A general method for finding extremal states of Hamiltonian dynamical systems, with applications to perfect fluids

In addition to the Hamiltonian functional itself, non-canonical Hamiltonian dynamical systems generally possess integral invariants known as ‘Casimir functionals’. In the case of the Euler equations for a perfect fluid, the Casimir functionals correspond to the vortex topology, whose invariance derives from the particle-relabelling symmetry of the underlying Lagrangian equations of motion. In a recent paper, Vallis, Carnevale & Young (1989) have presented algorithms for finding steady states of the Euler equations that represent extrema of energy subject to given vortex topology, and are therefore stable. The purpose of this note is to point out a very general method for modifying any Hamiltonian dynamical system into an algorithm that is analogous to those of Vallis etal. in that it will systematically increase or decrease the energy of the system while preserving all of the Casimir invariants. By incorporating momentum into the extremization procedure, the algorithm is able to find steadily-translating as well as steady stable states. The method is applied to a variety of perfect-fluid systems, including Euler flow as well as compressible and incompressible stratified flow.

An exact local conservation theorem for finite-amplitude disturbances to non-parallel shear flows, with remarks on Hamiltonian structure and on Arnol'd's stability theorems

Disturbances of arbitrary amplitude are superposed on a basic flow which is assumed to be steady and either (a) two-dimensional, homogeneous, and incompressible (rotating or non-rotating) or (b) stably stratified and quasi-geostrophic. Flow over shallow topography is allowed in either case. The basic flow, as well as the disturbance, is assumed to be subject neither to external forcing nor to dissipative processes like viscosity. An exact, local ‘wave-activity conservation theorem’ is derived in which the density A and flux F are second-order ‘wave properties’ or ‘disturbance properties’, meaning that they are O(a2) in magnitude as disturbance amplitude a [rightward arrow] 0, and that they are evaluable correct to O(a2) from linear theory, to O(a3) from second-order theory, and so on to higher orders in a. For a disturbance in the form of a single, slowly varying, non-stationary Rossby wavetrain, $\overline{F}/\overline{A}$ reduces approximately to the Rossby-wave group velocity, where (${}^{-}$) is an appropriate averaging operator. F and A have the formal appearance of Eulerian quantities, but generally involve a multivalued function the correct branch of which requires a certain amount of Lagrangian information for its determination. It is shown that, in a certain sense, the construction of conservable, quasi-Eulerian wave properties like A is unique and that the multivaluedness is inescapable in general. The connection with the concepts of pseudoenergy (quasi-energy), pseudomomentum (quasi-momentum), and ‘Eliassen-Palm wave activity’ is noted. The relationship of this and similar conservation theorems to dynamical fundamentals and to Arnol'd's nonlinear stability theorems is discussed in the light of recent advances in Hamiltonian dynamics. These show where such conservation theorems come from and how to construct them in other cases. An elementary proof of the Hamiltonian structure of two-dimensional Eulerian vortex dynamics is put on record, with explicit attention to the boundary conditions. The connection between Arnol'd's second stability theorem and the suppression of shear and self-tuning resonant instabilities by boundary constraints is discussed, and a finite-amplitude counterpart to Rayleigh's inflection-point theorem noted

Spectral nonlocality, absolute equilibria and Kraichnan-Leith-Batchelor phenomenology in two-dimensional turbulent energy cascades

We study the degree to which Kraichnan–Leith–Batchelor (KLB) phenomenology describes two-dimensional energy cascades in α turbulence, governed by ∂θ/∂t+J(ψ,θ)=ν∇2θ+f, where θ=(−Δ)α/2ψ is generalized vorticity, and ψ^(k)=k−αθ^(k) in Fourier space. These models differ in spectral non-locality, and include surface quasigeostrophic flow (α=1), regular two-dimensional flow (α=2) and rotating shallow flow (α=3), which is the isotropic limit of a mantle convection model. We re-examine arguments for dual inverse energy and direct enstrophy cascades, including Fjørtoft analysis, which we extend to general α, and point out their limitations. Using an α-dependent eddy-damped quasinormal Markovian (EDQNM) closure, we seek self-similar inertial range solutions and study their characteristics. Our present focus is not on coherent structures, which the EDQNM filters out, but on any self-similar and approximately Gaussian turbulent component that may exist in the flow and be described by KLB phenomenology. For this, the EDQNM is an appropriate tool. Non-local triads contribute increasingly to the energy flux as α increases. More importantly, the energy cascade is downscale in the self-similar inertial range for 2.5<α<10. At α=2.5 and α=10, the KLB spectra correspond, respectively, to enstrophy and energy equipartition, and the triad energy transfers and flux vanish identically. Eddy turnover time and strain rate arguments suggest the inverse energy cascade should obey KLB phenomenology and be self-similar for α<4. However, downscale energy flux in the EDQNM self-similar inertial range for α>2.5 leads us to predict that any inverse cascade for α≥2.5 will not exhibit KLB phenomenology, and specifically the KLB energy spectrum. Numerical simulations confirm this: the inverse cascade energy spectrum for α≥2.5 is significantly steeper than the KLB prediction, while for α<2.5 we obtain the KLB spectrum.

Flow-induced morphological instability of a mushy layer

A morphological instability of a mushy layer due to a forced flow in the melt is analysed. The instability is caused by flow induced in the mushy layer by Bernoulli suction at the crests of a sinusoidally perturbed mush–melt interface. The flow in the mushy layer advects heat away from crests which promotes solidification. Two linear stability analyses are presented: the fundamental mechanism for instability is elucidated by considering the case of uniform flow of an inviscid melt; a more complete analysis is then presented for the case of a parallel shear flow of a viscous melt. The novel instability mechanism we analyse here is contrasted with that investigated by Gilpin et al. (1980) and is found to be more potent for the case of newly forming sea ice.

Similarity solutions describing the melting of a mushy layer

A model of the melting of a mushy region in the absence of fluid flow is presented. Similarity solutions are obtained which are used to describe melting from a hot plate with and without the generation of a completely molten region. These solutions are extended to describe the melting of a mushy region in contact with a hot liquid. A significant feature of melting mushy regions is that the phase change occurs internally by dissolution. Our solutions for melting of a mushy region are used to investigate this internal phase change and are compared with the classical Neumann solutions for melting of a pure substance.

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.

Biology and reproductive behavior of Murgantia histrionica (Heteroptera: Pentatomidae)

Life history parameters and reproductive behaviors of the harlequin bug, Murgantia histrionica Hahn (Heteroptera: Pentatomidae), were determined. Total developmental time from egg to adult was ≈48 d. After a sexual maturation period of ≈7 d, both sexes mated repeatedly, with females laying multiple egg masses of 12 eggs at intervals of 3 d. Adult females lived an average of 41 d, whereas adult males lived an average of 25 d. Courtship and copulation activities peaked in the middle of the photophase. In mating experiments in which mixed sex pairs of virgin and previously mated bugs were combined in all possible combinations, the durations of courtship and copulation by virgin males were significantly longer with both virgin and previously mated females than the same behaviors for previously mated males. When given a choice between a virgin or previously mated female, previously mated males preferred to mate with virgin females, whereas virgin males showed no preference for virgin over previously mated females. Analyses of mating behaviors with ethograms and behavioral transition matrices suggested that a primary reason for failure to copulate by virgin males was the incorrect rotation of their pygophores to the copulation position, so that successful alignment of the genitalia could not occur.

Technical note: how accurate can stalagmite formation temperatures be determined using vapour bubble radius measurements in fluid inclusions?

Stalagmites are natural archives containing detailed information on continental climate variability of the past. Microthermometric measurements of fluid inclusion homogenisation temperatures allow determination of stalagmite formation temperatures by measuring the radius of stable laser-induced vapour bubbles inside the inclusions. A reliable method for precisely measuring the radius of vapour bubbles is presented. The method is applied to stalagmite samples for which the formation temperature is known. An assessment of the bubble radius measurement accuracy and how this error influences the uncertainty in determining the formation temperature is provided. We demonstrate that the nominal homogenisation temperature of a single inclusion can be determined with an accuracy of ±0.25 °C, if the volume of the inclusion is larger than 105 μm3. With this method, we could measure in a proof-of-principle investigation that the formation temperature of 10–20 yr old inclusions in a stalagmite taken from the Milandre cave is 9.87 ± 0.80 °C, while the mean annual surface temperature, that in the case of the Milandre cave correlates well with the cave temperature, was 9.6 ± 0.15 °C, calculated from actual measurements at that time, showing a very good agreement. Formation temperatures of inclusions formed during the last 450 yr are found in a temperature range between 8.4 and 9.6 °C, which corresponds to the calculated average surface temperature. Paleotemperatures can thus be determined within ±1.0 °C.

Glacial-interglacial temperature change in the tropical West Pacific: a comparison of stalagmite-based paleo-thermometers

In the tropics, geochemical records from stalagmites have so far mainly been used to qualitatively reconstruct changes in precipitation, but several new methods to reconstruct past temperatures from stalagmite material have emerged recently: i) liquid–vapor homogenization of fluid inclusion water ii) noble gas concentrations in fluid inclusion water, iii) the partitioning of oxygen isotopes between fluid inclusion water and calcite, and iv) the abundance of the 13C18O16O (‘clumped’) isotopologue in calcite. We present, for the first time, a direct comparison of these four paleo-thermometers by applying them to a fossil stalagmite covering nearly two glacial–interglacial cycles (Marine Isotope Stages (MIS) 12–9) and to two modern stalagmites, all from northern Borneo. The temperature estimates from the different methods agree in most cases within errors for both the old and recent samples; reconstructed formation temperatures of the recent samples match within 2-sigma errors with measured cave temperatures. However, slight but systematic deviations are observed between noble gas and liquid–vapor homogenization temperatures. Whereas the temperature sensitivity of fluid inclusion δ18O and clumped isotopes is currently debated, we find that the calibration of Tremaine et al. (2011) for fluid inclusion δ18O and a synthetic calcite-based clumped isotope calibration (Ziegler et al., in prep.) yield temperature estimates consistent with the other methods. All methods (with the potential exception of clumped isotopes) show excellent agreement on the amplitude of glacial–interglacial temperature change, indicating temperature shifts of 4–5 °C. This amplitude is similar to the amplitude of Mg/Ca-based regional sea surface temperature records, when correcting for sea level driven changes in cave elevation. Our reconstruction of tropical temperature evolution over the time period from 440 to 320 thousand years ago (ka) adds support to the view that climate sensitivity to varying greenhouse forcing is substantial also in the deep tropics.

Stability of probiotic Lactobacillus plantarum in dry microcapsules under accelerated storage conditions

This study investigated the stability of freeze dried and fluid bed dried alginate microcapsules coated with chitosan containing model probiotic bacteria, Lactobacillus plantarum, during storage for up to 45 days at different water activities (0.11, 0.23, 0.40 and 0.70) and temperatures (4, 30 and 37 °C). The loss in cell viability was around 0.8 log in the case of fluid bed drying and around 1.3 in the case of freeze drying, with the former method resulting in dried capsules of smaller size (~ 1 mm vs 1.3 mm), more irregular shape, and with a rougher surface. In both cases, the water activity and water content were less than 0.25 and 10% w/w, respectively, which favours high storage stability. The storage stability studies demonstrated that as the water activity and temperature decreased the survival of the dried encapsulated cells increased. Considerably better survival was observed for fluid bed dried encapsulated cells compared to freeze dried encapsulated cells and freeze dried free cells with 10% sucrose (control), and in some cases, e.g. at 4 and 30 °C at water activities of 0.11, 0.23 and 0.40, there was more than 1 log difference after 45 days, with concentrations higher than 108 CFU/g after 45 days of storage. The results indicate that fluid bed drying is an effective and efficient manufacturing method to produce probiotic containing capsules with enhanced storage stability.

Effects of oxidative stress on the cardiac myocyte proteome: modifications to peroxiredoxins and small heat shock proteins

Endogenous oxidative stress is a likely cause of cardiac myocyte death in vivo. We examined the early (0-2 h) changes in the proteome of isolated cardiac myocytes from neonatal rats exposed to H2O2 (0.1 mM), focussing on proteins with apparent molecular masses of between 20 and 30 kDa. Proteins were separated by two-dimensional gel electrophoresis (2DGE), located by silver-staining and identified by mass spectrometry. Incorporation of [35S]methionine or 32Pi was also studied. For selected proteins, transcript abundance was examined by reverse transcriptase-polymerase chain reaction. Of the 38 protein spots in the region, 23 were identified. Two families showed changes in 2DGE migration or abundance with H2O2 treatment: the peroxiredoxins and two small heat shock protein (Hsp) family members: heat shock 27 kDa protein 1 (Hsp25) and alphaB-crystallin. Peroxiredoxins shifted to lower pI values and this was probably attributable to 'over-oxidation' of active site Cys-residues. Hsp25 also shifted to lower pI values but this was attributable to phosphorylation. alphaB-crystallin migration was unchanged but its abundance decreased. Transcripts encoding peroxiredoxins 2 and 5 increased significantly. In addition, 10 further proteins were identified. For two (glutathione S-transferase pi, translationally-controlled tumour protein), we could not find any previous references indicating their occurrence in cardiac myocytes. We conclude that exposure of cardiac myocytes to oxidative stress causes post-translational modification in two protein families involved in cytoprotection. These changes may be potentially useful diagnostically. In the short term, oxidative stress causes few detectable changes in global protein abundance as assessed by silver-staining.