Vortex shedding from tapered, triangular plates: taper and aspect ratio effects

Further experiments on features of the vortex shedding from tapered flat plates normal to an airstream are described. The work extends that of Castro and Rogers (2002) and concentrates on the study of the effects of varying the spanwise aspect ratio for a fixed shape plate, by appropriate adjustment of end-plates, and of the nature of the shedding as the degree of taper becomes very large, so that the body is more like a triangular plate—e.g. an isosceles triangle—than a slightly tapered plate. With the taper ratio TR defined as the ratio of plate length to average cross-stream width, the paper concentrates on the range 0.58<TR<60. Reynolds numbers, based on the average plate width, exceed 104. It is confirmed that for a small enough taper ratio the geometrical three-dimensionality is sufficiently strong that all signs of periodic vortex shedding cease. For all other cases, however, the flow at different locations along the span can vary substantially, depending on taper. There appear to be at least four different regimes, each appropriate for a different range of taper ratio. These various regimes are described

What explains the invading success of the aquatic mud snail Potamopyrgus antipodarum (Hydrobiidae, Mollusca)?

The spread of non-native species is one of the most harmful and least reversible disturbances in ecosystems. Species have to overcome several filters to become a pest (transport, establishment, spread and impact). Few studies have checked the traits that confer ability to overcome these steps in the same species. The aim of the present study is to review the available information on the life-history and ecological traits of the mud snail, Potamopyrgus antipodarum Gray (Hydrobiidae, Mollusca), native from New Zealand, in order to explain its invasive success at different aquatic ecosystems around the world. A wide tolerance range to physico-chemical factors has been found to be a key trait for successful transport. A high competitive ability at early stages of succession can explains its establishment success in human-altered ecosystems. A high reproduction rate, high capacity for active and passive dispersal, and the escape from native predators and parasites explains its spread success. The high reproduction and the ability to monopolize invertebrate secondary production explain its high impact in the invaded ecosystems. However, further research is needed to understand how other factors, such as population density or the degree of human perturbation can modify the invasive success of this aquatic snai

Large-eddy simulation for flow and dispersion in urban streets

Large-eddy simulations (LES) with our recently developed inflow approach (Xie &Castro, 2008a) have been used for flow and dispersion within a genuine city area -the DAPPLE site, located at the intersection of Marylebone Rd and Gloucester Plin Central London. Numerical results up to second-order statistics are reported fora computational domain of 1.2km (streamwise) x 0.8km (lateral) x 0.2km (in fullscale), with a resolution down to approximately one meter in space and one secondin time. They are in reasonable agreement with the experimental data. Such a comprehensiveurban geometry is often, as here, composed of staggered, aligned, squarearrays of blocks with non-uniform height and non-uniform base, street canyons andintersections. Both the integrative and local effect of flow and dispersion to thesegeometrical patterns were investigated. For example, it was found that the peaksof spatially averaged urms, vrms, wrms and < u0w0 > occurred neither at the meanheight nor at the maximum height, but at the height of large and tall buildings. Itwas also found that the mean and fluctuating concentrations in the near-source fieldis highly dependent on the source location and the local geometry pattern, whereasin the far field (e.g. >0.1km) they are not. In summary, it is demonstrated thatfull-scale resolution of around one meter is sufficient to yield accurate prediction ofthe flow and mean dispersion characteristics and to provide reasonable estimationof concentration fluctuation

Bounds for partial derivatives: necessity of UMD and sharp constants

We prove the necessity of the UMD condition, with a quantitative estimate of the UMD constant, for any inequality in a family of $L^p$ bounds between different partial derivatives $\partial^\beta u$ of $u\in C^\infty_c(\mathbb{R}^n,X)$. In particular, we show that the estimate $\|u_{xy}\|_p\leq K(\|u_{xx}\|_p+\|u_{yy}\|_p)$ characterizes the UMD property, and the best constant $K$ is equal to one half of the UMD constant. This precise value of $K$ seems to be new even for scalar-valued functions.Comment: v2: corrected typo in the reference

New solutions of the D-dimensional Klein-Gordon equation via mapping onto the nonrelativistic one-dimensional Morse potential

New exact analytical bound-state solutions of the D-dimensional Klein-Gordon equation for a large set of couplings and potential functions are obtained via mapping onto the nonrelativistic bound-state solutions of the one-dimensional generalized Morse potential. The eigenfunctions are expressed in terms of generalized Laguerre polynomials, and the eigenenergies are expressed in terms of solutions of irrational equations at the worst. Several analytical results found in the literature, including the so-called Klein-Gordon oscillator, are obtained as particular cases of this unified approac