On the energetics of stratified turbulent mixing, irreversible thermodynamics, Boussinesq models and the ocean heat engine controversy

In this paper, the available potential energy (APE) framework of Winters et al. (J. Fluid Mech., vol. 289, 1995, p. 115) is extended to the fully compressible Navier– Stokes equations, with the aims of clarifying (i) the nature of the energy conversions taking place in turbulent thermally stratified fluids; and (ii) the role of surface buoyancy fluxes in the Munk & Wunsch (Deep-Sea Res., vol. 45, 1998, p. 1977) constraint on the mechanical energy sources of stirring required to maintain diapycnal mixing in the oceans. The new framework reveals that the observed turbulent rate of increase in the background gravitational potential energy GPEr , commonly thought to occur at the expense of the diffusively dissipated APE, actually occurs at the expense of internal energy, as in the laminar case. The APE dissipated by molecular diffusion, on the other hand, is found to be converted into internal energy (IE), similar to the viscously dissipated kinetic energy KE. Turbulent stirring, therefore, does not introduce a new APE/GPEr mechanical-to-mechanical energy conversion, but simply enhances the existing IE/GPEr conversion rate, in addition to enhancing the viscous dissipation and the entropy production rates. This, in turn, implies that molecular diffusion contributes to the dissipation of the available mechanical energy ME =APE +KE, along with viscous dissipation. This result has important implications for the interpretation of the concepts of mixing efficiency γmixing and flux Richardson number Rf , for which new physically based definitions are proposed and contrasted with previous definitions. The new framework allows for a more rigorous and general re-derivation from the first principles of Munk & Wunsch (1998, hereafter MW98)’s constraint, also valid for a non-Boussinesq ocean: G(KE) ≈ 1 − ξ Rf ξ Rf Wr, forcing = 1 + (1 − ξ )γmixing ξ γmixing Wr, forcing , where G(KE) is the work rate done by the mechanical forcing, Wr, forcing is the rate of loss of GPEr due to high-latitude cooling and ξ is a nonlinearity parameter such that ξ =1 for a linear equation of state (as considered by MW98), but ξ <1 otherwise. The most important result is that G(APE), the work rate done by the surface buoyancy fluxes, must be numerically as large as Wr, forcing and, therefore, as important as the mechanical forcing in stirring and driving the oceans. As a consequence, the overall mixing efficiency of the oceans is likely to be larger than the value γmixing =0.2 presently used, thereby possibly eliminating the apparent shortfall in mechanical stirring energy that results from using γmixing =0.2 in the above formula.

Understanding mixing efficiency in the oceans. Do the nonlinearities of the equation of state matter?

There exist two central measures of turbulent mixing in turbulent stratified fluids that are both caused by molecular diffusion: 1) the dissipation rate D(APE) of available potential energy APE; 2) the turbulent rate of change Wr, turbulent of background gravitational potential energy GPEr. So far, these two quantities have often been regarded as the same energy conversion, namely the irreversible conversion of APE into GPEr, owing to the well known exact equality D(APE)=Wr, turbulent for a Boussinesq fluid with a linear equation of state. Recently, however, Tailleux (2009) pointed out that the above equality no longer holds for a thermally-stratified compressible, with the ratio ξ=Wr, turbulent/D(APE) being generally lower than unity and sometimes even negative for water or seawater, and argued that D(APE) and Wr, turbulent actually represent two distinct types of energy conversion, respectively the dissipation of APE into one particular subcomponent of internal energy called the "dead" internal energy IE0, and the conversion between GPEr and a different subcomponent of internal energy called "exergy" IEexergy. In this paper, the behaviour of the ratio ξ is examined for different stratifications having all the same buoyancy frequency N vertical profile, but different vertical profiles of the parameter Υ=α P/(ρCp), where α is the thermal expansion coefficient, P the hydrostatic pressure, ρ the density, and Cp the specific heat capacity at constant pressure, the equation of state being that for seawater for different particular constant values of salinity. It is found that ξ and Wr, turbulent depend critically on the sign and magnitude of dΥ/dz, in contrast with D(APE), which appears largely unaffected by the latter. These results have important consequences for how the mixing efficiency should be defined and measured in practice, which are discussed.

Conservative upwind difference schemes for the Euler equations for real gas flows in a duct

In a recent paper [P. Glaister, Conservative upwind difference schemes for compressible flows in a Duct, Comput. Math. Appl. 56 (2008) 1787–1796] numerical schemes based on a conservative linearisation are presented for the Euler equations governing compressible flows of an ideal gas in a duct of variable cross-section, and in [P. Glaister, Conservative upwind difference schemes for compressible flows of a real gas, Comput. Math. Appl. 48 (2004) 469–480] schemes based on this philosophy are presented for real gas flows with slab symmetry. In this paper we seek to extend these ideas to encompass compressible flows of real gases in a duct. This will incorporate the handling of additional terms arising out of the variable geometry and the non-ideal nature of the gas.

Quantifying the effect of buffer zones, crop areas and spatial aggregation on the externalities of genetically modified crops at landscape level

The development of genetically modified (GM) crops has led the European Union (EU) to put forward the concept of 'coexistence' to give fanners the freedom to plant both conventional and GM varieties. Should a premium for non-GM varieties emerge in the market, 'contamination' by GM pollen would generate a negative externality to conventional growers. It is therefore important to assess the effect of different 'policy variables'on the magnitude of the externality to identify suitable policies to manage coexistence. In this paper, taking GM herbicide tolerant oilseed rape as a model crop, we start from the model developed in Ceddia et al. [Ceddia, M.G., Bartlett, M., Perrings, C., 2007. Landscape gene flow, coexistence and threshold effect: the case of genetically modified herbicide tolerant oilseed rape (Brassica napus). Ecol. Modell. 205, pp. 169-180] use a Monte Carlo experiment to generate data and then estimate the effect of the number of GM and conventional fields, width of buffer areas and the degree of spatial aggregation (i.e. the 'policy variables') on the magnitude of the externality at the landscape level. To represent realistic conditions in agricultural production, we assume that detection of GM material in conventional produce might occur at the field level (no grain mixing occurs) or at the silos level (where grain mixing from different fields in the landscape occurs). In the former case, the magnitude of the externality will depend on the number of conventional fields with average transgenic presence above a certain threshold. In the latter case, the magnitude of the externality will depend on whether the average transgenic presence across all conventional fields exceeds the threshold. In order to quantify the effect of the relevant' policy variables', we compute the marginal effects and the elasticities. Our results show that when relying on marginal effects to assess the impact of the different 'policy variables', spatial aggregation is far more important when transgenic material is detected at field level, corroborating previous research. However, when elasticity is used, the effectiveness of spatial aggregation in reducing the externality is almost identical whether detection occurs at field level or at silos level. Our results show also that the area planted with GM is the most important 'policy variable' in affecting the externality to conventional growers and that buffer areas on conventional fields are more effective than those on GM fields. The implications of the results for the coexistence policies in the EU are discussed. (C) 2008 Elsevier B.V. All rights reserved.

Seeds of growth? Agricultural productivity and the transitional dynamics of the Ramsey model

A two-sector Ramsey-type model of growth is developed to investigate the relationship between agricultural productivity and economy-wide growth. The framework takes into account the peculiarities of agriculture both in production ( reliance on a fixed natural resource base) and in consumption (life-sustaining role and low income elasticity of food demand). The transitional dynamics of the model establish that when preferences respect Engel's law, the level and growth rate of agricultural productivity influence the speed of capital accumulation. A calibration exercise shows that a small difference in agricultural productivity has drastic implications for the rate and pattern of growth of the economy. Hence, low agricultural productivity can form a bottleneck limiting growth, because high food prices result in a low saving rate.

Time patterns in UK demand for alcohol and tobacco: an application of the EM algorithm

Capturing the pattern of structural change is a relevant task in applied demand analysis, as consumer preferences may vary significantly over time. Filtering and smoothing techniques have recently played an increasingly relevant role. A dynamic Almost Ideal Demand System with random walk parameters is estimated in order to detect modifications in consumer habits and preferences, as well as changes in the behavioural response to prices and income. Systemwise estimation, consistent with the underlying constraints from economic theory, is achieved through the EM algorithm. The proposed model is applied to UK aggregate consumption of alcohol and tobacco, using quarterly data from 1963 to 2003. Increased alcohol consumption is explained by a preference shift, addictive behaviour and a lower price elasticity. The dynamic and time-varying specification is consistent with the theoretical requirements imposed at each sample point. (c) 2005 Elsevier B.V. All rights reserved.

Shrinking the posterior: A note on the Nerlovian model

Diebold and Lamb (1997) argue that since the long-run elasticity of supply derived from the Nerlovian model entails a ratio of random variables, it is without moments. They propose minimum expected loss estimation to correct this problem but in so-doing ignore the fact that a non white-noise-error is implicit in the model. We show that, as a consequence the estimator is biased and demonstrate that Bayesian estimation which fully accounts for the error structure is preferable.

Demographic models and the management of endangered species: a case study of the critically endangered Seychelles magpie robin

1. Demographic models are assuming an important role in management decisions for endangered species. Elasticity analysis and scope for management analysis are two such applications. Elasticity analysis determines the vital rates that have the greatest impact on population growth. Scope for management analysis examines the effects that feasible management might have on vital rates and population growth. Both methods target management in an attempt to maximize population growth. 2. The Seychelles magpie robin Copsychus sechellarum is a critically endangered island endemic, the population of which underwent significant growth in the early 1990s following the implementation of a recovery programme. We examined how the formal use of elasticity and scope for management analyses might have shaped management in the recovery programme, and assessed their effectiveness by comparison with the actual population growth achieved. 3. The magpie robin population doubled from about 25 birds in 1990 to more than 50 by 1995. A simple two-stage demographic model showed that this growth was driven primarily by a significant increase in the annual survival probability of first-year birds and an increase in the birth rate. Neither the annual survival probability of adults nor the probability of a female breeding at age 1 changed significantly over time. 4. Elasticity analysis showed that the annual survival probability of adults had the greatest impact on population growth. There was some scope to use management to increase survival, but because survival rates were already high (> 0.9) this had a negligible effect on population growth. Scope for management analysis showed that significant population growth could have been achieved by targeting management measures at the birth rate and survival probability of first-year birds, although predicted growth rates were lower than those achieved by the recovery programme when all management measures were in place (i.e. 1992-95). 5. Synthesis and applications. We argue that scope for management analysis can provide a useful basis for management but will inevitably be limited to some extent by a lack of data, as our study shows. This means that identifying perceived ecological problems and designing management to alleviate them must be an important component of endangered species management. The corollary of this is that it will not be possible or wise to consider only management options for which there is a demonstrable ecological benefit. Given these constraints, we see little role for elasticity analysis because, when data are available, a scope for management analysis will always be of greater practical value and, when data are lacking, precautionary management demands that as many perceived ecological problems as possible are tackled.

Toughness & cutting: A new way of determining ductile fracture toughness and strength

A review is given of the mechanics of cutting, ranging from the slicing of thin floppy offcuts (where there is negligible elasticity and no permanent deformation of the offcut) to the machining of ductile metals (where there is severe permanent distortion of the offcut/chip). Materials scientists employ the former conditions to determine the fracture toughness of ‘soft’ solids such as biological materials and foodstuffs. In contrast, traditional analyses of metalcutting are based on plasticity and friction only, and do not incorporate toughness. The machining theories are inadequate in a number of ways but a recent paper has shown that when ductile work of fracture is included many, if not all, of the shortcomings are removed. Support for the new analysis is given by examination of FEM simulations of metalcutting which reveal that a ‘separation criterion’ has to be employed at the tool tip. Some consideration shows that the separation criteria are versions of void-initiation-growth-and-coalescence models employed in ductile fracture mechanics. The new analysis shows that cutting forces for ductile materials depend upon the fracture toughness as well as plasticity and friction, and reveals a simple way of determining both toughness and flow stress from cutting experiments. Examples are given for a wide range of materials including metals, polymers and wood, and comparison is made with the same properties independently determined using conventional testpieces. Because cutting can be steady state, a new way is presented for simultaneously measuring toughness and flow stress at controlled speeds and strain rates.

Mechanical effects of plant cell wall enzymes on xyloglucan/cellulose composites

Xyloglucan-acting enzymes are believed to have effects on type I primary plant cell wall mechanical properties. In order to get a better understanding of these effects, a range of enzymes with different in vitro modes of action were tested against cell wall analogues (bio-composite materials based on Acetobacter xylinus cellulose and xyloglucan). Tomato pericarp xyloglucan endo transglycosylase (tXET) and nasturtium seed xyloglucanase (nXGase) were produced heterologously in Pichia pastoris. Their action against the cell wall analogues was compared with that of a commercial preparation of Trichoderma endo-glucanase (EndoGase). Both 'hydrolytic' enzymes (nXGase and EndoGase) were able to depolymerise not only the cross-link xyloglucan fraction but also the surface-bound fraction. Consequent major changes in cellulose fibril architecture were observed. In mechanical terms, removal of xyloglucan cross-links from composites resulted in increased stiffness (at high strain) and decreased visco-elasticity with similar extensibility. On the other hand, true transglycosylase activity (tXET) did not affect the cellulose/xyloglucan ratio. No change in composite stiffness or extensibility resulted, but a significant increase in creep behaviour was observed in the presence of active tXET. These results provide direct in vitro evidence for the involvement of cell wall xyloglucan-specific enzymes in mechanical changes underlying plant cell wall re-modelling and growth processes. Mechanical consequences of tXET action are shown to be complimentary to those of cucumber expansin.

QTLs for shelf life in lettuce co-locate with those for leaf biophysical properties but not with those for leaf developmental traits

Developmental and biophysical leaf characteristics that influence post-harvest shelf life in lettuce, an important leafy crop, have been examined. The traits were studied using 60 informative F-9 recombinant inbed lines (RILs) derived from a cross between cultivated lettuce (Lactuca sativa cv. Salinas) and wild lettuce (L. serriola acc. UC96US23). Quantitative trait loci (QTLs) for shelf life co-located most closely with those for leaf biophysical properties such as plasticity, elasticity, and breakstrength, suggesting that these are appropriate targets for molecular breeding for improved shelf life. Significant correlations were found between shelf life and leaf size, leaf weight, leaf chlorophyll content, leaf stomatal index, and epidermal cell number per leaf, indicating that these pre-harvest leaf development traits confer post-harvest properties. By studying the population in two contrasting environments in northern and southern Europe, the genotype by environment interaction effects of the QTLs relevant to leaf development and shelf life were assessed. In total, 107 QTLs, distributed on all nine linkage groups, were detected from the 29 traits. Only five QTLs were common in both environments. Several areas where many QTLs co-located (hotspots) on the genome were identified, with relatively little overlap between developmental hotspots and those relating to shelf life. However, QTLs for leaf biophysical properties (breakstrength, plasticity, and elasticity) and cell area correlated well with shelf life, confirming that the ideal ideotype lettuce should have small cells with strong cell walls. The identification of QTLs for leaf development, strength, and longevity will lead to a better understanding of processability at a genetic and cellular level, and allow the improvement of salad leaf quality through marker-assisted breeding.

Comparison of small and large deformation rheological properties of wheat dough and gluten

The rheological properties of dough and gluten are important for end-use quality of flour but there is a lack of knowledge of the relationships between fundamental and empirical tests and how they relate to flour composition and gluten quality. Dough and gluten from six breadmaking wheat qualities were subjected to a range of rheological tests. Fundamental (small-deformation) rheological characterizations (dynamic oscillatory shear and creep recovery) were performed on gluten to avoid the nonlinear influence of the starch component, whereas large deformation tests were conducted on both dough and gluten. A number of variables from the various curves were considered and subjected to a principal component analysis (PCA) to get an overview of relationships between the various variables. The first component represented variability in protein quality, associated with elasticity and tenacity in large deformation (large positive loadings for resistance to extension and initial slope of dough and gluten extension curves recorded by the SMS/Kieffer dough and gluten extensibility rig, and the tenacity and strain hardening index of dough measured by the Dobraszczyk/Roberts dough inflation system), the elastic character of the hydrated gluten proteins (large positive loading for elastic modulus [G'], large negative loadings for tan delta and steady state compliance [J(e)(0)]), the presence of high molecular weight glutenin subunits (HMW-GS) 5+10 vs. 2+12, and a size distribution of glutenin polymers shifted toward the high-end range. The second principal component was associated with flour protein content. Certain rheological data were influenced by protein content in addition to protein quality (area under dough extension curves and dough inflation curves [W]). The approach made it possible to bridge the gap between fundamental rheological properties, empirical measurements of physical properties, protein composition, and size distribution. The interpretation of this study gave indications of the molecular basis for differences in breadmaking performance.

Can drug-bearing liposomes penetrate intact skin?

Using liposomes to deliver drugs to and through human skin is controversial, as their function varies with type and composition. Thus they may act as drug carriers controlling release of the medicinal agent. Alternatively, they may provide a localized depot in the skin so minimizing systemic effects or can be used for targeting delivery to skin appendages (hair follicles and sweat glands). Liposomes may also enhance transdermal drug delivery, increasing systemic drug concentrations. With such a multiplicity of functions, it is not surprising that mechanisms of liposomal delivery of therapeutic agents to and through the skin are unclear. Accordingly, this article provides an overview of the modes and mechanisms of action of different vesicles as drug delivery vectors in human skin. Our conclusion is that vesicles, depending on the composition and method of preparation, can vary with respect to size, lamellarity, charge, membrane fluidity or elasticity and drug entrapment. This variability allows for multiple functions ranging from local to transdermal effects. Application to dissimilar skins (animal or human) via diverse protocols may reveal different mechanisms of action with possible vesicle skin penetration reaching different depths, from surface assimilation to (rarely) the viable tissue and subsequent systemic absorption.

Flux difference splitting for inviscid, real gases with non-equilibrium chemistry

A flux-difference splitting method is presented for the inviscid terms of the compressible flow equations for chemical non-equilibrium gases

An efficient flux difference splitting algorithm for unsteady duct flows of a real gas

A numerical scheme is presented for the solution of the Euler equations of compressible flow of a real gas in a single spatial coordinate. This includes flow in a duct of variable cross-section, as well as flow with slab, cylindrical or spherical symmetry, as well as the case of an ideal gas, and can be useful when testing codes for the two-dimensional equations governing compressible flow of a real gas. The resulting scheme requires an average of the flow variables across the interface between cells, and this average is chosen to be the arithmetic mean for computational efficiency, which is in contrast to the usual “square root” averages found in this type of scheme. The scheme is applied with success to five problems with either slab or cylindrical symmetry and for a number of equations of state. The results compare favourably with the results from other schemes.