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.

Energetics of climate models: net energy balance and meridional enthalpy transport

We analyze the publicly released outputs of the simulations performed by climate models (CMs) in preindustrial (PI) and Special Report on Emissions Scenarios A1B (SRESA1B) conditions. In the PI simulations, most CMs feature biases of the order of 1 W m −2 for the net global and the net atmospheric, oceanic, and land energy balances. This does not result from transient effects but depends on the imperfect closure of the energy cycle in the fluid components and on inconsistencies over land. Thus, the planetary emission temperature is underestimated, which may explain the CMs' cold bias. In the PI scenario, CMs agree on the meridional atmospheric enthalpy transport's peak location (around 40°N/S), while discrepancies of ∼20% exist on the intensity. Disagreements on the oceanic transport peaks' location and intensity amount to ∼10° and ∼50%, respectively. In the SRESA1B runs, the atmospheric transport's peak shifts poleward, and its intensity increases up to ∼10% in both hemispheres. In most CMs, the Northern Hemispheric oceanic transport decreases, and the peaks shift equatorward in both hemispheres. The Bjerknes compensation mechanism is active both on climatological and interannual time scales. The total meridional transport peaks around 35° in both hemispheres and scenarios, whereas disagreements on the intensity reach ∼20%. With increased CO 2 concentration, the total transport increases up to ∼10%, thus contributing to polar amplification of global warming. Advances are needed for achieving a self-consistent representation of climate as a nonequilibrium thermodynamical system. This is crucial for improving the CMs' skill in representing past and future climate changes.

Computer simulations of structures, energetics and dynamics of myoglobin center dot center dot center dot ligand complexes

Myoglobin has been studied in considerable detail using different experimental and computational techniques over the past decades. Recent developments in time-resolved spectroscopy have provided experimental data amenable to detailed atomistic simulations. The main theme of the present review are results on the structures, energetics and dynamics of ligands ( CO, NO) interacting with myoglobin from computer simulations. Modern computational methods including free energy simulations, mixed quantum mechanics/molecular mechanics simulations, and reactive molecular dynamics simulations provide insight into the dynamics of ligand dynamics in confined spaces complementary to experiment. Application of these methods to calculate and understand experimental observations for myoglobin interacting with CO and NO are presented and discussed.

Computational chemistry for elucidating protein function: energetics and dynamics of myoglobin-ligand systems

State-of-the-art computational methodologies are used to investigate the energetics and dynamics of photodissociated CO and NO in myoglobin (Mb···CO and Mb···NO). This includes the combination of molecular dynamics, ab initio MD, free energy sampling, and effective dynamics methods to compare the results with studies using X-ray crystallography and ultrafast spectroscopy metho ds. It is shown that modern simulation techniques along with careful description of the intermolecular interactions can give quantitative agreement with experiments on complex molecular systems. Based on this agreement predictions for as yet uncharacterized species can be made.

How well do coupled models replicate ocean energetics relevant to ENSO?

Accurate replication of the processes associated with the energetics of the tropical ocean is necessary if coupled GCMs are to simulate the physics of ENSO correctly, including the transfer of energy from the winds to the ocean thermocline and energy dissipation during the ENSO cycle. Here, we analyze ocean energetics in coupled GCMs in terms of two integral parameters describing net energy loss in the system using the approach recently proposed by Brown and Fedorov (J Clim 23:1563–1580, 2010a) and Fedorov (J Clim 20:1108–1117, 2007). These parameters are (1) the efficiency c of the conversion of wind power into the buoyancy power that controls the rate of change of the available potential energy (APE) in the ocean and (2) the e-folding rate a that characterizes the damping of APE by turbulent diffusion and other processes. Estimating these two parameters for coupled models reveals potential deficiencies (and large differences) in how state-of-the-art coupled GCMs reproduce the ocean energetics as compared to ocean-only models and data assimilating models. The majority of the coupled models we analyzed show a lower efficiency (values of c in the range of 10–50% versus 50–60% for ocean-only simulations or reanalysis) and a relatively strong energy damping (values of a-1 in the range 0.4–1 years versus 0.9–1.2 years). These differences in the model energetics appear to reflect differences in the simulated thermal structure of the tropical ocean, the structure of ocean equatorial currents, and deficiencies in the way coupled models simulate ENSO.

Energetics, lifestyle, and reproduction in birds

Theoretical and empirical studies of life history aim to account for resource allocation to the different components of fitness: survival, growth, and reproduction. The pioneering evolutionary ecologist David Lack [(1968) Ecological Adaptations for Breeding in Birds (Methuen and Co.,London)] suggested that reproductive output in birds reflects adaptation to environmental factors such as availability of food and risk of predation, but subsequent studies have not always supported Lack’s interpretation. Here using a dataset for 980 bird species (Dataset S1), a phylogeny, and an explicit measure of reproductive productivity, we test predictions for how mass-specific productivity varies with body size, phylogeny,and lifestyle traits. We find that productivity varies negatively with body size and energetic demands of parental care and positively with extrinsic mortality. Specifically: (i) altricial species are 50% less productive than precocial species; (ii) species with female-only care of offspring are about 20% less productive than species with other methods of parental care; (iii) nonmigrants are 14% less productive than migrants; (iv) frugivores and nectarivores are about 20% less productive than those eating other foods; and (v) pelagic foragers are 40% less productive than those feeding in other habitats. A strong signal of phylogeny suggests that syndromes of similar life-history traits tend to be conservative within clades but also to have evolved independently in different clades. Our results generally support both Lack’s pioneering studies and subsequent research on avian life history.

Energetics of a symmetric circulation including momentum constraints

A theory of available potential energy (APE) for symmetric circulations, which includes momentum constraints, is presented. The theory is a generalization of the classical theory of APE, which includes only thermal constraints on the circulation. Physically, centrifugal potential energy is included along with gravitational potential energy. The generalization relies on the Hamiltonian structure of the conservative dynamics, although (as with classical APE) it still defines the energetics in a nonconservative framework. It follows that the theory is exact at finite amplitude, has a local form, and can be applied to a variety of fluid models. It is applied here to the f -plane Boussinesq equations. It is shown that, by including momentum constraints, the APE of a symmetrically stable flow is zero, while the energetics of a mechanically driven symmetric circulation properly reflect its causality.

The importance of moisture distribution for the growth and energetics of mid-latitude systems

A primitive equation model is used to study the sensitivity of baroclinic wave life cycles to the initial latitude-height distribution of humidity. Diabatic heating is parametrized only as a consequence of condensation in regions of large-scale ascent. Experiments are performed in which the initial relative humidity is a simple function of model level, and in some cases latitude bands are specified which are initially relatively dry. It is found that the presence of moisture can either increase or decrease the peak eddy kinetic energy of the developing wave, depending on the initial moisture distribution. A relative abundance of moisture at mid-latitudes tends to weaken the wave, while a relative abundance at low latitudes tends to strengthen it. This sensitivity exists because competing processes are at work. These processes are described in terms of energy box diagnostics. The most realistic case lies on the cusp of this sensitivity. Further physical parametrizations are then added, including surface fluxes and upright moist convection. These have the effect of increasing wave amplitude, but the sensitivity to initial conditions of relative humidity remains. Finally, 'control' and 'doubled CO2' life cycles are performed, with initial conditions taken from the time-mean zonal-mean output of equilibrium GCM experiments. The attenuation of the wave resulting from reduced baroclinicity is more pronounced than any effect due to changes in initial moisture.

On the validity of single-parcel energetics to assess the importance of internal energy and compressibility effects in stratified fluids

It is often assumed on the basis of single-parcel energetics that compressible effects and conversions with internal energy are negligible whenever typical displacements of fluid parcels are small relative to the scale height of the fluid (defined as the ratio of the squared speed of sound over gravitational acceleration). This paper shows that the above approach is flawed, however, and that a correct assessment of compressible effects and internal energy conversions requires considering the energetics of at least two parcels, or more generally, of mass conserving parcel re-arrangements. As a consequence, it is shown that it is the adiabatic lapse rate and its derivative with respect to pressure, rather than the scale height, which controls the relative importance of compressible effects and internal energy conversions when considering the global energy budget of a stratied fluid. Only when mass conservation is properly accounted for is it possible to explain why available internal energy can account for up to 40 percent of the total available potential energy in the oceans. This is considerably larger than the prediction of single-parcel energetics, according to which this number should be no more than about 2 percent.

Observational and energetics constraints on the non-conservation of potential/Conservative Temperature and implications for ocean modelling

This paper seeks to elucidate the fundamental differences between the nonconservation of potential temperature and that of Conservative Temperature, in order to better understand the relative merits of each quantity for use as the heat variable in numerical ocean models. The main result is that potential temperature is found to behave similarly to entropy, in the sense that its nonconservation primarily reflects production/destruction by surface heat and freshwater fluxes; in contrast, the nonconservation of Conservative Temperature is found to reflect primarily the overall compressible work of expansion/contraction. This paper then shows how this can be exploited to constrain the nonconservation of potential temperature and entropy from observed surface heat fluxes, and the nonconservation of Conservative Temperature from published estimates of the mechanical energy budgets of ocean numerical models. Finally, the paper shows how to modify the evolution equation for potential temperature so that it is exactly equivalent to using an exactly conservative evolution equation for Conservative Temperature, as was recently recommended by IOC et al. (2010). This result should in principle allow ocean modellers to test the equivalence between the two formulations, and to indirectly investigate to what extent the budget of derived nonconservative quantities such as buoyancy and entropy can be expected to be accurately represented in ocean models.

Structure-based energetics of protein interfaces guides foot-and-mouth disease virus vaccine design

Virus capsids are primed for disassembly, yet capsid integrity is key to generating a protective immune response. Foot-and-mouth disease virus (FMDV) capsids comprise identical pentameric protein subunits held together by tenuous noncovalent interactions and are often unstable. Chemically inactivated or recombinant empty capsids, which could form the basis of future vaccines, are even less stable than live virus. Here we devised a computational method to assess the relative stability of protein-protein interfaces and used it to design improved candidate vaccines for two poorly stable, but globally important, serotypes of FMDV: O and SAT2. We used a restrained molecular dynamics strategy to rank mutations predicted to strengthen the pentamer interfaces and applied the results to produce stabilized capsids. Structural analyses and stability assays confirmed the predictions, and vaccinated animals generated improved neutralizing-antibody responses to stabilized particles compared to parental viruses and wild-type capsids.

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.

Probing protein−tannin interactions by isothermal titration microcalorimetry

Isothermal titration microcalorimetry (ITC) has been applied to investigate protein−tannin interactions. Two hydrolyzable tannins were studied, namely myrabolan and tara tannins, for their interaction with bovine serum albumin (BSA), a model globular protein, and gelatin, a model proline-rich random coil protein. Calorimetry data indicate that protein−tannin interaction mechanisms are dependent upon the nature of the protein involved. Tannins apparently interact nonspecifically with the globular BSA, leading to binding saturation at estimated tannin/BSA molar ratios of 48:1 for tara- and 178:1 for myrabolan tannins. Tannins bind to the random coil protein gelatin by a two-stage mechanism. The energetics of the first stage show evidence for cooperative binding of tannins to the protein, while the second stage indicates gradual saturation of binding sites as observed for interaction with BSA. The structure and flexibility of the tannins themselves alters the stoichiometry of the interaction, but does not appear to have any significant affect on the overall binding mechanism observed. This study demonstrates the potential of ITC for providing an insight into the nature of protein−tannin interactions.

Probing protein-tannin interactions by isothermal titration microcalorimetry

Isothermal titration microcalorimetry (ITC) has been applied to investigate protein-tannin interactions. Two hydrolyzable tannins were studied, namely myrabolan and tara tannins, for their interaction with bovine serum albumin (BSA), a model globular protein, and gelatin, a model proline-rich random coil protein. Calorimetry data indicate that protein-tannin interaction mechanisms are dependent upon the nature of the protein involved. Tannins apparently interact nonspecifically with the globular BSA, leading to binding saturation at estimated tannin/BSA molar ratios of 48:1 for tara- and 178:1 for myrabolan tannins. Tannins bind to the random coil protein gelatin by a two-stage mechanism. The energetics of the first stage show evidence for cooperative binding of tannins to the protein, while the second stage indicates gradual saturation of binding sites as observed for interaction with BSA. The structure and flexibility of the tannins themselves alters the stoichiometry of the interaction, but does not appear to have any significant affect on the overall binding mechanism observed. This study demonstrates the potential of ITC for providing an insight into the nature of protein-tannin interactions.

Probing protein-tannin interactions by isothermal titration microcalorimetry

Isothermal titration microcalorimetry (ITC) has been applied to investigate protein-tannin interactions. Two hydrolyzable tannins were studied, namely myrabolan and tara tannins, for their interaction with bovine serum albumin (BSA), a model globular protein, and gelatin, a model proline-rich random coil protein. Calorimetry data indicate that protein-tannin interaction mechanisms are dependent upon the nature of the protein involved. Tannins apparently interact nonspecifically with the globular BSA, leading to binding saturation at estimated tannin/BSA molar ratios of 48:1 for tara- and 178:1 for myrabolan tannins. Tannins bind to the random coil protein gelatin by a two-stage mechanism. The energetics of the first stage show evidence for cooperative binding of tannins to the protein, while the second stage indicates gradual saturation of binding sites as observed for interaction with BSA. The structure and flexibility of the tannins themselves alters the stoichiometry of the interaction, but does not appear to have any significant affect on the overall binding mechanism observed. This study demonstrates the potential of ITC for providing an insight into the nature of protein-tannin interactions.