Outer Scale Research Articles

Wigner distribution function and kurtosis parameter of vortex beams propagating through turbulent atmosphere

Based on the extended Huygens-Fresnel integral, the analytical expressions for the Wigner distribution function (WDF) and kurtosis parameter of partially coherent flat-topped vortex (PCFTV) beams propagating through atmospheric turbulence and free space are derived. The WDF and kurtosis parameter of PCFTV beams through turbulent atmosphere are discussed with numerical examples. The numerical results show that the beam quality depends on the structure constants, the inner scale turbulence, the outer scale turbulence, the spatial correlation length, the wave length and the beam order. PCFTV beams are less affected by turbulence than partially flat-topped coherent (PCFT) beams under the same conditions, and will be useful in free-space optical communications.

Magnetohydrodynamic Turbulence Mediated by Reconnection

Abstract Magnetic field fluctuations in magnetohydrodynamic turbulence can be viewed as current sheets that are progressively more anisotropic at smaller scales. As suggested by Loureiro & Boldyrev and Mallet et al., below a certain critical thickness, , such current sheets become tearing-unstable. We propose that the tearing instability changes the effective alignment of the magnetic field lines in such a way as to balance the eddy turnover rate at all scales smaller than . As a result, turbulent fluctuations become progressively less anisotropic at smaller scales, with the alignment angle increasing as , where is the resistive dissipation scale. Here L 0 is the outer scale of the turbulence, S 0 is the corresponding Lundquist number, and is a parameter. The resulting Fourier energy spectrum is , where is the wavenumber normal to the local mean magnetic field, and the critical scale is . The simplest model corresponds to β = 0, in which case the predicted scaling formally agrees with one of the solutions obtained in Mallet et al. from a discrete hierarchical model of abruptly collapsing current sheets, an approach different from and complementary to ours. We also show that the reconnection-mediated interval is non-universal with respect to the dissipation mechanism. Hyper-resistivity of the form leads (in the simplest case of β = 0) to the different transition scale and the energy spectrum , where is the corresponding hyper-resistive Lundquist number.

Numerical Simulation of Aero-Optical Effects in a Supersonic Cavity Flow

A hybrid large-eddy simulation/Reynolds-averaged Navier–Stokes turbulence model is applied to compute the wave-front aberrations in an optical beam passing through a supersonic open cavity flow. The turbulence model blends a Reynolds-averaged Navier–Stokes-type closure near solid walls with a subgrid model in the freestream based on the ratios of estimated inner and outer turbulent length scales. The cavity geometry is modeled using an immersed boundary method, and an auxiliary flat-plate simulation is performed to replicate the effects of the wind-tunnel boundary layer on the computed optical path difference. Two-dimensional proper orthogonal decomposition modes of the optical wave front are computed; these compare favorably with wind-tunnel data, despite uncertainties about inflow turbulence levels and boundary-layer thicknesses over the wind-tunnel window. Dynamic mode decomposition of a planar wave front spanning the entire cavity reveals that wave-front distortions are driven by shear-layer oscillation at the Rossiter frequencies; these disturbances create eddy shocklets that propagate into the freestream and create additional optical path disturbances.

Scale Properties of Anisotropic and Isotropic Turbulence in the Urban Surface Layer

The scale properties of anisotropic and isotropic turbulence in the urban surface layer are investigated. A dimensionless anisotropic tensor is introduced and the turbulent tensor anisotropic coefficient, defined as C, where $$C = 3d_{3}\,+\,1 (d_{3}$$ is the minimum eigenvalue of the tensor) is used to characterize the turbulence anisotropy or isotropy. Turbulence is isotropic when $$C \approx 1$$ , and anisotropic when $$C \ll 1$$ . Three-dimensional velocity data collected using a sonic anemometer are analyzed to obtain the anisotropic characteristics of atmospheric turbulence in the urban surface layer, and the tensor anisotropic coefficient of turbulent eddies at different spatial scales calculated. The analysis shows that C is strongly dependent on atmospheric stability $$\xi = (z-z_{\mathrm{d}})/L_{{\textit{MO}}}$$ , where z is the measurement height, $$z_{\mathrm{d}}$$ is the displacement height, and $$L_{{\textit{MO}}}$$ is the Obukhov length. The turbulence at a specific scale in unstable conditions (i.e., $$\xi < 0$$ ) is closer to isotropic than that at the same scale under stable conditions. The maximum isotropic scale of turbulence is determined based on the characteristics of the power spectrum in three directions. Turbulence does not behave isotropically when the eddy scale is greater than the maximum isotropic scale, whereas it is horizontally isotropic at relatively large scales. The maximum isotropic scale of turbulence is compared to the outer scale of temperature, which is obtained by fitting the temperature fluctuation spectrum using the von Karman turbulent model. The results show that the outer scale of temperature is greater than the maximum isotropic scale of turbulence.

Exploring the bark thickness-stem diameter relationship: clues from lianas, successive cambia, monocots and gymnosperms.

Bark thickness is ecologically crucial, affecting functions from fire protection to photosynthesis. Bark thickness scales predictably with stem diameter, but there is little consensus on whether this scaling is a passive consequence of growth or an important adaptive phenomenon requiring explanation. With a comparative study across 913 species, we test the expectation that, if bark thickness-stem diameter scaling is adaptive, it should be possible to find ecological situations in which scaling is predictably altered, in this case between species with different types and deployments of phloem. 'Dicots' with successive cambia and monocots, which have phloem-free bark, had predictably thinner inner (mostly living) bark than plants with single cambia. Lianas, which supply large leaf areas with limited stem area, had much thicker inner bark than self-supporting plants. Gymnosperms had thicker outer bark than angiosperms. Inner bark probably scales with plant metabolic demands, for example with leaf area. Outer bark scales with stem diameter less predictably, probably reflecting diverse adaptive factors; for example, it tends to be thicker in fire-prone species and very thin when bark photosynthesis is favored. Predictable bark thickness-stem diameter scaling across plants with different photosynthate translocation demands and modes strongly supports the idea that this relationship is functionally important and adaptively significant.

Hints for Small Disks around Very Low Mass Stars and Brown Dwarfs∗

Abstract The properties of disks around brown dwarfs and very low mass stars (hereafter VLMOs) provide important boundary conditions on the process of planet formation and inform us about the numbers and masses of planets than can form in this regime. We use the Herschel Space Observatory PACS spectrometer to measure the continuum and [O i] 63 μm line emission toward 11 VLMOs with known disks in the Taurus and Chamaeleon I star-forming regions. We fit radiative transfer models to the spectral energy distributions of these sources. Additionally, we carry out a grid of radiative transfer models run in a regime that connects the luminosity of our sources with brighter T Tauri stars. We find that VLMO disks with sizes 1.3–78 au, smaller than typical T Tauri disks, fit well the spectral energy distributions assuming that disk geometry and dust properties are stellar mass independent. Reducing the disk size increases the disk temperature, and we show that VLMOs do not follow previously derived disk temperature–stellar luminosity relationships if the disk outer radius scales with stellar mass. Only 2 out of 11 sources are detected in [O i] despite a better sensitivity than was achieved for T Tauri stars, suggesting that VLMO disks are underluminous. Using thermochemical models, we show that smaller disks can lead to the unexpected [O i] 63 μm nondetections in our sample. The disk outer radius is an important factor in determining the gas and dust observables. Hence, spatially resolved observations with ALMA—to establish if and how disk radii scale with stellar mass—should be pursued further.

Spiral spectrum of Laguerre-Gaussian beams in slant non-Kolmogorov atmospheric turbulence

The beam carrying information will be affected by atmospheric turbulence as it propagates through the atmosphere. Under the modified Rytov method, using the non-Kolmogorov power spectrum, applying the atmospheric turbulent inner scale and the outer scale which changes with altitude, this paper obtained the expression of the spiral spectrum of the beam in slant atmospheric turbulence. The influences of wavelength, topological charge, zenith, waist radius, receiver aperture, radial index and inner scale on spiral spectrum are investigated. Numerical results reveal that spiral spectrum spread becomes more serious with longer distance, larger topological charge, larger zenith, smaller wavelength, larger receiver aperture and smaller inner scale. Radial index and waist radius have little effect on the spiral spectrum. In addition, the influence of the outer scale on the spiral spectrum under different fluctuation conditions is analyzed, the results show that if the outer scale is set as constant during the calculation of the spiral spectrum of the beam in the slant path, it will have little effect in the weak fluctuation area, but will bring large errors in the medium and strong fluctuation area.

Stokes flow singularity at a corner joining solid and porous walls at arbitrary angle

Motivated by the internal flow geometry of spiral-wound membrane modules with ladder-type spacers, we consider the Stokes flow singularity at a corner that joins porous and solid walls at arbitrary wedge angle varTheta . Seepage flux through the porous wall is coupled to the pressure field by Darcy’s law; slip is described by a variant of the Beavers–Joseph boundary condition. On a macroscopic, outer length scale, the singularity appears like a jump discontinuity in the normal velocity, characterized by a non-integrable 1 / r divergence of the pressure. For arbitrary varTheta , we develop an algebraic criterion to determine the admissible radial exponent(s) in a leading, inner similarity solution—which represents a weaker, integrable singularity in the pressure. A complete map of exponent versus varTheta is provided for 0< varTheta < 2 pi : this has an intricate structure with infinitely many solution branches clustering around varTheta = pi and varTheta = 2 pi . By generalizing the similarity form with a (ln r) term and iterating on the slip and seepage conditions, we can carry the outer and inner power series to arbitrarily high order. Nevertheless, a numerical splice is required in between. For this purpose, we apply an iterative, numerical-asymptotic patching scheme described by Nitsche and Parthasarathi (J Fluid Mech 713:183–215, 2012). Detailed velocity and pressure profiles are calculated for three wedge angles (varTheta = 3pi /4, pi /2, pi /4) and two dimensionless slip lengths (sigma = 20, 40). The general trends for decreasing wedge angle are (i) weakening of the pressure singularity, (ii) increasing magnitude of the radial component of velocity, and (iii) movement of the inner–outer transition farther from the corner. Wedges with varTheta < pi are seen to differ fundamentally from the flat wedge (varTheta = pi ) previously considered by Nitsche and Parthasarathi (2012).

Oxidation and creep properties at 1200 °C of cast quaternary Ni-Cr-C-Ti alloys

Three nickel-based alloys rich in chromium (25wt%) and containing carbon and titanium in quantities chosen to promote the appearance of titanium carbides (0.25C-1Ti, 0.50C-1Ti and 0.50C-2Ti, in wt%) were elaborated by casting in inert atmosphere. Their microstructures and their thermodynamic, chemical and mechanical behaviours at high temperature were studied. The as-cast microstructures of the obtained alloys are composed of a dendritic nickel matrix and of interdendritic carbides. These carbides are not TiC as expected, but Cr7C3, the whole titanium remaining in solid solution in the matrix. The applied {46h, 1200°C}-exposure in air led to the development of an external duplex oxide scale constituted of a thick inner chromia scale and a thin outer rutile scale. These oxide layers resisted spallation more than the ones of Ti-free ternary reference alloys in similar conditions. The bulk's chromium carbides became rounder and coarsened, with as result a decrease in room temperature hardness. The {5 or 20MPa, 1200°C}−3 points flexural creep tests showed a rather good behaviour, regarding the high test temperature. It is concluded that titanium seems hardening these bases of alloys at low and high temperatures. However the effects on the oxidation behaviour may be deleterious for the oxidation rate and subsurface Cr-impoverishment. In contrast Ti appears as beneficial for the resistances against spallation and possibly chromia volatilization. This needs to be further investigated.

Multi-scale interactions in a compressible boundary layer

ABSTRACTThe properties of spectral subranges of scales in a boundary layer at Mach=2.3 and friction Reynolds number Reτ = 570 are investigated by analysing DNS data. One major aim is to examine whether footprinting and modulation of small-scale near-wall motions by outer large structures, observed at high Reynolds numbers, also pertain to this low-Reynolds-number case, or whether the logarithmic layer simply contains a continuous hierarchy of motions without specific outer scales playing a distinctive role. To this end, the spectrum of scales is decomposed into modes by application of the “Empirical Mode Decomposition”. The properties of different scales are then investigated by means of spectra, maps of isotropy/anisotropy parameters, the premultiplied derivative of the second-order structure function, correlation coefficients and joint probability density function (PDF), the last constructed from conditionally sampled data for the small-scale motions within the large-scale footprints. A clear commonality is identified between interactions in high-Reynolds-number channel flow and the present low-Reynolds-number boundary layer.

Experimental investigation of optimum beam size for FSO uplink

In this paper, the effect of transmitter beam size on the performance of free space optical (FSO) communication has been determined experimentally. Irradiance profile for varying turbulence strength is obtained using optical turbulence generating (OTG) chamber inside laboratory environment. Based on the results, an optimum beam size is investigated using the semi-analytical method. Moreover, the combined effects of atmospheric scintillation and beam wander induced pointing errors are considered in order to determine the optimum beam size that minimizes the bit error rate (BER) of the system for a fixed transmitter power and link length. The results show that the optimum beam size for FSO uplink depends upon Fried parameter and outer scale of the turbulence. Further, it is observed that the optimum beam size increases with the increase in zenith angle but has negligible effect with the increase in fade threshold level at low turbulence levels and has a marginal effect at high turbulence levels. Finally, the obtained outcome is useful for FSO system design and BER performance analysis.

Influence of a silicon-bearing film on the early stage oxidation of pure titanium

Oxidation of pure titanium with and without silicon-bearing thin films was investigated using transmission electron microscopy, X-ray energy-dispersive spectroscopy, and nanoindentation to understand the initial stages of scale formation mechanisms. For pure titanium, results showed a two-layer oxide scale with dense outer and porous inner layers attributed to the simultaneous outward titanium and inward oxygen diffusion fluxes assessed through the use of a marker layer. Titanium specimens coated with Si before oxidation yielded a thinner oxide with an outer columnar scale and minimal porous inner oxide growth. These findings suggest that Si hinders oxygen transport to the oxide/metal interface, thus reducing overall oxide growth and oxygen ingress into the titanium metal substrate over short-term exposures.

Isothermal Oxidation Comparison of Three Ni-Based Superalloys

Ni-based superalloys are used for high-temperature components of gas turbines in both industrial and aerospace applications due to their ability to maintain dimensional stability under conditions of high stress and strain. The oxidation resistance of these alloys often dictates their service lifetime. This study focuses on the isothermal oxidation behavior of three Ni-based superalloys, namely, polycrystalline cast IN738LC, single-crystal N5, and a ternary Ni-Fe-Cr (TAS) powder metallurgy alloy. The isothermal oxidation tests were conducted at 900 °C in the static air up to 1000 h, and the specific aspects studied were the oxidation behavior of these chromia-forming and alumina-forming alloys that are used extensively in industry. In particular, the behavior of oxide scale growth and subsurface changes were analyzed in detail using various techniques such as SEM, EDS, and AFM. From the isothermal oxidation kinetics, the oxidation rate constant, k p, was calculated for each alloy and found to be; k p = 2.79 × 10−6 mg2 cm−4 s−1 for IN738LC, k p = 1.42 × 10−7 mg2 cm−4 s−1 for N5 and k p = 1.62 × 10−7 mg2 cm−4 s−1 for TAS. Based on a microstructural analysis, IN738LC exhibited a continuous dense outer scale of Cr2O3 and discontinuous inner scale of Al2O3, whereas N5 and TAS showed a dense outer scale of Al2O3 alone. The results suggested that the N5 and PM-TAS alloys are more oxidation resistant than the IN738LC under these conditions.

Effects of inner and outer scale on the modulation transfer function for a Gaussian wave propagating through anisotropic non-Kolmogorov turbulence

Both experimental results and empirical research have shown that the atmospheric turbulence can present the anisotropic property not only at a few meters above the ground but also at high altitudes of up to several kilometers. This paper investigates the modulation transfer function of a Gaussian beam propagating along a horizontal path in weak anisotropic non-Kolmogorov turbulence. Mathematical expressions are obtained based on the generalized exponential spectrum for anisotropic turbulence, which includes the spectral power law value, the finite inner and outer scales of turbulence, the anisotropic factor, and other essential optical parameters of the Gaussian beam. The numerical results indicate that the atmospheric turbulence would produce less negative effects on the wireless optical communication system with an increase in the anisotropic factor.

Salt fog corrosion behavior in a powder-processed icosahedral-phase-strengthened aluminum alloy

The pitting corrosion resistance has been evaluated for a powder-processed Al-Cr-Mn-Co-Zr alloy which contains ≈35% by volume of an icosahedral quasi-crystalline phase and a little Al9Co2 in an Al matrix. ASTM standard salt fog exposure tests show that the alloy exhibits far lower corrosion pit densities and depths than commercial high-strength aerospace Al alloys under the same conditions. Electron microscopy data show that the salt fog exposure leads to the selective oxidation of the face-centered cubic Al matrix around the other phases, and to the development of a porous outer oxide scale.

Optimal bursts in turbulent channel flow

Bursts are recurrent, transient, highly energetic events characterized by localized variations of velocity and vorticity in turbulent wall-bounded flows. In this work, a nonlinear energy optimization strategy is employed to investigate whether the origin of such bursting events in a turbulent channel flow can be related to the presence of high-amplitude coherent structures. The results show that bursting events correspond to optimal energy flow structures embedded in the fully turbulent flow. In particular, optimal structures inducing energy peaks at short time are initially composed of highly oscillating vortices and streaks near the wall. At moderate friction Reynolds numbers, through the bursts, energy is exchanged between the streaks and packets of hairpin vortices of different sizes reaching the outer scale. Such an optimal flow configuration reproduces well the spatial spectra as well as the probability density function typical of turbulent flows, recovering the mechanism of direct-inverse energy cascade. These results represent an important step towards understanding the dynamics of turbulence at moderate Reynolds numbers and pave the way to new nonlinear techniques to manipulate and control the self-sustained turbulence dynamics.

Bit error rate performance of free-space optical link under effect of plasma sheath turbulence

Based on the power spectrum of the refractive-index fluctuation in the plasma sheath turbulence, the expressions for wave structure functions and scintillation index of optical wave propagating in a turbulent plasma sheath are derived. The effect of the turbulence microstructure on the propagation characteristics of optical waves are simulated and analyzed. Finally, the bit error performance of a free-space optical (FSO) link is investigated under the effect of plasma sheath turbulence. The results indicate that the spherical waves have a better communication performance in the FSO link. In addition, a greater variance of the refractive index fluctuation causes a more severe fluctuation in electron density, temperature, and collision frequency inside the plasma sheath. However, when the outer scale is close to the thickness of the plasma sheath, the turbulence eddies have almost no influence on the wave propagation. Therefore, the bit error rate (BER) obviously increases with the increase in variance of the refractive index fluctuation and the decrease in the outer scale. These results are fundamental for evaluating the performance of the FSO link under the effect of plasma sheath turbulence.

Charged Particle Diffusion in Isotropic Random Magnetic Fields

Abstract The investigation of the diffusive transport of charged particles in a turbulent magnetic field remains a subject of considerable interest. Research has most frequently concentrated on determining the diffusion coefficient in the presence of a mean magnetic field. Here we consider the diffusion of charged particles in fully three-dimensional isotropic turbulent magnetic fields with no mean field, which may be pertinent to many astrophysical situations. We identify different ranges of particle energy depending upon the ratio of Larmor radius to the characteristic outer length scale of turbulence. Two different theoretical models are proposed to calculate the diffusion coefficient, each applicable to a distinct range of particle energies. The theoretical results are compared to those from computer simulations, showing good agreement.

Effect of Al and Cr Content on Air and Steam Oxidation of FeCrAl Alloys and Commercial APMT Alloy

To develop the next generation of accident-tolerant fuel cladding for light-water nuclear reactors, wrought FeCrAlY alloys with varying amounts of Cr and Al and commercial Kanthal APMT alloy were evaluated for short-term (4 h) oxidation resistance in steam and air at 1200–1475 °C. Model alloys with lower Cr contents and higher Al contents were evaluated as lower Cr contents are desirable for radiation damage resistance during operation. As expected, a synergistic effect was found between the Cr and Al contents to enable protective Al2O3 formation under these conditions. Characterization of the alumina scales formed in steam found that the scale morphology was affected by the alloy Y content and detailed scanning transmission electron microscopy (STEM) detected Y segregation along scale grain boundaries at 1200 °C. However, after 4 h at 1475 °C, Y and Hf were not segregated to the oxide grain boundaries formed on APMT and the scale had a single layer structure. Compared to oxidation in air, STEM characterization of the outer scale showed differences in the Fe and Cr distributions in steam.

Dormancy and bud burst in sultana vines

Dormancy and bud burst have been studied for sultana vines in the Murray Valley, Australia. The vines are in deep dormancy at the beginning of autumn and the intensity of dormancy decreases gradually during autumn and winter. Bud burst of cuttings taken during the dormant period occurs the more rapidly the higher the temperature at which they are held. There is evidence to suggest that sultanas have no chilling requirement and no clear distinction between organic and enforced dormancy. Treatment with 3 ml of ethylene chlorhydrin in a.201 container for 24 hours is effective in breaking dormancy. The most effective treatment veries slightly with the intensity of dormancy. Removing the outer bud scales or soaking buds in water decreases the intensity of dormancy. The pattern of bud burst found on canes in the field is established on pruned canes at least one month before the shoots appear. Both auxin and gibberellin will delay bud burst and reduce the proportion of buds which burst but auxin will not affect a bud above the point of application whereas gibberellin will do so.