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

Local form interference in biological motion perception

Peer reviewedPublisher PD

Revisiting the 1954 Suspension Experiments of R. A.Bagnold

In 1954 R. A. Bagnold published his seminal findings on the rheological properties of a liquid-solid suspension. Although this work has been cited extensively over the last fifty years, there has not been a critical review of the experiments. The purpose of this study is to examine the work and to suggest an alternative reason for the experimental findings. The concentric cylinder rheometer was designed to measure simultaneously the shear and normal forces for a wide range of solid concentrations, fluid viscosities and shear rates. As presented by Bagnold, the analysis and experiments demonstrated that the shear and normal forces depended linearly on the shear rate in the 'macroviscous' regime; as the grain-to-grain interactions increased in the 'grain-inertia' regime, the stresses depended on the square of the shear rate and were independent of the fluid viscosity. These results, however, appear to be dictated by the design of the experimental facility. In Bagnold's experiments, the height (h) of the rheometer was relatively short compared to the spacing (t) between the rotating outer and stationary inner cylinder (h/t=4.6). Since the top and bottom end plates rotated with the outer cylinder, the flow contained two axisymmetric counter-rotating cells in which flow moved outward along the end plates and inward through the central region of the annulus. At higher Reynolds numbers, these cells contributed significantly to the measured torque, as demonstrated by comparing Bagnold's pure-fluid measurements with studies on laminar-to-turbulent transitions that pre-date the 1954 study. By accounting for the torque along the end walls, Bagnold's shear stress measurements can be estimated by modelling the liquid-solid mixture as a Newtonian fluid with a corrected viscosity that depends on the solids concentration. An analysis of the normal stress measurements was problematic because the gross measurements were not reported and could not be obtained

TAXATION-FEDERAL ESTATE TAX-TRANSFERS OF LIFE INSURANCE IN CONTEMPLATION OF DEATH

Insurance policies on the life of a decedent are ordinarily included in his gross estate according to the provisions of section 811 (g) of the Internal Revenue Code. Where the policy is payable to a beneficiary other than the executor, it is taxable under section 811(g)(2): (1) if the decedent paid premiums on the policy, in proportion to the amount of premiums paid by him in relation to the total premiums paid, or (2) if the decedent possessed at his death any of the incidents of ownership. However, these provisions are not exclusive; even though section 811 (g) is inapplicable, insurance policies transferred by the decedent during his lifetime may still be subject to estate tax if the transfer falls within section 811(c), as a transfer in contemplation of death or intended to take effect in possession or enjoyment at or after death. At present, the interpretations of the possession or enjoyment clause would indicate that where the transfer is irrevocable, the transfer of insurance would not be taxable as intended to take effect in possession or enjoyment at or after death. Although it is not easy in all cases to distinguish the two clauses, our principal concern is with the contemplation of death provision

Explaining two circumnuclear star forming rings in NGC5248

The distribution of gas in the central kiloparsec of a galaxy has a dynamically rapid evolution. Nonaxisymmetries in the gravitational potential of the galactic disk, such as a large scale stellar bar or spiral, can lead to significant radial motion of gaseous material from larger radii to the central region. The large influx of gas and the subsequent star formation keep the central region constantly changing. However, the ability of gas to reach the nucleus proper to fuel an AGN phase is not guaranteed. Gas inflow can be halted at a circumnuclear star forming ring several hundred parsec away. The nearby galaxy NGC5248 is especially interesting in this sense since it is said to host 2 circumnuclear star forming rings at 100pc and 370pc from its quiescent nucleus. Here we present new subarcsecond PdBI+30m CO(2-1) emission line observations of the central region. For the first time the molecular gas distribution at the smallest stellar ring is resolved into a gas ring, consistent with the presence of a quiescent nucleus. However, the molecular gas shows no ring structure at the larger ring. We combine analyses of the gaseous and stellar content in the central kiloparsec of this galaxy to understand the gas distribution and dynamics of this star forming central region. We discuss the probability of two scenarios leading to the current observations, given our full understanding of this system, and discuss whether there are really two circumnuclear star forming rings in this galaxy.Comment: Accepted for publication in A&A, 14pages + long tabl

Evidence for CO2-rich fluids in rocks from the type charnockite area near Pallavaram, Tamil Nadu

Fluid inclusion and mineral chemistry data was presented for samples from the type charnockite area near Pallavaram (Tamil Nadu, India). The results indicate the presence of a dense CO2 fluid phase, but the data cannot distinguish between influx of this fluid from elsewhere or localized migration of CO2-rich fluids associated with dehydration melting

K3-fibered Calabi-Yau threefolds I, the twist map

A construction of Calabi-Yaus as quotients of products of lower-dimensional spaces in the context of weighted hypersurfaces is discussed, including desingularisation. The construction leads to Calabi-Yaus which have a fiber structure, in particular one case has K3 surfaces as fibers. These Calabi-Yaus are of some interest in connection with Type II -heterotic string dualities in dimension 4. A section at the end of the paper summarises this for the non-expert mathematician.Comment: 31 pages LaTeX, 11pt, 2 figures. To appear in International Journal of Mathematics. On the web at http://personal-homepages.mis.mpg.de/bhunt/preprints.html , #

Molecular gas in NUclei of GAlaxies (NUGA) XV. Molecular gas kinematics in the inner 3kpc of NGC6951

Within the NUclei of GAlaxies project we have obtained IRAM PdBI and 30m 12CO(1-0) and 12CO(2-1) observations of the spiral galaxy NGC 6951. Previous work shows that there is indirect evidence of gas inflow from 3 kpc down to small radii: a large-scale stellar bar, a prominent starburst ring (r~580 pc) and a LINER/Seyfert 2 nucleus. In this paper we study the gas kinematics as traced by the CO line emission in detail. We quantify the influence of the large-scale stellar bar by constructing an analytical model of the evolution of gas particles in a barred potential. From this model gravitational torques and mass accumulation rates are computed. We compare our model-based gravitational torque results with previous observationally-based ones. The model also shows that the large-scale stellar bar is indeed the dominant force for driving the gas inward, to the starburst ring. Inside the ring itself a nuclear stellar oval might play an important role. Detailed analysis of the CO gas kinematics there shows that emission arises from two co-spatial, but kinematically distinct components at several locations. The main emission component can always be related to the overall bar-driven gas kinematics. The second component exhibits velocities that are larger than expected for gas on stable orbits, has a molecular gas mass of 1.8x10^6Msun, is very likely connected to the nuclear stellar oval, and is consistent with inflowing motion towards the very center. This may form the last link in the chain of gas inflow towards the active galactic nucleus in NGC 6951.Comment: 17 pages, accepted by A&A (17 feb 2011

Effect of Polyethylene Glycol Treatment on Acetic Acid Emissions from Wood

Acetic acid is known to be emitted from sound wood and can accelerate damage to heritage materials, particularly metals. However, few studies have investigated the extent of acetic acid emissions from archaeological wood. This research utilised Solid-Phase-Micro-Extraction (SPME) GC–MS and lead coupon corrosion to identify volatile emissions from polyethylene glycol (PEG)-treated archaeological wood from the Mary Rose collection and assess if they could cause accelerated damage. In addition, the effect of PEG treatment on acetic acid emissions was investigated using sound wood samples. For sound wood, the PEG treatment acted as a barrier to acetic acid emissions, with higher-molecular-weight PEGs preventing more emissions. Archaeological wood, despite its age and high-molecular-weight PEG treatment, still emitted detectable concentrations of acetic acid. Moreover, they emitted a wider array of compounds compared to sound wood, including carbon disulphide. Like sound wood, when the archaeological wood samples were in a sealed environment with lead coupons, they caused accelerated corrosion to lead. This evidences that archaeological wood can emit high enough concentrations of volatile compounds to cause damage and further investigation should be performed to evaluate if this can occur inside museum display cases