Constraints on the spectral distribution of energy and enstrophy dissipation in forced two-dimensional turbulence

We study two-dimensional (2D) turbulence in a doubly periodic domain driven by a monoscale-like forcing and damped by various dissipation mechanisms of the form νμ(−Δ)μ. By “monoscale-like” we mean that the forcing is applied over a finite range of wavenumbers kmin≤k≤kmax, and that the ratio of enstrophy injection η≥0 to energy injection ε≥0 is bounded by kmin2ε≤η≤kmax2ε. Such a forcing is frequently considered in theoretical and numerical studies of 2D turbulence. It is shown that for μ≥0 the asymptotic behaviour satisfies ∥u∥12≤kmax2∥u∥2, where ∥u∥2 and ∥u∥12 are the energy and enstrophy, respectively. If the condition of monoscale-like forcing holds only in a time-mean sense, then the inequality holds in the time mean. It is also shown that for Navier–Stokes turbulence (μ=1), the time-mean enstrophy dissipation rate is bounded from above by 2ν1kmax2. These results place strong constraints on the spectral distribution of energy and enstrophy and of their dissipation, and thereby on the existence of energy and enstrophy cascades, in such systems. In particular, the classical dual cascade picture is shown to be invalid for forced 2D Navier–Stokes turbulence (μ=1) when it is forced in this manner. Inclusion of Ekman drag (μ=0) along with molecular viscosity permits a dual cascade, but is incompatible with the log-modified −3 power law for the energy spectrum in the enstrophy-cascading inertial range. In order to achieve the latter, it is necessary to invoke an inverse viscosity (μ<0). These constraints on permissible power laws apply for any spectrally localized forcing, not just for monoscale-like forcing.

Extended Canadian middle atmosphere model: zonal-mean climatology and physical parameterizations

This paper describes the energetics and zonal-mean state of the upward extension of the Canadian Middle Atmosphere Model, which extends from the ground to ~210 km. The model includes realistic parameterizations of the major physical processes from the ground up to the lower thermosphere and exhibits a broad spectrum of geophysical variability. The rationale for the extended model is to examine the nature of the physical and dynamical processes in the mesosphere/lower thermosphere (MLT) region without the artificial effects of an imposed sponge layer which can modify the circulation in an unrealistic manner. The zonal-mean distributions of temperature and zonal wind are found to be in reasonable agreement with observations in most parts of the model domain below ~150 km. Analysis of the global-average energy and momentum budgets reveals a balance between solar extreme ultraviolet heating and molecular diffusion and a thermally direct viscous meridional circulation above 130 km, with the viscosity coming from molecular diffusion and ion drag. Below 70 km, radiative equilibrium prevails in the global mean. In the MLT region between ~70 and 120 km, many processes contribute to the global energy budget. At solstice, there is a thermally indirect meridional circulation driven mainly by parameterized nonorographic gravity-wave drag. This circulation provides a net global cooling of up to 25 K d^-1.

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

Synthesis of novel hyperbranched polymers featuring oxazoline linear units and their application in fast-drying solvent-borne coating formulations

Novel acid-terminated hyperbranched polymers (HBPs) containing adipic acid and oxazoline monomers derived from oleic and linoleic acid have been synthesized via a bulk polymerization procedure. Branching was achieved as a consequence of an acid-catalyzed opening of the oxazoline ring to produce a trifunctional monomer in situ which delivered branching levels of >45% as determined by 1H and 13C NMR spectroscopy. The HBPs were soluble in common solvents, such as CHCl3, acetone, tetrahydrofuran, dimethylformamide, and dimethyl sulfoxide and were further functionalized by addition of citronellol to afford white-spirit soluble materials that could be used in coating formulations. During end group modification, a reduction in branching levels of the HBPs (down to 12–24%) was observed, predominantly on account of oxazoline ring reformation and trans-esterification processes under the reaction conditions used. In comparison to commercial alkyd resin paint coatings, formulations of the citronellol-functionalized hyperbranched materials blended with a commercial alkyd resin exhibited dramatic decreases of the blend viscosity when the HBP content was increased. The curing characteristics of the HBP/alkyd blend formulations were studied by dynamic mechanical analysis which revealed that the new coatings cured more quickly and produced tougher materials than otherwise identical coatings prepared from only the commercial alkyd resins.

Ice internal friction: Standard theoretical perspectives on friction codified, adapted for the unusual rheology of ice, and unified

Sea ice contains flaws including frictional contacts. We aim to describe quantitatively the mechanics of those contacts, providing local physics for geophysical models. With a focus on the internal friction of ice, we review standard micro-mechanical models of friction. The solid's deformation under normal load may be ductile or elastic. The shear failure of the contact may be by ductile flow, brittle fracture, or melting and hydrodynamic lubrication. Combinations of these give a total of six rheological models. When the material under study is ice, several of the rheological parameters in the standard models are not constant, but depend on the temperature of the bulk, on the normal stress under which samples are pressed together, or on the sliding velocity and acceleration. This has the effect of making the shear stress required for sliding dependent on sliding velocity, acceleration, and temperature. In some cases, it also perturbs the exponent in the normal-stress dependence of that shear stress away from the value that applies to most materials. We unify the models by a principle of maximum displacement for normal deformation, and of minimum stress for shear failure, reducing the controversy over the mechanism of internal friction in ice to the choice of values of four parameters in a single model. The four parameters represent, for a typical asperity contact, the sliding distance required to expel melt-water, the sliding distance required to break contact, the normal strain in the asperity, and the thickness of any ductile shear zone.

Potential sources of mouth drying in beverages fortified with dairy proteins: a comparison of casein and whey-rich ingredients

Oral nutritional supplement drinks (ONS) are beverages high in dairy proteins that are prescribed to individuals at risk of malnutrition. Consumption of ONS is poor in elderly care facilities, with patients commenting that the sensory attributes of these drinks reduce their enjoyment and willingness to consume. Mouth drying is an attribute of ONS found to build with repeated consumption, which may further limit liking of these products. This study investigated the sources of drying sensations by sequential profiling, with a trained sensory panel rating a range of model milk systems and ONS over repeated sips and during after-effects. Sequential profiling found that fortification of milk with both caseinate and whey protein concentrate significantly increased the perception of mouth drying over repeated consumption, increasing by between 35 and 85% over consumption of 40mL. Enrichment of ONS with either whey protein concentrate or milk protein concentrate to a total protein content of 8.7% (wt/wt) resulted in whey and casein levels of 4.3:4.4% and 1.7:7.0% respectively. The product higher in whey protein was substantially more mouth drying, implying that whey proteins may be the most important contributor to mouth drying in ONS. However, efforts to mask mouth drying of protein-fortified milk by increasing sweetness or fat level were unsuccessful at the levels tested. Increasing the viscosity of protein-fortified milk led to a small but significant reduction in mouth drying. However, this approach was not successful when tested within complete ONS. Further analysis is required into the mechanism of protein-derived mouth drying to mask negative sensations and improve the enjoyment and consumption of protein-rich ONS.

Ozonolysis of methyl oleate monolayers at the air–water interface: oxidation kinetics, reaction products and atmospheric implications

Ozonolysis of methyl oleate monolayers at the air–water interface results in surprisingly rapid loss of material through cleavage of the C[double bond, length as m-dash]C bond and evaporation/dissolution of reaction products. We determine using neutron reflectometry a rate coefficient of (5.7 ± 0.9) × 10−10 cm2 molecule−1 s−1 and an uptake coefficient of [similar]3 × 10−5 for the oxidation of a methyl ester monolayer: the atmospheric lifetime is [similar]10 min. We obtained direct experimental evidence that <2% of organic material remains at the surface on atmospheric timescales. Therefore known long atmospheric residence times of unsaturated fatty acids suggest that these molecules cannot be present at the interface throughout their ageing cycle, i.e. the reported atmospheric longevity is likely to be attributed to presence in the bulk and viscosity-limited reactive loss. Possible reaction products were characterized by ellipsometry and uncertainties in the atmospheric fate of organic surfactants such as oleic acid and its methyl ester are discussed. Our results suggest that a minor change to the structure of the molecule (fatty acid vs. its methyl ester) considerably impacts on reactivity and fate of the organic film.

Creep and recovery of magnetorheological fluids: experiments and simulations

A direct comparative study on the creep-recovery behavior of conventional MR fluids is carried out using magnetorheometry and particle-level simulations. Two particle concentrations are investigated (ϕ=0.05 and 0.30) at two different magnetic field strengths (53 kA•m-1 and 173 kA•m-1) in order to match the yield stresses developed in both systems for easier comparison. Simulations are mostly started with random initial structures with some additional tests of using preassembled single chains in the low concentration case. Experimental and simulation data are in good qualitative agreement. The results demonstrate three regions in the creep curves: i) In the initial viscoelastic region, the chain-like (at ϕ=0.05) or percolated three-dimensional network (at ϕ=0.30) structures fill up the gap and the average cluster size remains constant; ii) Above a critical strain of 10 %, in the retardation region, these structures begin to break and rearrange under shear. At large enough imposed stress values, they transform into thin sheet-like or thick lamellar structures, depending on the particle concentration; iii) Finally in the case of larger strain values either the viscosity diverges (at low stress values) or reaches a constant low value (at high stress values), showing a clear bifurcation behavior. For stresses below the bifurcation point the MR fluid is capable to recover the strain by a certain fraction. However, no recovery is observed for large stress values.

Formulation and implementation of a residual-mean ocean circulation model

A parameterization of mesoscale eddies in coarse-resolution ocean general circulation models (GCM) is formulated and implemented using a residual-mean formalism. In that framework, mean buoyancy is advected by the residual velocity (the sum of the Eulerian and eddy-induced velocities) and modified by a residual flux which accounts for the diabatic effects of mesoscale eddies. The residual velocity is obtained by stepping forward a residual-mean momentum equation in which eddy stresses appear as forcing terms. Study of the spatial distribution of eddy stresses, derived by using them as control parameters to ‘‘fit’’ the residual-mean model to observations, supports the idea that eddy stresses can be likened to a vertical down-gradient flux of momentum with a coefficient which is constant in the vertical. The residual eddy flux is set to zero in the ocean interior, where mesoscale eddies are assumed to be quasi-adiabatic, but is parameterized by a horizontal down-gradient diffusivity near the surface where eddies develop a diabatic component as they stir properties horizontally across steep isopycnals. The residual-mean model is implemented and tested in the MIT general circulation model. It is shown that the resulting model (1) has a climatology that is superior to that obtained using the Gent and McWilliams parameterization scheme with a spatially uniform diffusivity and (2) allows one to significantly reduce the (spurious) horizontal viscosity used in coarse resolution GCMs.

Ring-opening polymerization in molten PEEK: transient reduction of melt-viscosity by macrocyclic aromatic thioetherketones

Blends of PEEK with macrocyclic thioether-ketones show initial melt-viscosities reduced by more than an order of magnitude relative to the polymer itself, enabling more facile processing and fabrication. On raising the temperature of the melt, however, the macrocycle undergoes spontaneous, entropically-driven ring-opening polymerization (ED-ROP), so that the properties of the final polymer should not, in principle, be compromised by the presence of low-MW macrocyclic material.

Optimization of a sponge cake formulation with inulin as fat replacer: structure, physicochemical, and sensory properties

The effects of several fat replacement levels (0%, 35%, 50%, 70%, and 100%) by inulin in sponge cake microstructure and physicochemical properties were studied. Oil substitution for inulin decreased significantly (P < 0.05) batter viscosity, giving heterogeneous bubbles size distributions as it was observed by light microscopy. Using confocal laser scanning microscopy the fat was observed to be located at the bubbles’ interface, enabling an optimum crumb cake structure development during baking. Cryo-SEM micrographs of cake crumbs showed a continuous matrix with embedded starch granules and coated with oil; when fat replacement levels increased, starch granules appeared as detached structures. Cakes with fat replacement up to 70% had a high crumb air cell values; they were softer and rated as acceptable by an untrained sensory panel (n = 51). So, the reformulation of a standard sponge cake recipe to obtain a new product with additional health benefits and accepted by consumers is achieved.

Functionality of lipase and emulsifiers in low-fat cakes with inulin

The functional effects of lipase (0.003 and 0.006 g/100 g of flour) and emulsifier (0.5 and 1 g/100 g of flour) on fat-replaced (0%, 50% and 70%) batters and cakes with inulin (0, 7.5 and 10 g/100 g/of flour, respectively) were studied. Emulsifier addition significantly lowered the relative density of the batter. Emulsifier incorporation increased the viscoelastic properties of the batter. In contrast, lipase incorporation decreased the degree of system structuring. The evolution of the dynamic moduli and complex viscosity with rising temperatures were studied. Batters with 1 g/100 g emulsifier displayed a significantly lower complex viscosity during heating, resulting in collapsed cakes. Differential scanning calorimetry results revealed that the thermal setting in the control cakes occurred at higher temperatures, and accordingly, greater cake expansion was observed. Cakes with 0.003 g/100 g lipase or 0.5 g/100 g emulsifier displayed volume and crumb cell structure that were similar to those of control cakes. Higher concentrations of both improvers gave rise to cakes with lower volume, higher hardness and lower springiness. During storage time, cakes with lipase displayed lower hardness. Both improvers, at low concentrations, could improve certain physical characteristics, such as crumb structure, of fat-replaced cakes with inulin.

Dehydrodipeptide hydrogelators containing naproxen N‑Capped tryptophan: self-assembly, hydrogel characterization, and evaluation as potential drug nanocarriers

In this work, we introduce dipeptides containing tryptophan N-capped with the nonsteroidal anti-inflammatory drug naproxen and C-terminal dehydroamino acids, dehydrophenylalanine (ΔPhe), dehydroaminobutyric acid (ΔAbu), and dehydroalanine (ΔAla) as efficacious protease resistant hydrogelators. Optimized conditions for gel formation are reported. Transmission electron microscopy experiments revealed that the hydrogels consist of networks of micro/nanosized fibers formed by peptide self-assembly. Fluorescence and circular dichroism spectroscopy indicate that the self-assembly process is driven by stacking interactions of the aromatic groups. The naphthalene groups of the naproxen moieties are highly organized in the fibers through chiral stacking. Rheological experiments demonstrated that the most hydrophobic peptide (containing C-terminal ΔPhe) formed more elastic gels at lower critical gelation concentrations. This gel revealed irreversible breakup, while the C-terminal ΔAbu and ΔAla gels, although less elastic, exhibited structural recovery and partial healing of the elastic properties. A potential antitumor thieno[3,2-b]pyridine derivative was incorporated (noncovalently) into the gel formed by the hydrogelator containing C-terminal ΔPhe residue. Fluorescence and Förster resonance energy transfer measurements indicate that the drug is located in a hydrophobic environment, near/associated with the peptide fibers, establishing this type of hydrogel as a good drug-nanocarrier candidate.

An adhesive elastomeric supramolecular polyurethane healable at body temperature

In this paper, we report the synthesis and healing ability of a non-cytotoxic supramolecular polyurethane network whose mechanical properties can be recovered efficiently (> 99%) at the temperature of the human body (37 ºC). Rheological analysis revealed an acceleration in the drop of the storage modulus above 37 ºC, on account of the dissociation of the supramolecular polyurethane network, and this decrease in viscosity enables the efficient recovery of the mechanical properties. Microscopic and mechanical characterisation has shown that this material is able to recover mechanical properties across a damage site with minimal contact required between the interfaces and also demonstrated that the mechanical properties improved when compared to other low temperature healing elastomers or gel-like materials. The supramolecular polyurethane was found to be non-toxic in a cytotoxicity assay carried out in human skin fibroblasts (cell viability > 94% and non-significantly different compared to the untreated control). This supramolecular network material also exhibited excellent adhesion to pig skin and could be healed completely in situ post damage indicating that biomedical applications could be targeted, such as artificial skin or wound dressings with supramolecular materials of this type.