Outer Scale Research Articles

Influence of moderate-to-strong anisotropic non-Kolmogorov turbulence on intensity fluctuations of a Gaussian–Schell model beam in marine atmosphere**Project supported by the Open Research Fund of State Key Laboratory of Pulsed Power Laser Technology (Grant No. SKL2016KF05), the Key Industrial Innovation Chain Project in Industrial Domain, China (Grant No. 2017ZDCXL-GY-06-02), the Huawei Innovation Research Program, China (Grant No. HO2017050001AG), and the Foundation

The scintillation index (SI) of a Gaussian–Schell model (GSM) beam in a moderate-to-strong anisotropic non-Kolmogorov turbulent atmosphere is developed based on the extended Rytov theory. The on-axis SI in a marine atmosphere is higher than that in a terrestrial atmosphere, but the off-axis SI exhibits the opposite trend. The on-axis SI first increases and then begins to decrease and saturate as the turbulence strength increases. Turbulence inner and outer scales have different effects on the on-axis SI in different turbulent fluctuation regions. The anisotropy characteristic of atmospheric turbulence leads to the decline in the on-axis SI, and the rise in the off-axis SI. The on-axis SI can be lowered by increasing the anisotropy of turbulence, wavelength, and source partial coherence before entering the saturation attenuation region. The developed model may be useful for evaluating ship-to-ship/shore free-space optical communication system performance.

Infection criteria, inoculum sources and splash dispersal pattern of Colletotrichum acutatum causing bitter rot of apple in New Zealand

Infection of Malus x domestica cv. Royal Gala fruit by Colletotrichum acutatum causing bitter rot was studied in the temperate climate of New Zealand. Temperatures above 15 °C were required for lesions to develop on detached apple wound-inoculated or inoculated without wounding with C. acutatum spores, regardless of maturity. A wetness period of 72 h was required for infection of mature detached apple fruit without wounding. On wound-inoculated detached apple fruits, sporulation was related to temperature and followed a similar pattern. In the field, a mean temperature above 15 °C for 72 h after wound-inoculation was required for lesions to develop. Buds were a more important source of inoculum than twigs, and it was shown that C. acutatum could be isolated more frequently from outer bud scales than from inner scales. Asymptomatic infection of vegetative and reproductive buds was detected. C. acutatum was detected on asymptomic surface-sterilised petals and fruit, more commonly during summer than spring. Symptomless sterilised leaves generally yielded C. acutatum throughout the season, but isolations were more frequent in summer. Recovery of inoculum using a splash meter to detect vertical dispersal showed that in summer inoculum was primarily splashed up from the ground. In spring, inoculum was recovered in similar quantities from all heights up to a metre, suggesting that splash dispersal occurs from the canopy as well as from the ground. A disease cycle for C. acutatum infecting apples and causing bitter rot in New Zealand is suggested.

STEM and APT characterization of scale formation on a La,Hf,Ti-doped NiCrAl model alloy

A thermally grown scale formed on a cast NiCrAl model alloy doped with lanthanum, hafnium, and titanium was examined after isothermal exposure at 1100 °C for 100 h in dry flowing O2 to understand the dopant segregation along scale grain boundaries. The complex scale formed on the alloy surface was composed of two types of substrates: phase-dependent, thin (<250 nm) outer layers and a columnar-grained ∼3.5 μm inner alumina layer. Two types of oxides formed between the inner and outer scale layers: small (3–15 nm) La2O3 and larger (≤50 nm) HfO2 oxide precipitates. Nonuniform distributions of the hafnium, lanthanum, and titanium dopants were observed along the inner scale grain boundaries, with hafnium dominating in most of the grain boundaries of α-Al2O3. The concentration of reactive elements (RE) seemed to strongly depend on the grain boundary structure. The level of titanium grain boundary segregation in the inner scale decreased toward the model alloy (substrate), confirming the fast outward diffusion of titanium. Hafnium was also observed at the metal–scale interface and in the γ′ (Ni3Al) phase of the alloy. High-resolution scanning transmission electron microscopy (STEM) confirmed the substitution of REs for aluminum atoms at the scale grain boundaries, consistent with both the semiconducting band structure and the site-blocking models. Both STEM and atom probe tomography allowed quantification of REs along the scale grain boundaries across the scale thickness. Analysis of the scale morphology after isothermal exposure in flowing oxygen revealed a myriad of new precipitate phases, RE segregation dependence on grain boundary type, and atomic arrangement along scale grain boundaries, which is expected to influence the scale growth rate, stability, and mechanical properties.

Channel correlation and BER performance analysis of coherent optical communication systems with receive diversity over moderate-to-strong non-Kolmogorov turbulence.

In this paper, new expressions of the channel-correlation coefficient and its components (the large- and small-scale channel-correlation coefficients) for a plane wave are derived for a horizontal link in moderate-to-strong non-Kolmogorov turbulence using a generalized effective atmospheric spectrum which includes finite-turbulence inner and outer scales and high-wave-number "bump". The closed-form expression of the average bit error rate (BER) of the coherent free-space optical communication system is derived using the derived channel-correlation coefficients and an α-μ distribution to approximate the sum of the square root of arbitrarily correlated Gamma-Gamma random variables. Analytical results are provided to investigate the channel correlation and evaluate the average BER performance. The validity of the proposed approximation is illustrated by Monte Carlo simulations. This work will help with further investigation of the fading correlation in spatial diversity systems.

Outer scales and parameters of adverse-pressure-gradient turbulent boundary layers

A clear and consistent framework for the analysis of the outer region of adverse-pressure-gradient turbulent boundary layers is established in this paper based on basic principles and theory, and the help of six adverse-pressure-gradient turbulent boundary layer databases and a zero-pressure-gradient one. Outer velocity and length scales for the mean velocity defect and the Reynolds stresses are discussed first. The conditions of validity of four velocity scales are determined in terms of the shape factor, since one scale is restricted to small velocity-defect boundary layers (the friction velocity $u_{\unicode[STIX]{x1D70F}}$), one to large-defect ones (the pressure-gradient velocity $U_{po}$), while the two others are proper scales for all velocity-defect conditions (the Zagarola–Smits velocity $U_{zs}$ and the mixing-layer-type velocity $U_{m}$). The turbulent boundary layer equations are then used to bring out, in a consistent manner and without assuming any self-similar behaviour, a set of non-dimensional parameters characterizing the outer region of turbulent boundary layers with arbitrary pressure gradients. In terms of a generic outer length scale $L_{o}$ and velocity scale $U_{o}$, these non-dimensional parameters are the pressure-gradient parameter $\unicode[STIX]{x1D6FD}_{o}=L_{o}/(\unicode[STIX]{x1D70C}U_{o}^{2})\,\text{d}p_{e}/\text{d}x$, the Reynolds number $Re_{o}=U_{o}L_{o}/\unicode[STIX]{x1D708}(U_{o}/U_{e})$ and the inertial parameter $\unicode[STIX]{x1D6FC}_{o}=U_{e}V_{e}/U_{o}^{2}$, where $U_{e}$ and $V_{e}$ are respectively the streamwise and wall-normal components of mean velocity at the boundary layer edge. These parameters have a clear physical meaning: they are ratios of the order of magnitude of forces, with the Reynolds shear stress gradient (apparent turbulent force) as the reference force – inertial to apparent turbulent forces for $\unicode[STIX]{x1D6FC}_{o}$, pressure to apparent turbulent forces for $\unicode[STIX]{x1D6FD}_{o}$ and apparent turbulent to viscous forces for $Re_{o}$. We discuss at length their significance and determine under what conditions they retain their meaning depending on the outer velocity scale that is considered. The seven boundary layer databases are analysed and compared using the established framework. An astonishing and impressive result is obtained: by choosing $U_{o}=U_{zs}$, the streamwise evolution of the three ratios of forces in the outer region can be accurately followed with $\unicode[STIX]{x1D6FD}_{zs}$, $\unicode[STIX]{x1D6FC}_{zs}$ and $Re_{zs}$ in all these flows – not just the order of magnitude of these ratios. This cannot be achieved with $u_{\unicode[STIX]{x1D70F}}$ and $U_{po}$, and only imperfectly with $U_{m}$. Consequently, $\unicode[STIX]{x1D6FD}_{zs}$, $\unicode[STIX]{x1D6FC}_{zs}$ and $Re_{zs}$ can be used to follow – in a global sense – the streamwise evolution of the streamwise mean momentum balance in the outer region.

Amplitude fluctuations for optical waves propagation through non-Kolmogorov coronal solar wind turbulence channels.

Optical communication has a great potential for the future deep space communication, while the amplitude fluctuations caused by the coronal solar wind irregularities has been a challenging topic during superior solar conjunction. In this paper, a closed-form amplitude fluctuations expression for optical waves propagation through non-Kolmogorov solar wind turbulence is derived by establishing a generalized coronal turbulence spectrum model. The profound impact of the coronal parameters on the bit error rate (BER) performance of the free space optical system is also investigated based on the derived amplitude fluctuations model. The derived expression allows easy analysis of the evolution of the amplitude fluctuations and, in particular, an understanding of the imposed effects caused by the parameters during the waves propagation. The combined effect of the optical wavelength, non-Kolmogorov spectral index, turbulence outer scale, relative solar wind density fluctuation factor, and link distance on amplitude fluctuations are evaluated. Numerical calculations show that these parameters produce obvious effects on the amplitude fluctuations and the BER. The large optical wavelength can mitigate the influence of the coronal turbulence. Our results have potential applications for evaluating the link performance of the future deep space communication.

Corrosion behavior and mechanism of 3Cr steel in CO2 environment with various Ca2+ concentration

The effect of Ca2+ on the corrosion behavior of 3Cr steel was investigated using immersion tests and electrochemical measurements. The results demonstrated that with an increase in Ca2+ concentration in the solution, the corrosion rate of 3Cr steel decreased and the Ca2+ content in the corrosion scale increased. Ca is involved in the formation of both the inner and outer corrosion scales of 3Cr steel. Polarization curves revealed that Ca2+ could enhance the pseudopassivation of 3Cr steel. EIS results demonstrated that Ca2+ can decrease the porosity of corrosion films. Additionally, Ca2+ could accelerate the precipitation of FeCO3 (CaxFe1−xCO3) by reducing its solubility and saturation degree.

A hierarchical random additive model for passive scalars in wall-bounded flows at high Reynolds numbers.

The kinematics of a fully developed passive scalar is modelled using the hierarchical random additive process (HRAP) formalism. Here, 'a fully developed passive scalar' refers to a scalar field whose instantaneous fluctuations are statistically stationary, and the 'HRAP formalism' is a recently proposed interpretation of the Townsend attached eddy hypothesis. The HRAP model was previously used to model the kinematics of velocity fluctuations in wall turbulence: , where the instantaneous streamwise velocity fluctuation at a generic wall-normal location z is modelled as a sum of additive contributions from wall-attached eddies (a i ) and the number of addends is N z ~ log(δ/z). The HRAP model admits generalized logarithmic scalings including 〈ϕ 2〉~log(δ/z), 〈ϕ(x)ϕ(x+r x )〉 ~ log(δ/r x ), 〈(ϕ(x) - ϕ(x+r x ))2〉 ~ log(r x /z), where ϕ is the streamwise velocity fluctuation, δ is an outer length scale, r x is the two-point displacement in the streamwise direction and 〈·〉 denotes ensemble averaging. If the statistical behaviours of the streamwise velocity fluctuation and the fluctuation of a passive scalar are similar, we can expect first that the above mentioned scalings also exist for passive scalars (i.e. for ϕ being fluctuations of scalar concentration) and second that the instantaneous fluctuations of a passive scalar can be modelled using the HRAP model as well. Such expectations are confirmed using large-eddy simulations. Hence the work here presents a framework for modelling scalar turbulence in high Reynolds number wall-bounded flows.

The reactive element effect of yttrium and yttrium silicon on high temperature oxidation of NiCrAl coating

The microstructure formed on the bond coat affects the oxidation resistance, particularly the formation of a protective oxide layer. The adhesion of bond coat and TGO increased significantly by addition of reactive element. In the present work, the effect of yttrium and yttrium silicon as reactive element (RE) on NiCrAl coating was investigated. The NiCrAl (without RE) and NiCrAlX (X:Y or YSi) bond coating were deposited on Hastelloy C-276 substrate by High Velocity Oxygen Fuel (HVOF) method. Isothermal oxidation was carried out at 1000 °C for 100 hours. The results showed that the addition of RE could prevent the breakaway oxidation. Therefore, the coating with reactive element were more protective against high temperature oxidation. Furthermore, the oxidation rate of NiCrAlY coating was lower than NiCrAlYSi coating with the total mass change was ±2.394 mg/cm2 after 100 hours of oxidation. The thickness of oxide scale was approximately 1.18 μm consisting of duplex oxide scale of spinel NiCr2O4 in outer scale and protective α-Al2O3 in inner scale.

Effects of anisotropic turbulence on the long term beam spread and beam wander of Gaussian beam

Experiments and theoretical investigations have shown that the isotropic turbulence is not the only possible turbulence in the atmosphere. Researches about the anisotropic non-Kolmogorov have attracted more and more attentions recently. In this work, the spreading and wandering of Gaussian beam under weak anisotropic turbulence are investigated. New theoretical expressions for these two kinds of turbulence effects are developed. They are observed against the variations in the effective anisotropic factor, finite turbulence inner and outer scales, and the general spectral power law. It is found that the increased effective anisotropic factor decreases the influence of anisotropic turbulence on the long term beam spread and beam wander. The increased turbulence inner scale is advantageous for decreasing the long term beam spread. While the increased turbulence outer scale is disadvantageous for alleviating the beam wander. The theoretical investigations performed in this work are helpful to better understand the optical waves’ propagation under anisotropic turbulence.

Non-Markov character of sound propagation over relatively short ranges in the turbulent atmosphere

The Markov approximation is widely used in wave propagation in random media, including sound propagation in the turbulent atmosphere. This approximation, which significantly simplifies formulations for the statistical moments of the propagating field, is valid if the propagation range is greater than the outer length scale of random inhomogeneities. For sound propagation in the turbulent atmosphere, this length scale can be as large as 400–500 m (23% of the height of the atmospheric boundary layer), indicating that the Markov approximation might not be applicable for relatively short ranges. In this paper, the statistical characteristics of a sound field propagating in the turbulent atmosphere, such as the correlation functions of the log-amplitude and phase fluctuations, the mean sound field, and the mutual coherence function are calculated, without using the Markov approximation. The new results are then compared with those obtained in the Markov approximation. The difference between the two formulation...

Effect of Ti and Ta on Oxidation Kinetic of Chromia Forming Ni-Base Superalloys in Ar-O2-Based Atmosphere

AbstractIn the present study, two commercially available Ni-base superalloys, namely Rene 80 which contains Ti and IN 792 containing Ti and Ta, were investigated during isothermal oxidation at 1,050°C in Ar–20% O2 gas up to 50 h. It was found that IN 792 showed a slightly lower oxidation rate as compared to Rene 80. Also differences in oxide scale microstructures and thicknesses were found. Both alloys formed qualitatively similar oxide scales consisting of outer TiO2 on top of a Cr2O3 scale and internally oxidized Al2O3. The IN 792 formed a thinner oxide scale in general as well as a thinner outer TiO2 scale. Also the depth of the internally oxidized Al2O3 precipitates is smaller in case of IN 792. These findings were correlated with the formation of TiTaO4, which in turn hampered outer Ti and inward oxygen flux.

Further analysis of scintillation index for a laser beam propagating through moderate-to-strong non-Kolmogorov turbulence based on generalized effective atmospheric spectral model

A new expression of the scintillation index (SI) for a Gaussian-beam wave propagating through moderate-to-strong non-Kolmogorov turbulence is derived, using a generalized effective atmospheric spectrum and the extended Rytov approximation theory. Finite inner and outer scale parameters and high wave number “bump” are considered in the spectrum with a generalized spectral power law in the range of 3–4, instead of the fixed classical Kolmogorov power law of 11/3. The obtained SI expression is then used to analyze the effects of the spectral power law and the inner scale and outer scale on SI under various non-Kolmogorov fluctuation conditions. These results will be useful in future investigations of optical wave propagation through atmospheric turbulence.

Turbulence in the Outer Heliosheath

Abstract We present in situ observations of magnetic turbulence in the draped interstellar magnetic field measured by Voyager 1 during an undisturbed interval from 2015.3987 to 2016.6759 confirming the existence of the turbulence observed previously from 2013.3593 to 2014.6373. The power spectral density of the turbulence was the same in both cases. The turbulence had a Kolmogorov k −5/3 spectrum in the range from k = 1.3 × 10−13 cm−1 to 4 × 10−12 cm−1. The ratio of the turbulent fluctuations to the average magnetic field strength was only 0.02, indicating that the turbulence was very weak. Extrapolating the power-law slope to lower frequencies yields an upper limit on the turbulence outer scale of 0.01 pc = 2000 au, which may be regarded as the distance at which Voyager 1 will enter the undisturbed local interstellar medium, beyond the outer heliosheath or bow wave in the upstream direction. The maximum variance of the fluctuations was in the two directions transverse to the average magnetic field in the recent interval, whereas it was parallel to the average magnetic field in the earlier interval, suggesting a transformation from turbulence with a dominant compressive component to turbulence dominated by transverse fluctuations. As the magnitude of the fluctuations was approaching that of the uncertainties of the measurements, the latter result requires confirmation by further observations.

Effect of angle-of-arrival fluctuation on heterodyne detection in slant atmospheric turbulence.

A mathematical model of the effect of random pointing errors on the mixing efficiency of heterodyne detection is established, and the effect of angle-of-arrival fluctuation on the mixing efficiency of heterodyne detection is investigated. The results show that the average mixing efficiency is significantly affected by the angle-of-arrival fluctuation in the outer scale. The larger the obscuration ratio and receiving aperture of the optical system, the lower the average mixing efficiency is. The closer the value of D/r0 is to 0.79, the closer the bit error rate of heterodyne detection is to 1×10-9 under weak turbulence.

Synthetic generation of equilibrium boundary layer turbulence from modeled statistics

An improved synthetic digital filtering method (SDFM) for the generation of equilibrium turbulence is described, with emphasis on the ease of application to complex configurations. This is achieved by facilitating the use of modeled (RANS) statistics for the mean flow and Reynolds stress profiles, instead of simulated (DNS or LES) statistics that are not readily available for three-dimensional flows. The effects on boundary layer relaxation with modeled statistics are first quantified for a well-known canonical situation, specifically, Mach 2 equilibrium turbulent boundary layers over 250 < Reθ < 2220. Various convergence criteria are assessed in terms of the streamwise coordinate (x) normalized by the incoming boundary layer thickness (δ0). These include skin-friction, which requires x/δ0 ≈ 12 for equilibrium, inner scale mean velocity (x/δ0 ≈ 16), inner scale Reynolds stresses (x/δ0 ≈ 18), as well as outer scale mean velocity, Reynolds stresses, and spatio-temporal correlations (x/δ0 ≈ 40–50). Development lengths are shown to be inversely related to Reynolds number. In terms of boundary layer relaxation length, initializing the method with RANS (versus simulated) statistics incurs a negligible penalty in inner coordinates and a mild penalty (x/δ0 ≈ 5–10) in outer coordinates. The effectiveness of this approach is then demonstrated by application to significantly more complex three-dimensional flows, including internal single and multi-stream flows, for which synthetic turbulence generation techniques are necessary, but precursor high-fidelity simulations are not available. Thus, the RANS-initialized SDFM provides a rapidly adaptable method for the synthetic generation of wall-bounded turbulence.

A new model for the profiles of optical turbulence outer scale and Cn2 on the coast

Atmospheric optical turbulence severely restricts the performances of electro-optical systems. The turbulent atmosphere causes the intensity of a light beam to fluctuate or scintillate, leads the light beam to wander and makes the images randomly displace, which directly relates to the refractive index structure parameter Cn2. Therefore the knowledge of Cn2 is essential to evaluate and to predict the effects of optical turbulence on electro-optical imagery systems. During the period from December 13, 2016 to January 2, 2017, 30 sets of sounding data, which include temperatures, humidities, pressures, wind speeds, wind directions and atmospheric refractive index structure parameters, are obtained by using a self-developed meteorological radiosonde for turbulence at Marine Meteorological Science Experiment Base at Bohe of Maoming. On the basis of the HMNSP99 outer scale model, an atmospheric optical turbulence outer scale formula of Maoming is obtained by fitting the sounding data. At the same time, the experimental data of the turbulence profiles are statistically averaged, and then based on the Hufnagel-Valley model, a statistical model is obtained, which is appropriate to the variation of the turbulence profile on the coast. According to Tatarski turbulence parameterization and the Maoming outer scale formula, the new estimated Cn2 values are compared with their experimental observations and the results from other already defined models, respectively. Statistical analysis shows that the overall correlation coefficients of log10(Cn2) between observed values and estimated values by using the new fitting Maoming outer scale formula, the HMNSP99 model, the Dewan model and the Coulman model are 0.924, 0.848, 0.763 and 0.651, respectively. Also, both the trends and magnitudes for these four outer scale models are consistent with each other. The errors of the above four outer scale models are very small:their overall average absolute errors and average relative errors are 0.514 and 2.963%, 0.627 and 3.612%, 0.943 and 5.439%, 0.766 and 4.417%, respectively, and the error of the Maoming outer scale model is smallest. The reliabilities and validities of the new outer scale and Cn2 models are further verified. In addition, it is found that the occurrence of upper air optical turbulence is closely related to wind shear and temperature gradient. The results support the prediction of the atmospheric optical turbulence profile required for electro-optical engineering on the coast.

Magnetic effect on oxide-scale growth of Fe-5Cr alloy

The oxidation behaviour of Fe-5Cr alloy was investigated at 650°C in the presence of magnetic field. Results indicated that the oxide scales were both consisted of an outer Fe-oxide scale and an inner mixed-oxide scale in the presence or absence of magnetic field. The oxide-scale growth of Fe-5Cr alloy, gained by measuring the oxide-scale thickness, was verified to follow parabolic lawyer. And the oxidation kinetics showed that the applied magnetic field retarded the oxide-scale growth of Fe-5Cr alloy.

Quasiperiodic oscillations of the sub-mHz band in near-sun plasma according to the coherent radio occultation data

In 2013 and 2015, investigations of the internal solar wind were carried out using the method of two-frequency radio sounding by signals from the Mars Express European spacecraft. The values of the S- and X-bands’ frequency and the differential frequency were registered with a sampling rate of 1s at the American and European networks of ground-based tracking stations. The spatial distribution of the frequency fluctuation’s level has been studied. It has been shown that the intensity of frequency fluctuation considerably decreases at high heliolatitudes. In some radio sounding sessions, quasiperiodic oscillations of sub-mHz band have been observed in the temporal spectra of frequency fluctuations; they are supposed to be associated with the density inhomogeneities, the sizes of which are close to the turbulence outer scale.

Investigation of feasibility of wind turbulence measurement by a pulsed coherent doppler lidar in the atmospheric boundary layer

Feasibilities of determination of the wind turbulence parameters from data measured by the Stream Line coherent Doppler lidar under different atmospheric conditions have been studied experimentally. It has been found that the spatial structure of the turbulence is described well by the von Karman model in the layer of intensive mixing. From the lidar measurements at night under stable conditions the estimation of the outer scale of turbulence with the use of the von Karman model is not possible.