Propagation properties of partially coherent Hermite-Gaussian beams through non-Kolmogorov turbulence

The propagation properties of partially coherent Hermite-Gaussian beams through non-Kolmogorov atmospheric turbulence are studied. The effects of non-Kolmogorov turbulence and beam nonparaxiality on the average intensity evolution and the beam-width spreading are stressed. It is found that the evolution of the average intensity distribution and the beam-width spreading depends on the generalized exponent factor, namely, on the non-Kolmogorov turbulence strength for the paraxial case. For the non-paraxial case the effect of the turbulence is negiigibl% while the beam-width spreading becomes very large. The analytical results are illustrated numerically and interpreted physically.

Average Capacity of OAM-Multiplexed FSO System with Vortex Beam Propagating Through Non-Kolmogorov Turbulence

The propagation of vortex beam in atmospheric turbulence is of significant importance in theoretical study and practical applications. Based on extended Huygens-Fresnel integral and the Rytov approximation, the average capacity of orbital angular momentum(OAM)-multiplexed Laguerre-Gaussian(LG) beam propagating through non-Kolmogorov turbulence is presented, and the analytical expression of spiral spectrum of LG beam has been deduced. The average capacity of FSO system is numerically calculated and the influence of exponent parameter, transmission height, structure constant, wavelength, outer scale and inner scale on average capacity are also analyzed in detail. Outcomes show that smaller structure constant, outer scale, higher transmission height and larger wavelength, inner scale are conducive to improve average capacity in different extent. Results acquires in this paper have potential application value in optical communication within non-Kolmogorov turbulence.

Quantum polarization fluctuations of partially coherent dark hollow beams in non-Kolmogorov turbulence atmosphere

Non-classical polarization properties of dark hollow beams propagating through non-Kolmogorov turbulence are studied. The analytic equation for the polarization degree of the quantization partially coherent dark hollow beams is obtained.It is found that the polarization fluctuations of the quantization partially coherent dark hollow beams are dependent on the turbulence factors and beam parameters with the detection photon numbers. Furthermore, an investigation of the changes in the on-axis propagation point and off-axis propagation point shows that the polarization degree of the quantization partially coherent dark hollow beams presents oscillation for a short propagation distance and gradually returns to zero for a sufficiently long distance.

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 approx- imation 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.

A further study on the spreading and directionality of Gaussian array beams in non-Kolmogorov turbulence

It is found that in free space, the curves of the mean-squared beam width may each have a cross point at a certain propagation distance Zc. For Gaussian array beams, the analytical expressions of zc are derived. For the coherent com- bination, Zc is larger than that for the incoherent combination. However, in non-Kolmogorov turbulence, the cross point disappears, and the Gaussian array beams will have the same directionality in terms of the angular spread. Furthermore, a short propagation distance is needed to reach the same directionality when the generalized exponent is equal to 3.108. In particular, it is shown that the condition obtained in previous studies is not necessary for laser beams to have the same directionality in turbulence, which is explained physically. On the other hand, the relative average intensity distributions at the position where the Gaussian array beams have the same mean-squared beam width are also examined.

Propagation of Partially Coherent Elegant Hermite-Cosh-Gaussian Beam in Non-Kolmogorov Turbulence

Based on the extended Huygens-Fresnel integral, analytical propagation expressions for the rms beam width and angular of partially coherent elegant Hermite cosh Caussian beam （EHChCB） in non-Kolmogorov turbulence are derived. The effects of exponent value, inner and outer scales of non-Kolmogorov turbulence on partially coherent EFIChGB are investigated quantitatively.

Influence of moderate-to-strong anisotropic non-Kolmogorov turbulence on intensity fluctuations of a Gaussian–Schell model beam in marine atmosphere

The scintillation index（SI） of a Gaussian–Schell model（GSM） beam in a moderate-to-strong anisotropic nonKolmogorov 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.

Propagation factor of electromagnetic concentric rings Schell-model beams in non-Kolmogorov turbulence

We derive an analytical expression for the propagation factor（known as M2-factor） of electromagnetic concentric rings Schell-model（EM CRSM） beams in non-Kolmogorov turbulence by utilizing the extended Huygens–Fresnel diffraction integral formula and the second-order moments of the Wigner distribution function（WDF）. Our results show that the EM CRSM beam has advantage over the scalar CRSM beam for reducing the turbulence-induced degradation under suitable conditions. The EM CRSM beam with multi-rings far-fields in free space is less affected by the turbulence than the one with dark-hollow far-fields or the electromagnetic Gaussian Schell-model（EGSM） beam. The dependence of the M2-factor on the beam parameters and the turbulence are investigated in detail.

Robust autofocusing propagation in turbulence

Turbulence in complex environments such as the atmosphere and biological media has always been a great challenge to the application of beam propagation in optical communication, optical trapping and manipulation. To overcome this challenge, this study comprehensively investigates the robust propagation of traditional Gaussian and autofocusing beams in turbulent environments. In order to select stable beams that exhibit high intensity and high field gradient at the focal position in complex environments, Kolmogorov turbulence theory is used to simulate the propagation of beams in atmospheric turbulence based on the multi-phase screen method. We systematically analyze the intensity fluctuations, the variation of the coherence factor and the change in the scintillation index with propagation distance. The analysis reveals that the intensity fluctuations of autofocusing beams are significantly smaller than those of Gaussian beams, and the coherence of autofocusing beams is better than that of Gaussian beams under turbulence. Moreover, autofocusing beams exhibit less oscillation than Gaussian beams, indicating that autofocusing beams propagate in complex environments with less distortion and intensity fluctuation. Overall, this work clearly demonstrates that autofocusing beams exhibit higher stability in propagation compared with Gaussian beams, showing great promise for applications such as optical trapping and manipulation in complex environments.

Baseline design of the KunLun Turbulence Profiler instrument

Adaptive optics systems are the most powerful tools to counteract the image blurring caused by atmospheric turbulence,allowing ground-based telescopes to capture high-resolution images.A critical parameter influencing adaptive optics system performance is the atmospheric refractive index structure constant,C_(n)^(2),which characterizes the intensity of atmospheric optical turbulence as a function of altitude.Given its simplicity,the lunar scintillometer is the preferred method for detecting atmospheric turbulence in challenging environments like Dome A in Antarctica,where sites are still in the developmental stages and local environmental conditions are extremely harsh.However,optimizing the performance of such instruments requires carefully determining the baseline configuration of photon sensors according to each site's specific optical turbulence profile characteristics.This study uses a Monte Carlo method to identify the optimal configuration for the KunLun Turbulence Profiler(KLTP),an instrument comparable to the lunar scintillometer,developed for use at Dome A.Simulations conducted using the obtained optimal baseline configuration recovered three different model optical turbulence profiles,demonstrating the effectiveness of our method in obtaining an optimal baseline configuration.Our approach can be easily applied to baseline design for similar turbulence profilers at other sites.

An improved TDE technique for derivation of 2D turbulence structures based on GPI data in toroidal plasma

This paper reports an improved time-delay estimation(TDE)technique for the derivation of turbulence structures based on gas-puff imaging data.The improved TDE technique,integrating an inverse timing search and hierarchical strategy,offers superior accuracy in calculating turbulent velocity field maps and analyzing blob dynamics,which has the power to obtain the radial profiles of equilibrium poloidal velocity,blob size and its radial velocity,even the fluctuation analysis,such as geodesic acoustic modes and quasi-coherent mode,etc.This improved technique could provide important 2D information for the study of edge turbulence and blob dynamics,advancing the understanding of edge turbulence physics in fusion plasmas.

Properties of focused Laguerre–Gaussian beam propagating in anisotropic ocean turbulence

We analyze the properties of a focused Laguerre–Gaussian(LG)beam propagating through anisotropic ocean turbulence based on the Huygens–Fresnel principle.Under the Rytov approximation theory,we derive the analytical formula of the channel capacity of the focused LG beam in the anisotropic ocean turbulence,and analyze the relationship between the capacity and the light source parameters as well as the turbulent ocean parameters.It is found that the focusing mirror can greatly enhance the channel capacity of the system at the geometric focal plane in oceanic turbulence.The results also demonstrate that the communication link can obtain high channel capacity by adopting longer beam wavelength,greater initial beam waist radius,and larger number of transmission channels.Further,the capacity of the system increases with the decrease of the mean squared temperature dissipation rate,temperature-salinity contribution ratio and turbulence outer scale factor,and with the increase of the kinetic energy dissipation rate per unit mass of fluid,turbulence inner scale factor and anisotropy factor.Compared to a Hankel–Bessel beam with diffraction-free characteristics and unfocused LG beam,the focused LG beam shows superior anti-turbulence interference properties,which provide a theoretical reference for research and development of underwater optical communication links using focused LG beams.

Gyro-Landau-fluid simulations of impurity effects on ion temperature gradient driven turbulence transport

The effects of impurities on ion temperature gradient(ITG)driven turbulence transport in tokamak core plasmas are investigated numerically via global simulations of microturbulence with carbon impurities and adiabatic electrons.The simulations use an extended fluid code(ExFC)based on a four-field gyro-Landau-fluid(GLF)model.The multispecies form of the normalized GLF equations is presented,which guarantees the self-consistent evolution of both bulk ions and impurities.With parametric profiles of the cyclone base case,well-benchmarked ExFC is employed to perform simulations focusing on different impurity density profiles.For a fixed temperature profile,it is found that the turbulent heat diffusivity of bulk ions in a quasi-steady state is usually lower than that without impurities,which is contrary to the linear and quasilinear predictions.The evolutions of the temperature gradient and heat diffusivity exhibit a fast relaxation process,indicating that the destabilization of the outwardly peaked impurity profile is a transient state response.Furthermore,the impurity effects from different profiles can obviously influence the nonlinear critical temperature gradient,which is likely to be dominated by linear effects.These results suggest that the improvement in plasma confinement could be attributed to the impurities,most likely through adjusting both heat diffusivity and the critical temperature gradient.

Turbine Passage Secondary Flow Dynamics and Endwall Heat Transfer Under Different Inflow Turbulence

This study presents endwall hydrodynamics and heat transfer in a linear turbine cascade at Re 5×105 at low and high intensities of turbulence.Results are numerically predicted using the standard SST model and Reθ-γtransition model as well as using the high-resolution LES separately.The major secondary flow components,comprising the horseshoe,corner,and passage vortices are recognized and the impact on heat or mass transfer is investigated.The complicated behavior of turbine passage secondary flow generation and establishment are impacted by the perspective of boundary layer attributes and inflow turbulence.The passage vortex concerning the latest big leading-edge vane is generated by the enlargement of the circulation developed at the first instance adjacent to the pressure side becomes powerful and mixes with other vortex systems during its migration towards the suction side.The study conclusions reveal that substantial enhancements are attained on the endwall surface,for the entire spanwise blade extension on the pressure surface,and in the highly 3-D region close to the endwall on the suction surface.The forecasted suction surface thermal exchange depicts great conformity with the measurement values and precisely reproduces the enhanced thermal exchange owing to the development and lateral distribution of the secondary flows along the midspan of the blade passage downstream.The impacts of the different secondary flow structures on the endwall thermal exchange are described in depth.

Mapping Network-Coordinated Stacked Gated Recurrent Units for Turbulence Prediction

Accurately predicting fluid forces acting on the sur-face of a structure is crucial in engineering design.However,this task becomes particularly challenging in turbulent flow,due to the complex and irregular changes in the flow field.In this study,we propose a novel deep learning method,named mapping net-work-coordinated stacked gated recurrent units(MSU),for pre-dicting pressure on a circular cylinder from velocity data.Specifi-cally,our coordinated learning strategy is designed to extract the most critical velocity point for prediction,a process that has not been explored before.In our experiments,MSU extracts one point from a velocity field containing 121 points and utilizes this point to accurately predict 100 pressure points on the cylinder.This method significantly reduces the workload of data measure-ment in practical engineering applications.Our experimental results demonstrate that MSU predictions are highly similar to the real turbulent data in both spatio-temporal and individual aspects.Furthermore,the comparison results show that MSU predicts more precise results,even outperforming models that use all velocity field points.Compared with state-of-the-art methods,MSU has an average improvement of more than 45%in various indicators such as root mean square error(RMSE).Through comprehensive and authoritative physical verification,we estab-lished that MSU’s prediction results closely align with pressure field data obtained in real turbulence fields.This confirmation underscores the considerable potential of MSU for practical applications in real engineering scenarios.The code is available at https://github.com/zhangzm0128/MSU.

Development of a 2D spatial displacement estimation method for turbulence velocimetry of the gas puff imaging system on EAST

A gas puff imaging(GPI)diagnostic has been developed and operated on EAST since 2012,and the time-delay estimation(TDE)method is used to derive the propagation velocity of fluctuations from the two-dimensional GPI data.However,with the TDE method it is difficult to analyze the data with fast transient events,such as edge-localized mode(ELM).Consequently,a method called the spatial displacement estimation(SDE)algorithm is developed to estimate the turbulence velocity with high temporal resolution.Based on the SDE algorithm,we make some improvements,including an adaptive median filter and super-resolution technology.After the development of the algorithm,a straight-line movement and a curved-line movement are used to test the accuracy of the algorithm,and the calculated speed agrees well with preset speed.This SDE algorithm is applied to the EAST GPI data analysis,and the derived propagation velocity of turbulence is consistent with that from the TDE method,but with much higher temporal resolution.

A sub-grid scale model for Burgers turbulence based on the artificial neuralnetwork method

The present study proposes a sub-grid scale model for the one-dimensional Burgers turbulence based on the neuralnetwork and deep learning method.The filtered data of the direct numerical simulation is used to establish thetraining data set,the validation data set,and the test data set.The artificial neural network(ANN)methodand Back Propagation method are employed to train parameters in the ANN.The developed ANN is applied toconstruct the sub-grid scale model for the large eddy simulation of the Burgers turbulence in the one-dimensionalspace.The proposed model well predicts the time correlation and the space correlation of the Burgers turbulence.

Bessel–Gauss photon beams with fractional order vortex propagation in weak non-Kolmogorov turbulence

We model the effects of weak fluctuations on the probability densities and normalized powers of vortex models for the Bessel–Gauss photon beam with fractional topological charge in the paraxial non-Kolmogorov turbulence channel. We find that probability density of signal vortex models is a function of deviation from the center of the photon beam, and the farther away from the beam center it is, the smaller the probability density is. For fractional topological charge, the average probability densities of signal/crosstalk vortex modes oscillate along the beam radius except the half-integer order. As the beam waist of the photon source grows, the average probability density of signal and crosstalk vortex modes grow together. Moreover, the peak of the average probability density of crosstalk vortex modes shifts outward from the beam center as the beam waist gets larger. The results also show that the smaller index of non-Kolmogorov turbulence and the smaller generalized refractive-index structure parameter may lead to the higher average probability densities of signal vortex modes and lower average probability densities of crosstalk vortex modes. Lower-coherence radius or beam waist can give rise to less reduction of the normalized powers of the signal vortex modes, which is opposite to the normalized powers of crosstalk vortex modes.

Influence of the upper mixed layer depth on Langmuir turbulence characteristics

The upper mixed layer depth(h)has a significant seasonal variation in the real ocean and the low-order statistics of Langmuir turbulence are dramatically influenced by the upper mixed layer depth.To explore the influence of the upper mixed layer depth on Langmuir turbulence under the condition of the wind and wave equilibrium,the changes of Langmuir turbulence characteristics with the idealized variation of the upper mixed layer depth from very shallow(h=5 m)to deep enough(h=40 m)are studied using a non-hydrostatic large eddy simulation model.The simulation results show that there is a direct entrainment depth induced by Langmuir turbulence(h_(LT))within the thermocline.The normalized depthaveraged vertical velocity variance is smaller and larger than the downwind velocity variance for the ratio of the upper mixed layer to a direct entrainment depth induced by Langmuir turbulence h/h_(LT)<1 and h/h_(LT)>1,respectively,indicating that turbulence characteristics have the essential change(i.e.,depth-averaged vertical velocity variance(DAVV)DADV for Langmuir turbulence)between h/h_(LT)<1 and h/h_(LT)>1.The rate of change of the normalized depth-averaged low-order statistics for h/h_(LT)<1 is much larger than that for h/h_(LT)>1.The reason is that the downward pressure perturbation induced by Langmuir cells is strongly inhibited by the upward reactive force of the strong stratified thermocline for h/h_(LT)<1 and the eff ect of upward reactive force on the downward pressure perturbation becomes weak for h/h_(LT)>1.Hence,the upper mixed layer depth has significant influences on Langmuir turbulence characteristics.

Aero-Hydrodynamic Coupled Dynamic Characteristics of Semi-Submersible Floating Offshore Wind Turbines Under Inflow Turbulence

In this study,the frequency characteristics of the turbulent wind and the effects of wind-wave coupling on the low-and high-frequency responses of semi-submersible floating offshore wind turbines(FOWT)are investigated.Various wave load components,such as first-order wave loads,combined first-and second-order difference-frequency wave loads,combined first-and second-order sum-frequency wave loads,and first-and complete second-order wave loads are taken into consideration,while different turbulent environments are considered in aerodynamic loads.The com-parison is based on time histories and frequency spectra of platform motions and structural load responses and statistical values.The findings indicate that the second-order difference-frequency wave loads will significantly increase the natural frequency of low-frequency motion in the responses of the platform motion and structure load of the semi-submersible platform,which will cause structural fatigue damage.Under the action of turbulent wind,the influences of second-order wave loads on the platform motion and structural load response cannot be ignored,especially under extreme sea conditions.Therefore,in order to evaluate the dynamic responses of semi-submersible FOWT more accurately,the actual environment should be simulated more realistically.