ALBERT

Description: During the motion of a fluid interface undergoing Rayleigh-Taylor instability, vorticity is generated on the interface baronclinically. This vorticity is then subject to Kelvin-Helmholtz instability. For the related problem of evolution of a nearly flat vortex sheet without density stratification (and with viscosity and surface tension neglected), Kelvin-Helmholtz instability has been shown to lead to development of curvature singularities in the sheet. In this paper, a simple approximate theory is developed for Rayleigh-Taylor instability as a generalization of Moore's approximation for vortex sheets. For the approximate theory, a family of exact solutions is found for which singularities develop on the fluid interface. The resulting predictions for the time and type of the singularity are directly verified by numerical computation of the full equations. These computations are performed using a point vortex method, and singularities for the numerical solution are detected using a form fit for the Fourier components at high wavenumber. Excellent agreement between the theoretical predictions and the numerical results is demonstrated for small to medium values of the Atwood number A, i.e. for A between 0 and approximately 0.9. For A near 1, however, the singularities actually slow down when close to the real axis. In particular, for A = 1, the numerical evidence suggests that the singularities do not reach the real axis in finite time. © 1993, Cambridge University Press. All rights reserved.

Description: The motion of vortex sheets is susceptible to the onset of the Kelvin-Helmholz instability. There is now a large body of evidence that the instability leads to the formation of a curvature singularity in finite time. Vortex blob methods provide a regularization for the motion of vortex sheets. Instead of forming a curvature singularity in finite time, the curves generated by vortex blob methods form spirals. Theory states that these spirals will converge to a classical weak solution of the Euler equations as the blob size vanishes. This theory assumes that the blob method is the result of a convolution of the sheet velocity with an appropriate choice of a smoothing function. We consider four different blob methods, two resulting from appropriate choices of smoothing functions and two not. Numerical results indicate that the curves generated by these methods form different spirals, but all approach the same weak limit as the blob size vanishes. By scaling distances and time appropriately with blob size, the family of spirals generated by different blob sizes collapse almost perfectly to a single spiral. This observation is the next step in developing an asymptotic theory to describe the nature of the weak solution in detail. © 2006 Cambridge University Press.

Description: The equations for the two-dimensional motion of a layer of uniform vorticity in an incompressible, inviscid fluid are examined in the limit of small thickness. Under the right circumstances, the limit is a vortex sheet whose strength is the vorticity multiplied by the local thickness of the layer. However, vortex sheets can develop singularities in finite time, and their subsequent nature is an open question. Vortex layers, on the other hand, have motions for all time, though they may develop singularities on their boundaries. Fortunately, a material curve within the layer does exist for all time. Under certain assumptions, its limiting motion is again the vortex sheet, and thus its behaviour may indicate the nature and possible existence of the vortex sheet after the singularity time. Similar asymptotic results are obtained also for the limiting behaviour of the centre curve as defined by Moore (1978). By examining the behaviour of a sequence of layers, some physical understanding of the formation of the curvature singularity for a vortex sheet is gained. A strain flow, induced partly by the periodic extension of the sheet, causes vorticity to be advected to a certain point on the sheet rapidly enough to form the singularity. A vortex layer, however, simply bulges outwards as a consequence of incompressibility and subsequently forms a core with trailing arms that wrap around it. The evidence indicates that no singularities form on the boundary curves of the layer. Beyond the singularity time of the vortex sheet, the limiting behaviour of the vortex layers is non-uniform. Away from the vortex core, the layers converge to a smooth curve which has the appearance of a doubly branched spiral. While the circulation around the core vanishes, approximations to the vortex sheet strength become unbounded, indicating a complex, local structure whose precise nature remains undetermined. © 1990, Cambridge University Press. All rights reserved.

Description: SUMMARYRice plants (Oryza saliva L., cv. IR30) were grown in paddy culture in outdoor, naturally sunlit, controlled-environment, plant growth chambers at Gainesville, Florida, USA, in 1987. The rice plants were exposed throughout the season to subambient (160 and 250), ambient (330) or superambient (500, 660, 900 μmol CO2/mol air) CO2 concentrations. Total shoot biomass, root biomass, tillering, and final grain yield increased with increasing CO2 concentration, thegreatest increase occurring between the 160 and 500 μmol CO2/mol air treatments. Early in the growing season, root:shoot biomass ratio increased with increasing CO2 concentration; although the ratio decreased during the growing season, net assimilation rate increased with increasingCO2 concentration and decreased during the growing season. Differences in biomass and lamina area among CO2 treatments were largely due to corresponding differences in tillering response. The number of panicles/plant was almost entirely responsible for differences in final grain yield among CO2 treatments. Doubling the CO2 concentration from 330 to 660 μmol CO2/mol air resulted in a 32 % increase in grain yield. These results suggest that important changes in the growth and yield of rice may be expected in the future as the CO2 concentration of the earth's atmosphere continues to rise.

Description: SUMMARYTwo varieties of Italian ryegrass (Lolium multiflorum Lam.), Tribune and RvP, were cut in each of 2 years, ensiled and individually fed, ad libitum, to dairy cows. In one year, two rates of supplementary concentrate feeding were compared and, in the other year, two types of concentrate and a silage-only diet. Tribune silage was more digestible, in vitro, and was lower in neutral detergent fibre and fibrosity index than RvP silage. There was no difference between the varieties, however, in the cows’ intake of silage. On the silage-only diet, the cows fed Tribune produced a higher yield of milk solids than did those fed RvP; on the other diets, there was no significant difference between varieties in the yield or composition of milk.The same two varieties were compared when grazed by herds of dairy cows in spring, summer and autumn of the first harvest year on six farms and in the second harvest year on four of the farms. Tribune persisted much better than RvP, in numbers of plants and tillers/m2 and in ground cover, and the herbage was more digestible than that of RvP. Milk yield/cow was c. 0·6 kg per day higher when grazing Tribune than when grazing RvP.

Description: SUMMARYThe study investigated the effects of chronic elevation or suppression of circulating prolactin levels on seasonal wool growth in Romney sheep. Ewes (n = 10/group) were housed indoors under natural lighting (latitude 34 °S) and received either 50 mg bromocriptine i.m./ewe/28 days (Group B), 1 mg spiperone s.c./ewe/day (Group S) or no treatment (Group C) commencing in summer. Wool growth and liveweight were measured every 4 weeks and venous blood samples were collected for prolactin determination. Plasma prolactin levels (mean±s.E.) in Group C exhibited a gradual seasonal decline from 121±29 ng/ml to 35±9 ng/ml. Bromocriptine suppressed prolactin levels rapidly from a pretreatment value of 118±2 ng/ml to below 12±7 ng/ml for the duration of the study. Prolactin levels in Group S were not significantly higher than Group C, with the exception of the first 14 days following the initial treatment. A seasonal reduction in wool growth of c. 25% was observed in all groups; however, no significant treatment effect was evident. Mean liveweight of all animals increased from 50·4±0·8 to 56·8±0·7 kg during the study. These results indicate that perturbation of the annual cyclic secretion of prolactin does not affect wool growth in the Romney ewe.