', where, instead of considering the destination of the injected particles, the origin of the particle being sampled is sought. In the case of small values of the log-conductivity variance ' 2 Y , it allows the derivation of an analytical expression for concentration mean, variance and pdf, while for aquifer characterized by high value in ' 2 Y , a numerical analysis based on a Monte Carlo approach using a reverse scheme is developed and applied for values of ' 2 Y up to 2. In this case, the use of a Beta function to fit the concentration pdf proves valid for practical applications. The comparison between the numerical and the analytical results defines the range of validity of the analytical ones. The relative role of large-scale dispersion processes and pore-scale effects is analyzed in terms of global variance in order to point out limits and accuracy of the Eulerian scheme in comparison with the Lagrangian one.

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