We describe a new high-resolution sampling technique which can be used to measure concentration fluctuations simultaneously at several points in space. The technique has been used to measure the probability distribution function as a function of the detector location relative to a continuous and steady source. Results are compared to previous experiments and theoretical predictions. The spectra of the concentration fluctuations are analyzed and their behaviour as a function of downwind distance from the source is described.

Characterization of concentration fluctuations of a surface plume in a neutral boundary layer

A lagrangian model for solid particles in turbulent flows

The relative velocity of two fluid particles in homogeneous and stationary turbulence is considered. Looking for reduced dynamics of turbulent dispersion, we apply the nonlinear Mori–Zwanzig projector method to the Navier–Stokes equations. The projector method decomposes the Lagrangian acceleration into a conditionally averaged part and a random force. The result is an exact generalized Langevin equation for the Lagrangian velocity differences accounting for the exact equation of the Eulerian probability density. From the generalized Langevin equation, we obtain a stochastic model of relative dispersion by stochastic estimation of conditional averages and by assuming the random force to be Gaussian white noise. This new approach to dispersion modelling generalizes and unifies stochastic models based on the well-mixed condition and the moments approximation. Furthermore, we incorporate viscous effects in a systematic way. At a moderate Reynolds number, the model agrees qualitatively with direct numerical simulations showing highly non-Gaussian separation and velocity statistics for particle pairs initially close together. At very large Reynolds numbers, the mean-square separation obeys a Richardson law with coefficient of the order of 0.1.

Generalized Langevin equation for relative turbulent dispersion

The immersed boundary approach for the modeling of complex geometries in incompressible flows is examined critically from the perspective of satisfying boundary conditions and mass conservation. It is shown that the system of discretized equations for mass and momentum can be inconsistent, if the velocity is used in defining the force density to satisfy the boundary conditions. As a result, the velocity is generally not divergence free and the pressure at locations in the vicinity of the immersed boundary is not physical. However, the use of the pseudo-velocities in defining the force density, as frequently done when the governing equations are solved using a fractional step or projection method, combined with the use of the specified velocity on the immersed boundary, is shown to result in a consistent set of equations which allows a divergence-free velocity but, depending on the time step, is shown to have the undesirable effects of inaccurately satisfying the boundary conditions and allowing a significant permeability of the immersed boundary. If the time step is reduced sufficiently, the boundary conditions on the immersed boundary can be satisfied. However, this entails an unacceptable increase in computational expense. Two new methods that satisfy the boundary conditions and allow a divergence-free velocity while avoiding the increased computational expense are presented and shown to be second-order accurate in space. The first new method is based on local time step reduction. This method is suitable for problems where the immersed boundary does not move. For these problems, the first new method is shown to be closely related to the second new method. The second new method uses an optimization scheme to minimize the deviation from the interpolation stencil used to represent the immersed boundary while ensuring a divergence-free velocity. This method performs well for all problems, including those where the immersed boundary moves relative to the grid. Additional results include showing that the force density that is added to satisfy the boundary conditions at the immersed boundary is unbounded as the time step is reduced and that the pressure in the vicinity of the immersed boundary is unphysical, being strongly a function of the time step. A method of computing the total force on an immersed boundary which takes into account the specifics of the numerical solver used in the iterative process and correctly computes the total force irrespective of the residual level is also presented. Copyright © 2007 John Wiley & Sons, Ltd.

A divergence‐free interpolation scheme for the immersed boundary method

Two-particle Lagrangian models in turbulence are used to consider dispersion in decaying isotropic homogeneous turbulence (i.e. approximating grid-generated wind-tunnel flows). Thomson's formulation is used, and his model is extended to incorporate molecular diffusivity and viscosity, i.e. the range of scales modelled includes the dissipation subranges as well as the inertial subrange. New terms are proposed which consistently provide well-mixed models and the impact on Saffman's well-known small-time results is considered. The new model is ideal for comparison with recent concentration-fluctuation measurements in decaying wind-tunnel turbulence and the results are encouraging. In particular, the fluctuation intensities, both along and across the wind tunnel, are well described by the new model. In addition, small source-size effects are far better explained when we include the molecular effects. A surprising result is the persistence in time of both source-geometry and molecular effects upon concentration fluctuations. Both of the effects are negligible at large times for mean concentrations, but persist for significant times for the fluctuations, indicating an important role for small-scale dynamics.

H. Kaplan

Papers

A three-dimensional stochastic model for concentration fluctuation statistics inisotropic homogeneous turbulence