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.

The effect of mechanical stirring on horizontal convection

An important experimental result, as yet poorly understood, is that mechanical stirring can significantly enhance the strength of horizontal convection. A contentious issue is whether this necessarily implies that the mechanical stirring replaces the buoyancy forcing as the main source of energy driving the observed overturning circulation, as has been suggested for the Atlantic meridional overturning circulation (AMOC). In this paper, rigorous energetics considerations and idealized numerical experiments reveal that the rate at which the surface buoyancy forcing supplies energy to the fluid, as measured by the production rate of available potential energy G(APE), does not solely depend upon the buoyancy forcing, as is often implicitly assumed, but also upon the vertical stratification, such that the deeper the thermocline depth, the larger G(APE). This suggests that mechanical stirring enhances horizontal convection because it causes more energy to be extracted from the buoyancy forcing. It does so by enhancing turbulent mixing, which allows surface heating to reach greater depths, which increases the thermocline depth and hence G(APE). This paper therefore proposes a new hypothesis, namely that mechanically stirred horizontal convection and the AMOC are best described as mechanically controlled heat engines.

Climate entropy budget of the HadCM3 atmosphere-ocean general circulation model and of FAMOUS, its low resolution version

The entropy budget is calculated of the coupled atmosphere–ocean general circulation model HadCM3. Estimates of the different entropy sources and sinks of the climate system are obtained directly from the diabatic heating terms, and an approximate estimate of the planetary entropy production is also provided. The rate of material entropy production of the climate system is found to be ∼50 mW m−2 K−1, a value intermediate in the range 30–70 mW m−2 K−1 previously reported from different models. The largest part of this is due to sensible and latent heat transport (∼38 mW m−2 K−1). Another 13 mW m−2 K−1 is due to dissipation of kinetic energy in the atmosphere by friction and Reynolds stresses. Numerical entropy production in the atmosphere dynamical core is found to be about 0.7 mW m−2 K−1. The material entropy production within the ocean due to turbulent mixing is ∼1 mW m−2 K−1, a very small contribution to the material entropy production of the climate system. The rate of change of entropy of the model climate system is about 1 mW m−2 K−1 or less, which is comparable with the typical size of the fluctuations of the entropy sources due to interannual variability, and a more accurate closure of the budget than achieved by previous analyses. Results are similar for FAMOUS, which has a lower spatial resolution but similar formulation to HadCM3, while more substantial differences are found with respect to other models, suggesting that the formulation of the model has an important influence on the climate entropy budget. Since this is the first diagnosis of the entropy budget in a climate model of the type and complexity used for projection of twenty-first century climate change, it would be valuable if similar analyses were carried out for other such models.

Selenium supplementation of lactating dairy cows: Effect on selenium concentration in blood, milk, urine and feces

The objectives were to determine effects of graded levels of selenized yeast derived from a specific strain of Saccharomyces cerevisiae (CNCM I-3060) on animal performance and in selenium concentrations in the blood, milk, feces, and urine of dairy cows compared with sodium selenite; and to provide preliminary data on the proportion of selenium as selenomethionine in the milk and blood. Twenty Holstein cows were used in a 5 × 5 Latin square design study in which all cows received the same total mixed rations, which varied only in source or concentration of dietary selenium. There were 5 experimental treatments. Total dietary selenium of treatment 1, which received no added selenium, was 0.15 mg/kg of dry matter, whereas values for treatments 2, 3, and 4, derived from selenized yeast, were 0.27, 0.33, and 0.40 mg/kg of dry matter, respectively. Treatment 5 contained 0.25 mg of selenium obtained from sodium selenite/kg of dry matter. There were no significant treatment effects on animal performance, and blood chemistry and hematology showed few treatment effects. Regression analysis noted significant positive linear effects of increasing dietary selenium derived from selenized yeast on selenium concentrations in the milk, blood, urine, and feces. In addition, milk selenium results indicated improved bioavailability of selenium from selenized yeast, compared with sodium selenite. Preliminary analyses showed that compared with sodium selenite, the use of selenized yeast increased the concentration of selenomethionine in the milk and blood. There was no indication of adverse effects on cow health associated with the use of selenized yeast.

Developments in near infrared spectroscopy

Vibrational spectroscopy at high excitation is an important research frontier for two reasons. Firstly, the near infrared is proving to be an important area for the analytical applications of spectroscopy, and we would therefore like to understand how the spectra we observe relate to the molecular structure of the absorbing species. Secondly, there is a fundamental interest in understanding molecular dynamics and energy flow within a polyatomic molecule at high excitation, because this is the boundary between spectroscopy and chemistry through which we try to understand the details of a chemical reaction. In this presentation I shall survey recent progress in this field.

Mono- and heterodimetallic FeII and RuII complexes based on a novel heteroditopic 4′-{bis(phosphanyl)aryl}-2,2′:6′,2″-terpyridine ligand

In the search for a versatile building block that allows the preparation of heteroditopic tpy-pincer bridging ligands, the synthon 14'-[C6H3(CH2Br)(2)-3,5]-2,2':6',2 ''-terpyridine was synthesized. Facile introduction of diphenylphosphanyl groups in this synthon gave the ligand 14'-[C6H3(CH2PPh2)2-3,5]-2,2':6',2"-terpyridine) ([tpyPC(H)Pj). The asymmetric mononuclear complex [Fe(tpy){tpyPC(H)P}](PF6)(2), prepared by selective coordination of [Fe(tpy)Cl-3] to the tpy moiety of [tpyPC(H)P], was used for the synthesis of the heterodimetallic complex [Fe(tpy)(tpyPCP)Ru(tpy)](PFC,)3, which applies the "complex as ligand" approach. Coordination of the ruthenium centre at the PC(H)P-pincer moiety of [Fe(tpy){tpyPC(H)P}](PF6)(2) has been achieved by applying a transcyclometallation procedure. The ground-state electronic properties of both complexes, investigated by cyclic and square-wave voltammetries and UV/Vis spectroscopy, are discussed and compared with those of [Fe(tPY)(2)](PF6)(2) and [Ru(PCP)(tpy)]Cl, which represent the mononuclear components of the heterodinuclear species. An in situ UV/Vis spectroelectrochemical study was performed in order to localize the oxidation and reduction steps and to gain information about the Fe-II-Ru-II communication in the heterodimetallic system [Fe(tpy)(tpyPCP)Ru(tpy)](PF6)(3) mediated by the bridging ligand [tpyPCP]. Both the voltammetric and spectroelectrochemical results point to only very limited electronic interaction between the metal centres in the ground state.

A ruthenium(II) complex stabilized by a highly fluorinated PCP pincer ligand

A novel Ru(II) complex containing an electron-poor, highly fluorinated PCPArF pincer ligand has been synthesized in good yield via a transcyclometalation reaction. The complex has been fully characterized by elemental analysis, 1D and 2D NMR techniques, LTV-vis spectroscopy, and cyclic voltammetry. Single-crystal X-ray structural analysis and DFT calculations were performed. The structural features and electronic properties of the remarkably stable PCPArF-Ru(II) complex 4 have been investigated and show unanticipated differences compared to its protio analogue.

Handling single node failures using agents in computer clusters

The work reported in this paper is motivated towards handling single node failures for parallel summation algorithms in computer clusters. An agent based approach is proposed in which a task to be executed is decomposed to sub-tasks and mapped onto agents that traverse computing nodes. The agents intercommunicate across computing nodes to share information during the event of a predicted node failure. Two single node failure scenarios are considered. The Message Passing Interface is employed for implementing the proposed approach. Quantitative results obtained from experiments reveal that the agent based approach can handle failures more efficiently than traditional failure handling approaches.

Exploring carrier agents in swarm-array computing

How can a bridge be built between autonomic computing approaches and parallel computing systems? The work reported in this paper is motivated towards bridging this gap by proposing a swarm-array computing approach based on ‘Intelligent Agents’ to achieve autonomy for distributed parallel computing systems. In the proposed approach, a task to be executed on parallel computing cores is carried onto a computing core by carrier agents that can seamlessly transfer between processing cores in the event of a predicted failure. The cognitive capabilities of the carrier agents on a parallel processing core serves in achieving the self-ware objectives of autonomic computing, hence applying autonomic computing concepts for the benefit of parallel computing systems. The feasibility of the proposed approach is validated by simulation studies using a multi-agent simulator on an FPGA (Field-Programmable Gate Array) and experimental studies using MPI (Message Passing Interface) on a computer cluster. Preliminary results confirm that applying autonomic computing principles to parallel computing systems is beneficial.