Molecular diffusion and viscous effects on concentration statistics in grid turbulence

Abstract

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 intertial 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 results 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.