Extension of a fluctuating plume model of tracer dispersion to a sheared boundary layer and to a large array of obstacles

Fluctuating plume models provide a useful conceptual paradigm in the understanding of plume dispersion in a turbulent flow. In particular, these models have enabled analytical predictions of higher-order concentration moments, and the form of the one-point concentration probability density function (PDF). In this paper, we extend the traditional formalism of these models, grounded in the theory of homogeneous and isotropic turbulent flow, to two cases: namely, a simple sheared boundary layer and a large array of regular obstacles. Some very high-resolution measurements of plume dispersion in a water channel, obtained using laser-induced fluorescence (LIF) line-scan techniques are utilised. These data enable us to extract time series of plume centroid position (plume meander) and dispersion in the relative frame of reference in unprecedented detail. Consequently, experimentally extracted PDFs are able to be directly compared with various theoretical forms proposed in the literature. This includes the PDF of plume centroid motion, the PDF of concentration in the relative frame, and a variety of concentration moments in the absolute and relative frames of reference. The analysis confirms the accuracy of some previously proposed functional forms of model components used in fluctuating plume models, as well as suggesting some new forms necessary to deal with the complex boundary conditions in the spatial domain.