The Effect of the Frozen Cloud Approximation on Longitudinal Dispersion Quantification

The ability to understand and predict how a solute will disperse longitudinally when introduced into a flow is vital to understand the fate of contaminates introduced into environmental flows. The pioneering work of Taylor (1953, 1954) showed that once sufficient time has elapsed after injection, the spatial distribution of the solute’s concentration can be described by a Gaussian distribution, using equations analogous to Fick’s law of diffusion. In the subsequent decades, many authors have conducted tracer experiments investigating these processes in further detail. However, unlike Taylor’s original work that described longitudinal dispersion by measuring a spatial concentration distribution, the vast majority of these studies measure the temporal variation in concentration at a fixed location (a much simpler experiment). The data is then processed by converting the temporal profile to a spatial equivalent using the flow’s mean velocity and the assumption that the dye has not dispersed significantly as it passes though the measurement site. This assumption is commonly referred to as ‘the frozen cloud approximation’. This paper presents preliminary results from a wider study conducted by the authors to fully assess the validity of this assumption for a range of flow conditions. The results obtained from this study improve the current understanding of underlying mixing and dispersion mechanisms in environmental flows and can be used to improve predictions within water quality models.