Outer Scale Research Articles

Dynamic evolution of coherent vortex dipole in atmospheric turbulence

The analytical expression for the cross-spectral density function of Gaussian Schell-model (GSM) beams with coherent vortex dipole (CVD) propagating through atmospheric turbulence is derived, which enables us to study the evolution process of CVD propagating through atmospheric turbulence, where the influences of the beams parameters and atmospheric turbulence parameters on the ratio of critical off-axis distance to the waist width are stressed. It shows that the evolution process of the CVD depends on the off-axis distance. The larger the off-axis distance is, the more the number of CVD is. When the off-axis distance is zero, the position of coherent vortices with positive and negative topological charge of CVD propagating through atmospheric turbulence is always symmetry. When the off-axis distance is big enough, compared with the situation at source plane, the orientation of the positive coherent vortex of inherent CVD and negative coherent vortex of that rotates 180° in the far field. The larger the structure constant and the waist width are, as well as the smaller the spatial correlation length and the inner scale are, the smaller the ratio ac/w0 is. Besides, the ratio ac/w0 will no longer change when the spatial correlation length or the inner scale increases to a certain value, whereas the outer scale has no effect on the ratio.

Effects of finite inner and outer scales on the scintillation index of turbulent slant path

In this paper, the effects of nonzero inner scales and finite outer scales are investigated, in the context of Gaussian beam propagation along a slant path under general turbulence conditions. Theoretical expressions for the cut-off spatial frequencies are derived with an approach method, and thereby a modified scintillation model is developed to incorporate inner scale and outer scale parameters in the analysis. Then, inner and outer scale effects on the downlink are analysed with respect to the zenith angle, the altitude of the transmitter, the initial beam radius, as well as the turbulence strength. Numerical results indicate that the effects of a finite outer scale mainly influence transmission that occurs at large zenith angles or high altitudes, while the inner scale effects are more prevalent. This study may be helpful to improve the accuracy of calculation of slant-path scintillation index, and thus benefit the characterization and optimization of space/air-ground laser communication systems.

Propagation factors of standard and elegant Laguerre Gaussian beams in non-Kolmogorov turbulence

Analytical formulae are derived for the propagation factors (M2-factors) of standard Laguerre Gaussian (SLG) beam and elegant Laguerre Gaussian (ELG) beam in non-Kolmogorov turbulence based on the extended Huygens-Fresnel principle and second order moments of the Wigner distribution function. The M2-factors of SLG beam and ELG beam in non-Kolmogorov turbulence have been discussed numerically and comparatively. It is shown that the relative M2-factors of ELG beam are more affected by the turbulence and keep the better beam quality in comparison with that of SLG beam. Furthermore, the normalized M2-factors of SLG beam and ELG beam with higher orders, longer wavelength, larger waist width, larger inner scale of turbulence and the generalized exponent parameter, smaller outer scale of turbulence and smaller the generalized structure parameter are less affected by the non-Kolmogorov turbulence.

High Temperature Oxidation Behavior of T91 Steel in Dry and Humid Condition

High temperature oxidation behavior of T91 ferritic/martensitic steel was examined over the temperature range of 500 to 700°C in dry and humid environments. The weight gain result revealed that oxidation occurs at all range of temperatures and its rate is accelerated by increasing the temperature. The weight gain of the oxidized steel at 700°C in steam condition was six times bigger than the dry oxidation.. SEM/EDX of the cross-sectional image showed that under dry condition, a protective and steady growth of the chromium oxide (Cr2O3) layer was formed on the steel with the thickness of 2.39±0.34 µm. Meanwhile for the humid environment, it is found that the iron oxide layer, which consists of the hematite (Fe2O3) and magnetite (Fe3O4) was formed as the outer scale, and spinnel as inner scale. This result indicated that the oxidation behavior of T91 steel was affected by its oxidation environment. The existence of water vapor in steam condition may prevent the formation of chromium oxide as protective layer.

Corrosion of Fe-2.25%Cr-1.6%W Steel at 600 and 700℃ in N2/(0.5, 2.5)%H2S-mixed Gas

ASTM T23 steel with a composition of Fe-2.25%Cr-1.6%W corroded at 600 and <TEX>$700^{\circ}C$</TEX> for 5-70 h in <TEX>$N_2$</TEX>/(0.5, 2.5)%<TEX>$H_2S$</TEX>-mixed gas at 1 atm. It corroded rapidly, forming the outer FeS scale and the inner (FeS, <TEX>$FeCr_2O_4$</TEX>)-mixed scale. The ensuing outward diffusion of <TEX>$Fe^{2+}$</TEX> ions during corrosion led to the protrusion of FeS platelets over the outer FeS scale. The formation of FeS at the surface facilitated the oxidation of Cr to <TEX>$FeCr_2O_4$</TEX> in the inner scale. Since the nonprotective FeS scale existed over the whole scale, T23 steel displayed poor corrosion resistance in the <TEX>$H_2S$</TEX>-containing atmosphere.

Turbulence in the ionized gas of the Orion nebula

In order to study the nature, origin, and impact of turbulent velocity fluctuations in the ionized gas of the Orion Nebula, we apply a variety of statistical techniques to observed velocity cubes. The cubes are derived from high resolving power ($R \approx 40,000$) longslit spectroscopy of optical emission lines that span a range of ionizations. From Velocity Channel Analysis (VCA), we find that the slope of the velocity power spectrum is consistent with predictions of Kolmogorov theory between scales of 8 and 22 arcsec (0.02 to 0.05 pc). The outer scale, which is the dominant scale of density fluctuations in the nebula, approximately coincides with the autocorrelation length of the velocity fluctuations that we determine from the second order velocity structure function. We propose that this is the principal driving scale of the turbulence, which originates in the autocorrelation length of dense cores in the Orion molecular filament. By combining analysis of the non-thermal line widths with the systematic trends of velocity centroid versus ionization, we find that the global champagne flow and smaller scale turbulence each contribute in equal measure to the total velocity dispersion, with respective root-mean-square widths of 4-5 km/s. The turbulence is subsonic and can account for only one half of the derived variance in ionized density, with the remaining variance provided by density gradients in photoevaporation flows from globules and filaments. Intercomparison with results from simulations implies that the ionized gas is confined to a thick shell and does not fill the interior of the nebula.

Influence of non-Kolmogorov atmospheric turbulence on the beam quality of vortex beams.

Based on the extended Huygens-Fresnel principle and the definition of second-order moments of the Wigner distribution function (WDF), the analytical expressions for the propagation factors (M2-factors) and Strehl ratio SR of the Gaussian Schell-model (GSM) vortex beams and GSM non-vortex beams propagation through non-Kolmogorov atmospheric turbulence are derived, and used to study the influence of non-Kolmogorov atmospheric turbulence on beam quality of the GSM vortex beams. It is shown that the smaller the generalized structure constant and the outer scale of turbulence are, and the bigger the inner scale of turbulence is, the smaller the normalized propagation factor is, the bigger the Strehl ratio is, and the better the beam quality of GSM vortex beams in atmospheric turbulence is. The variation of beam quality with the generalized exponent α is nonmonotonic, when α = 3.11, the beam quality of the GSM vortex beams is the poorest through non-Kolmogorov atmospheric turbulence. GSM vortex beams is less affected by turbulence than GSM non-vortex beams under certain condition, and will be useful in long-distance free-space optical communications.

Decoherence of orbital angular momentum tangled photons in non-Kolmogorov turbulence.

Orbital angular momentum (OAM) entangled photons propagating through non-Kolmogorov turbulence are studied by numerical simulations. Here, the paper uses the multiphase screen model, especially focusing on the influences of the azimuthal mode and the turbulence parameters (i.e., the generalized exponent, the outer scale of turbulence, and the inner scale of turbulence) on entanglement evolution in the weak scintillation regime. The results indicate that the azimuthal mode, the generalized exponent, and the outer scale of turbulence have obvious influences on OAM entanglement. However, the influence of the turbulence inner scale on OAM entanglement can be ignored.

Active control for drag reduction in turbulent channel flow: the opposition control schemes revisited

The opposition control schemes first proposed by Choi et al (1994 J. Fluid Mech. 262 75) employing wall-normal ( and spanwise ( velocity are revisited in the present study by performing direct numerical simulation to turbulent channel flow at Special attention is paid to the combined control, in which the wall-normal and spanwise velocities are imposed at the wall just instantaneously opposite to those at a small distance to the wall. In comparison to the v- and w-controls, combined-control could achieve the best drag reduction rate and control efficiency, with the greatest suppression of turbulence intensities. The influence of control on the statistical properties of vortices is scrutinized. By control, the numbers of vortices with every circulation and radius apparently decrease at the same normal location near the wall, while the vortex radius scaled by the actual wall-friction velocity almost remains the same. The streamwise vortices and the induced Reynolds shear stress undergo the greatest suppression by combined control. It is shown that combined control achieves a better efficacy, attributed to the co-work of the mechanisms of the v- and w-controls. At a higher Reynolds number combined control is also more effective than v- and w-controls. The better suppression effect on the outer large scales is the primary reason for the larger drag reduction rate in combined control.

Average intensity and scintillation of light in a turbulent biological tissue

Scintillation is one of the most important properties of light propagating through random media. The scintillation index of plane and spherical light waves as well as of a Gaussian beam propagating in the turbulent biological tissue is developed. Expressions of average intensity of Gaussian beams through turbulent tissue are also derived. Effects of the biological tissue turbulence on the average intensity and scintillation index are discussed in the numerical simulations. An analysis of the threshold between the weak and strong regimes of biological tissue turbulence is made with the variation of outer scale of turbulence. The results are of utmost importance for any applications involved light beam propagation through tissues, especially the cases where the average intensity and spreading properties of the light field should be taken into account to evaluate the system performance and investigations in the structures of biological tissue.

Scintillation index of optical spherical wave propagating through biological tissue

Effects of the tissue turbulence on the propagation of an optical spherical wave are analysed. For this purpose, scintillation index of an optical spherical wave which is propagating in a soft tissue is formulated and evaluated in weakly turbulent soft tissue. Scintillation index of the optical spherical wave is examined against the changes in the tissue parameters which are the tissue length between the optical spherical wave source and the detector, random variations in the refractive index of the tissue and the outer scale of the tissue turbulence. According to our graphical outputs, it is observed that increase in the random variations of the refractive index of the tissue results in an increase in the scintillation index at a certain realization of the turbulence spectrum. On the other hand, larger outer scales and longer tissue lengths yield larger scintillations. The variation of the scintillation index of the optical spherical wave versus the wavelength is also investigated. It is found that at small tissue lengths, wavelength has almost no effect on the scintillations; however, when the tissue length reaches a certain value, shorter wavelengths give rise to larger intensity fluctuations.

Simultaneous seeing measurement through the Subaru Telescope in the visible and near-infrared bands for the wavelength dependence evaluation

Stellar images have been obtained under natural seeing at visible and near-infrared wavelengths simultaneously through the Subaru Telescope at Mauna Kea. The image quality is evaluated by the full-width at the half-maximum (FWHM) of the stellar images. The observed ratio of FWHM in the V-band to the K-band is 1.54 ± 0.17 on average. The ratio shows tendency to decrease toward bad seeing as expected from the outer scale influence, though the number of the samples is still limited. The ratio is important for simulations to evaluate the performance of a ground-layer adaptive optics system at near-infrared wavelengths based on optical seeing statistics. The observed optical seeing is also compared with outside seeing to estimate the dome seeing of the Subaru Telescope.

Temporal properties of Zernike modes for non-Kolmogorov turbulence.

Temporal properties of Zernike modes are investigated for the case of light wave propagation through the non-Kolmogorov turbulence. The calculations are performed for the weak-turbulence conditions with constant turbulence parameters along the propagation path and taking into account the effects of the outer and inner scale of the turbulence. It is shown that the difference between effects produced by the Kolmogorov and non-Kolmogorov turbulence is getting smaller when the aberration order is growing up and when the outer scale magnitude is decreasing. Also it is shown that the correlation time of an aberration is decreasing with increasing of its order and with decreasing of spectral index.

Irradiance scintillation of Gaussian beam considering the concept of anisotropy at different scales in weak anisotropic turbulence

In this work, taking the concept of anisotropy at different scales of turbulence cells or eddies into considerations, new analytic expression of the irradiance scintillation index of a Gaussian beam is derived for Gaussian beam propagating through weak anisotropic non-Kolmogorov turbulence. The effective anisotropic factor is introduced to parameterize the asymmetry of turbulence cells or eddies in the horizontal and vertical directions. Also, the finite turbulence inner and outer scales, and the general spectral power law deviated from the classic 11/3 spectral power law behavior for Kolmogorov turbulence are considered in the investigations. The derived expression of irradiance scintillation index for a Gaussian beam can reduce correctly to the previously published results in the special cases of effective anisotropic factor equaling one. Calculations are conducted to analyze the influences of turbulence parameters on the irradiance scintillation index of Gaussian beam under weak anisotropic non-Kolmogorov turbulence.

Propagation properties and turbulence distance of partially coherent Sinh-Gaussian beams in non-Kolmogorov atmospheric turbulence

Propagation properties including mean-squared beam width, mean-squared angular spreading, beam propagation M2-factor and turbulence distance of partially coherent Sinh-Gaussian (ShG) beams in non-Kolmogorov atmospheric turbulence have been investigated. With a non-Kolmogorov spectrum, the analytical formulas for the mean-squared beam width, angular spreading and M2-factor have been derived in non-Kolmogorov turbulence. The impact of the turbulent parameter (spectral index, inner scale and outer scale) and the decentered parameter on partially coherent ShG beams is discussed by numerical methods. It can be shown that the mean-squared beam width, angular spreading and M2-factor increase then decrease with increasing spectral index from 3 to 4; and they decrease with increasing inner scale and decreasing outer scale. The turbulence distance decreases then increases with increasing spectral index, and increases with increasing inner scale and decreasing outer scale. In addition, the mean-squared beam width and the M2-factor decrease then increase and exist a minimum values with increasing decentered parameter, while the turbulence distance increases monotonously.

Solar seeing monitor MISOLFA: A new method for estimating atmospheric turbulence parameters

Daily observation conditions are needed when observing the Sun at high angular resolution. MISOLFA is a daytime seeing monitor developed for this purpose that allows the estimation of the spatial and temporal parameters of atmospheric turbulence. This information is necessary, for instance, for astrometric measurements of the solar radius performed at Calern Observatory (France) with SODISM II, the ground-based version of the SODISM instrument of the PICARD mission. We present a new way to estimate the spatial parameters of atmospheric turbulence for daily observations. This method is less sensitive to vibrations and guiding defaults of the telescope since it uses short-exposure images. It is based on the comparison of the optical transfer function obtained from solar data and the theoretical values deduced from the Kolmogorov and Von Ka`rma`n models. This method, previously tested on simulated solar images, is applied to real data recorded at Calern Observatory in July 2013 with the MISOLFA monitor. First, we use data recorded in the pupil plane mode of MISOLFA and evaluate the turbulence characteristic times of angle- of-arrival fluctuations: between 5 and 16 milliseconds. Second, we use the focal plane mode of MISOLFA to simultaneously record solar images to obtain isoplanatic angles: ranging from 1 to 5 arcseconds (in agreement with previously published values). These images and our new method allow Fried’s parameter to be measured; it ranges from 0.5 cm to 4.7 cm with a mean value of 1.5 cm when Kolmogorov’s model is considered, and from less than 0.5 to 2.6 cm with a mean value of 1.3 cm for the Von Ka`rma`n model. Measurements of the spatial coherence outer scale parameter are also obtained when using the Von Karman model; it ranges from 0.25 to 13 meters with a mean value of 3.4 meters for the four days of observation that we analyzed. We found that its value can undergo large variations in only a few hours and that more data analysis is needed to better define its statistics.

Irradiance scintillation index for Gaussian beam based on the generalized anisotropic von Karman spectrum

Experiments and theoretical investigations have shown that the atmosphere turbulence exhibits both anisotropic and non-Kolmogorov properties. In this paper, based on the anisotropic generalized von Karman spectrum and the Rytov approximation theory, new expression for the irradiance scintillation index of optical waves is derived for Gaussian beam propagating through weak anisotropic non-Kolmogorov turbulence. Compared with previously published results, it considers simultaneously the asymmetry property of turbulence cells or eddies in the orthogonal xy-plane, the general spectral power law in the range 3–4 instead of constant value of 11/3 for the Kolmogorov turbulence, and the finite turbulence inner and outer scales. Two anisotropic factors are introduced to parameterize the anisotropy of turbulence cells or eddies in horizontal and vertical directions. In the special cases of these two anisotropic factors equaling one and the finite turbulence inner and outer scales equaling separately zero and infinite, the derived expression can reduce correctly to the previously published results. Calculations are performed to analyze the derived results.

Temporal power spectra of plane wave considering finite turbulence inner and outer scales in anisotropic turbulence

Theoretical investigations and experiments have shown that the atmosphere turbulence exhibits both anisotropic and non-Kolmogorov properties compared with traditional atmospheric turbulence which takes the hypotheses of isotropy and homogeneity. There is an increasing interest for modeling atmosphere turbulence with a power spectrum that incorporates anisotropy and general spectral power law deviated from the standard value of 11/3 for the Kolmogorov turbulence. In this study, new analytic expressions for the temporal power spectra of irradiance fluctuations and angle of arrival (AOA) fluctuations have been derived based on the Rytov approximation theory for optical plane wave propagating through weak anisotropic non-Kolmogorov atmosphere turbulence. Compared with the previously published results, the effective anisotropic factor is introduced to the final results to include the anisotropy for different turbulence cells or eddies. The finite turbulence inner and outer scales and the general spectral power law in the range of 3–4 are also considered in the final derived models. The results in this work will help better understand the optical waves’ propagation through anisotropic non-Kolmogorov turbulence.

A theory of scintillation for two‐component power law irregularity spectra: Overview and numerical results

AbstractWe extend the power law phase screen theory for ionospheric scintillation to account for the case where the refractive index irregularities follow a two‐component inverse power law spectrum. The two‐component model includes, as special cases, an unmodified power law and a modified power law with spectral break that may assume the role of an outer scale, intermediate break scale, or inner scale. As such, it provides a framework for investigating the effects of a spectral break on the scintillation statistics. Using this spectral model, we solve the fourth moment equation governing intensity variations following propagation through two‐dimensional field‐aligned irregularities in the ionosphere. A specific normalization is invoked that exploits self‐similar properties of the structure to achieve a universal scaling, such that different combinations of perturbation strength, propagation distance, and frequency produce the same results. The numerical algorithm is validated using new theoretical predictions for the behavior of the scintillation index and intensity correlation length under strong scatter conditions. A series of numerical experiments are conducted to investigate the morphologies of the intensity spectrum, scintillation index, and intensity correlation length as functions of the spectral indices and strength of scatter; retrieve phase screen parameters from intensity scintillation observations; explore the relative contributions to the scintillation due to large‐ and small‐scale ionospheric structures; and quantify the conditions under which a general spectral break will influence the scintillation statistics.

A measure of scale-dependent asymmetry in turbulent boundary layer flows: scaling and Reynolds number similarity

The distribution of temporal scale-dependent streamwise velocity increments is investigated in turbulent boundary layer flows at laboratory and atmospheric Reynolds numbers, using the St. Anthony Falls Laboratory wind tunnel and the Surface Layer Turbulence and Environmental Science Test dataset, respectively. The third-order moments of velocity increments, or asymmetry index $A(a,z)$, is computed for varying wall distance $z$ and time scale separation $a$, where it was observed to leave a robust, distinct signature in the form of a hump, independent of Reynolds number and located across the inertial range. The hump is observed in wall region limited to $z^{+}&lt;5\times 10^{3}$, with a tendency to shift towards smaller time scales as the surface is approached ($z^{+}&lt;70$). Comparing the two datasets, the hump, and its location, are found to obey inner wall scaling and is regarded as a genuine feature of the canonical turbulent boundary layer. The magnitude cumulant analysis of the scale-dependent velocity increments further reveals that intermittency is also enhanced near the wall, in the same flow region where the asymmetry signature was observed. The combination of asymmetry and intermittency is inferred to point at non-local energy transfer and scale coupling across a range of scales. From a turbulent structure perspective, such non-local energy transfer can be seen as the result of strong scale-interaction processes between outer scale motions in the logarithmic layer impacting and distorting smaller scales at the wall, through abrupt energy transfer across scales bypassing the typical energy cascade of the inertial range.