Viscous coupling of shear-free turbulence across nearly flat fluid interfaces

The interactions between shear-free turbulence in two regions (denoted as + and − on either side of a nearly flat horizontal interface are shown here to be controlled by several mechanisms, which depend on the magnitudes of the ratios of the densities, ρ+/ρ−, and kinematic viscosities of the fluids, μ+/μ−, and the root mean square (r.m.s.) velocities of the turbulence, u0+/u0−, above and below the interface. This study focuses on gas–liquid interfaces so that ρ+/ρ− ≪ 1 and also on where turbulence is generated either above or below the interface so that u0+/u0− is either very large or very small. It is assumed that vertical buoyancy forces across the interface are much larger than internal forces so that the interface is nearly flat, and coupling between turbulence on either side of the interface is determined by viscous stresses. A formal linearized rapid-distortion analysis with viscous effects is developed by extending the previous study by Hunt & Graham (J. Fluid Mech., vol. 84, 1978, pp. 209–235) of shear-free turbulence near rigid plane boundaries. The physical processes accounted for in our model include both the blocking effect of the interface on normal components of the turbulence and the viscous coupling of the horizontal field across thin interfacial viscous boundary layers. The horizontal divergence in the perturbation velocity field in the viscous layer drives weak inviscid irrotational velocity fluctuations outside the viscous boundary layers in a mechanism analogous to Ekman pumping. The analysis shows the following. (i) The blocking effects are similar to those near rigid boundaries on each side of the interface, but through the action of the thin viscous layers above and below the interface, the horizontal and vertical velocity components differ from those near a rigid surface and are correlated or anti-correlated respectively. (ii) Because of the growth of the viscous layers on either side of the interface, the ratio uI/u0, where uI is the r.m.s. of the interfacial velocity fluctuations and u0 the r.m.s. of the homogeneous turbulence far from the interface, does not vary with time. If the turbulence is driven in the lower layer with ρ+/ρ− ≪ 1 and u0+/u0− ≪ 1, then uI/u0− ~ 1 when Re (=u0−L−/ν−) ≫ 1 and R = (ρ−/ρ+)(v−/v+)1/2 ≫ 1. If the turbulence is driven in the upper layer with ρ+/ρ− ≪ 1 and u0+/u0− ≫ 1, then uI/u0+ ~ 1/(1 + R). (iii) Nonlinear effects become significant over periods greater than Lagrangian time scales. When turbulence is generated in the lower layer, and the Reynolds number is high enough, motions in the upper viscous layer are turbulent. The horizontal vorticity tends to decrease, and the vertical vorticity of the eddies dominates their asymptotic structure. When turbulence is generated in the upper layer, and the Reynolds number is less than about 106–107, the fluctuations in the viscous layer do not become turbulent. Nonlinear processes at the interface increase the ratio uI/u0+ for sheared or shear-free turbulence in the gas above its linear value of uI/u0+ ~ 1/(1 + R) to (ρ+/ρ−)1/2 ~ 1/30 for air–water interfaces. This estimate agrees with the direct numerical simulation results from Lombardi, De Angelis & Bannerjee (Phys. Fluids, vol. 8, no. 6, 1996, pp. 1643–1665). Because the linear viscous–inertial coupling mechanism is still significant, the eddy motions on either side of the interface have a similar horizontal structure, although their vertical structure differs.

Impact of postprandial glycaemia on health and prevention of disease

Postprandial glucose, together with related hyperinsulinemia and lipidaemia, has been implicated in the development of chronic metabolic diseases like obesity, type 2 diabetes mellitus (T2DM) and cardiovascular disease (CVD). In this review, available evidence is discussed on postprandial glucose in relation to body weight control, the development of oxidative stress, T2DM, and CVD and in maintaining optimal exercise and cognitive performance. There is mechanistic evidence linking postprandial glycaemia or glycaemic variability to the development of these conditions or in the impairment in cognitive and exercise performance. Nevertheless, postprandial glycaemia is interrelated with many other (risk) factors as well as to fasting glucose. In many studies, meal-related glycaemic response is not sufficiently characterized, or the methodology with respect to the description of food or meal composition, or the duration of the measurement of postprandial glycaemia is limited. It is evident that more randomized controlled dietary intervention trials using effective low vs. high glucose response diets are necessary in order to draw more definite conclusions on the role of postprandial glycaemia in relation to health and disease. Also of importance is the evaluation of the potential role of the time course of postprandial glycaemia.

Interaction of plant growth regulators and reactive oxygen species to regulate petal senescence in wallflowers (Erysimum linifolium)

Background In many species floral senescence is coordinated by ethylene. Endogenous levels rise, and exogenous application accelerates senescence. Furthermore, floral senescence is often associated with increased reactive oxygen species, and is delayed by exogenously applied cytokinin. However, how these processes are linked remains largely unresolved. Erysimum linifolium (wallflower) provides an excellent model for understanding these interactions due to its easily staged flowers and close taxonomic relationship to Arabidopsis. This has facilitated microarray analysis of gene expression during petal senescence and provided gene markers for following the effects of treatments on different regulatory pathways. Results In detached Erysimum linifolium (wallflower) flowers ethylene production peaks in open flowers. Furthermore senescence is delayed by treatments with the ethylene signalling inhibitor silver thiosulphate, and accelerated with ethylene released by 2-chloroethylphosphonic acid. Both treatments with exogenous cytokinin, or 6-methyl purine (which is an inhibitor of cytokinin oxidase), delay petal senescence. However, treatment with cytokinin also increases ethylene biosynthesis. Despite the similar effects on senescence, transcript abundance of gene markers is affected differentially by the treatments. A significant rise in transcript abundance of WLS73 (a putative aminocyclopropanecarboxylate oxidase) was abolished by cytokinin or 6-methyl purine treatments. In contrast, WFSAG12 transcript (a senescence marker) continued to accumulate significantly, albeit at a reduced rate. Silver thiosulphate suppressed the increase in transcript abundance both of WFSAG12 and WLS73. Activity of reactive oxygen species scavenging enzymes changed during senescence. Treatments that increased cytokinin levels, or inhibited ethylene action, reduced accumulation of hydrogen peroxide. Furthermore, although auxin levels rose with senescence, treatments that delayed early senescence did not affect transcript abundance of WPS46, an auxin-induced gene. Conclusions A model for the interaction between cytokinins, ethylene, reactive oxygen species and auxin in the regulation of floral senescence in wallflowers is proposed. The combined increase in ethylene and reduction in cytokinin triggers the initiation of senescence and these two plant growth regulators directly or indirectly result in increased reactive oxygen species levels. A fall in conjugated auxin and/or the total auxin pool eventually triggers abscission.