Self-Similarity in Particle-Laden Flows at Constant Volume

This paper deals with the evolution of a localized, constant-volume initial condition on an incline into a spreading descending thin-film solution. Clear fluids in this geometry are known to have a front position that moves according to a t1/3 scaling law, based on similarity-solution analysis by Huppert (Nature 300:427–429, 1982). The same dynamics are investigated for particle-laden flow using a recently proposed lubrication model and physical experiments. The analysis includes the role of a precursor in the model. In the lubrication model, the height of the precursor significantly influences the position of the fluid front, independent of particles settling in the direction of flow. By comparing theory with experiments it is shown that the t1/3 scaling law persists, to leading order, for particle-laden flows with particle settling. However, additional physics is needed in the existing lubrication models to quantitatively explain departures from clear-fluid self-similarity due to particle settling

Diversity Over Time

Temporal turnover is a fundamental feature of ecological communities. Darwin 1859 noted the ecological and evolutionary significance of turnover, Fisher and Preston acknowledged its role in their models of species abundance, while this ongoing and entirely natural rearrangement of species underpins key ecological concepts such as MacArthur and Wilson's theory of island biogeography. However, the current focus on spatial patterns of diversity means that temporal changes are often overlooked. Here I argue that failure to take heed of the time frame over which data are collected can lead to both artefacts and artifictions. There are also deeper issues, such as the consequences for species richness estimation and rarefaction methods of a constantly changing community. Moreover, some of the confusion surrounding species abundance distributions may be resolved by taking account of time. A better appreciation of temporal turnover is essential for accurate diversity measurement and assessment, and, more importantly, will also lead to improved understanding of the processes that underpin community structure.</p