Two-scale momentum theory for time-dependent modelling of large wind farms

This paper presents a theory based on the law of momentum conservation to define and help analyse the problem of large wind farm aerodynamics. The theory splits the problem into two sub-problems; namely an 'external' (or farm-scale) problem, which is a time-dependent problem considering large-scale motions of the atmospheric boundary layer (ABL) to assess the amount of momentum available to the ABL's bottom resistance (due to wind turbines and land/sea surface) at a certain time; and an 'internal' (or turbine-scale) problem, which is a quasi-steady (in terms of large-scale motions of the ABL) problem describing the breakdown of the ABL's bottom resistance into wind turbine drag and land/sea surface friction. The two sub-problems are coupled to each other through a non-dimensional parameter called 'farm wind-speed reduction factor,' for which a simple analytic equation is derived that can be solved iteratively using information obtained from both sub-problems. This general form of coupling allows us to use the present theory with various types of flow models at each scale, such as a numerical weather prediction (NWP) model for the external problem and a computational fluid dynamics (CFD) model for the internal problem. The theory is presented for a simplified wind farm situation first, followed by a discussion on how the theory can be applied (in an approximate manner) to real-world problems; for example, how to estimate the power loss due to the so-called 'wind farm blockage effect' for a given large wind farm under given environmental conditions.Comment: Under consideration for publication in J. Fluid Mech. (16 pages, 5 figures

An analytical model of momentum availability for predicting large wind farm power

Turbine-wake and farm-atmosphere interactions influence wind farm power production. For large offshore farms, the farm-atmosphere interaction is usually the more significant effect. This study proposes an analytical model of the `momentum availability factor' to predict the impact of farm-atmosphere interactions. It models the effects of net advection, pressure gradient forcing and turbulent entrainment, using steady quasi-1D flow assumptions. Turbulent entrainment is modelled by assuming self-similar vertical shear stress profiles. We used the model with the `two-scale momentum theory' to predict the power of large finite-sized farms. The model compared well with existing results of large-eddy simulations (LES) of finite wind farms in conventionally neutral boundary layers. The model captured most of the effects of atmospheric boundary layer (ABL) height on farm performance by considering the undisturbed vertical shear stress profile of the ABL as an input. In particular, the model predicted the power of staggered wind farms with a typical error of 5% or less. The developed model provides a novel way of instantly predicting the power of large wind farms, including the farm blockage effects. A further simplification of the model to analytically predict the 'wind extractability factor' is also presented. This study provides a novel framework for modelling farm-atmosphere interactions. Future studies can use the framework to better model large wind farms.Comment: 22 pages, 12 figures, 4 table

An analytical model of momentum availability for predicting large wind farm power

Turbine–wake and farm–atmosphere interactions influence wind farm power production. For large offshore farms, the farm–atmosphere interaction is usually the more significant effect. This study proposes an analytical model of the ‘momentum availability factor’ to predict the impact of farm–atmosphere interactions. It models the effects of net advection, pressure gradient forcing and turbulent entrainment, using steady quasi-one-dimensional flow assumptions. Turbulent entrainment is modelled by assuming self-similar vertical shear stress profiles. We used the model with the ‘two-scale momentum theory’ to predict the power of large finite-sized farms. The model compared well with existing results of large-eddy simulations of finite wind farms in conventionally neutral boundary layers. The model captured most of the effects of atmospheric boundary layer (ABL) height on farm performance by considering the undisturbed vertical shear stress profile of the ABL as an input. In particular, the model predicted the power of staggered wind farms with a typical error of 5 % or less. The developed model provides a novel way of predicting instantly the power of large wind farms, including the farm blockage effects. A further simplification of the model to predict analytically the ‘wind extractability factor’ is also presented. This study provides a novel framework for modelling farm–atmosphere interactions. Future studies can use the framework to better model large wind farms

Predicting Relaxation in Strained Epitaxial Layers

Strained epitaxial semiconductor layers, much thicker than the critical thickness, have been used as strain-relief buffer layers for many years. The most successful structure developed so far dates back to the 1960\u27s, and consists of a very thick ( ~30 μm) layer in which the misfit is gradually and continuously increased. These structures relax completely and have a sufficiently low threading dislocation density to allow a device structure to be grown on top. This process requires a very high growth rate to produce the buffer layer in a reasonable time, which is only provided by hydride vapourphase epitaxy. Recently, there has been interest in developing thinner structures using both graded and constant composition buffer layers, which, if successful, would resolve this problem. Here, we consider the mechanisms of strain relaxation, paying special attention to the changes in threading dislocation density and surface roughness that occur during misfit relief. An extensive series of experiments shows that the relaxation of constant composition layers, although not following current theoretical models, does appear to follow a simple empirical law. This result suggests an approach which can be used to predict the state of strain in any epitaxial structure, allowing more efficient strain-relief buffer layers to be designed

Graphite under uniaxial compression along the c axis: A parameter to relate out-of-plane strain to in-plane phonon frequency

Stacking graphene sheets forms graphite. Two in-plane vibrational modes of graphite, E1u and E2g(2), are derived from graphene E2g mode, the shifts of which under compression are all considered as results of in-plane bond shortening. Values of Gruneisen parameter have been reported to quantify such relation. However, the reason why the shift rates of these three modes with pressure differ is unclear. In this work, we introduce a new parameter to quantify the contribution of out-of-plane strain to the in-plane vibrational frequencies, suggesting that the compression of \pi-electrons plays a non-negligible part in both graphite and graphene under high pressure.Comment: 8 pages, 5 figures, 1 tabl

Unexpected softness of bilayer graphene and softening of A-A stacked graphene layers

Density functional theory has been used to investigate the behavior of the π electrons in bilayer graphene and graphite under compression along the c axis. We have studied both conventional Bernal (A-B) and A-A stackings of the graphene layers. In bilayer graphene, only about 0.5% of the π-electron density is squeezed through the sp2 network for a compression of 20%, regardless of the stacking order. However, this has a major effect, resulting in bilayer graphene being about six times softer than graphite along the c axis. Under compression along the c axis, the heavily deformed electron orbitals (mainly those of the π electrons) increase the interlayer interaction between the graphene layers as expected, but, surprisingly, to a similar extent for A-A and Bernal stackings. On the other hand, this compression shifts the in-plane phonon frequencies of A-A stacked graphene layers significantly and very differently from the Bernal stacked layers. We attribute these results to some sp2 electrons in A-A stacking escaping the graphene plane and filling lower charge-density regions when under compression, hence, resulting in a nonmonotonic change in the sp2-bond stiffness

Nautilus pompilius Life History and Demographics at the Osprey Reef Seamount, Coral Sea, Australia

Nautiloids are the subject of speculation as to their threatened status arising from the impacts of targeted fishing for the ornamental shell market. Life history knowledge is essential to understand the susceptibility of this group to overfishing and to the instigation of management frameworks. This study provides a comprehensive insight into the life of Nautilus in the wild. At Osprey Reef from 1998–2008, trapping for Nautilus was conducted on 354 occasions, with 2460 individuals of one species, Nautilus pompilius, captured and 247 individuals recaptured. Baited remote underwater video systems (BRUVS) were deployed on 15 occasions and six remotely operated vehicle (ROV) dives from 100–800 m were conducted to record Nautilus presence and behavior. Maturity, sex and size data were recorded, while measurements of recaptured individuals allowed estimation of growth rates to maturity, and longevity beyond maturity. We found sexual dimorphism in size at maturity (males: 131.9±SD = 2.6 mm; females: 118.9±7.5 mm shell diameter) in a population dominated by mature individuals (58%). Mean growth rates of 15 immature recaptured animals were 0.061±0.023 mm day−1 resulting in an estimate of around 15.5 years to maturation. Recaptures of mature animals after five years provide evidence of a lifespan exceeding 20 years. Juvenile Nautilus pompilius feeding behavior was recorded for the first time within the same depth range (200–610 m) as adults. Our results provide strong evidence of a K-selected life history for Nautilus from a detailed study of a ‘closed’ wild population. In conjunction with population size and density estimates established for the Osprey Reef Nautilus, this work allows calculations for sustainable catch and provides mechanisms to extrapolate these findings to other extant nautiloid populations (Nautilus and Allonautilus spp.) throughout the Indo-Pacific