Homogeneous Atmospheric Turbulence Research Articles

Circularly symmetric cusped random beams in free space and atmospheric turbulence.

A class of random stationary, scalar sources producing cusped average intensity profiles (i.e. profiles with concave curvature) in the far field is introduced by modeling the source degree of coherence as a Fractional Multi-Gaussian-correlated Schell-Model (FMGSM) function with rotational symmetry. The average intensity (spectral density) generated by such sources is investigated on propagation in free space and isotropic and homogeneous atmospheric turbulence. It is found that the FMGSM beam can retain the cusped shape on propagation at least in weak or moderate turbulence regimes; however, strong turbulence completely suppresses the cusped intensity profile. Under the same atmospheric conditions the spectral density of the FMGSM beam at the receiver is found to be much higher than that of the conventional Gaussian Schell-model (GSM) beam within the narrow central area, implying that for relatively small collecting apertures the power-in-bucket of the FMGSM beam is higher than that of the GSM beam. Our results are of importance to energy delivery, Free-Space Optical communications and imaging in the atmosphere.

Propagation of cosine-Gaussian-correlated Schell-model beams in atmospheric turbulence

A stochastic beam generated by a recently introduced source of Schell type with cosine-Gaussian spectral degree of coherence is shown to possess interesting novel features on propagation in isotropic and homogeneous atmospheric turbulence with general non-Kolmogorov power spectrum. It is shown that while at small distances from the source the beam's intensity exhibits annular profile with adjustable area of the dark region, the center disappears at sufficiently large distances and the beam's intensity tends to Gaussian form. Hence the 3D bottle beam is produced by the cumulative effect of the random source and the atmosphere. The distances at which the on-axis beam intensity has local minima and maxima are shown to have analytic dependence on the source and the atmospheric parameters. And the influence of the fractal constant of the atmospheric power spectrum and refractive-index structure constant on beam characteristics is analyzed in depth. The novel double-cycle qualitative change in the degree of coherence is shown to occur on atmospheric propagation which was not previously known for any other beams.

Sonic Boom Variability Due to Homogeneous Atmospheric Turbulence

This study describes the nondeterministic effect of homogeneous atmospheric turbulence on sonic boom propagation. The Sears-Haack body was calculated in three dimensions by computational fluid dynamics in inviscid flow (Euler) mode to create the near-field pressure wave. The homogeneous atmospheric turbulence field was represented by the finite sum of discrete Fourier modes based on the von Karman and Pao energy spectrum. The sonic boom signature was then calculated by the modified waveform parameter method, considering a random velocity of homogeneous atmospheric turbulence. The results of this study indicated that atmospheric turbulence has a marked influence on sonic boom overpressure during its propagation to the ground. In comparison to the no-turbulence condition, we found that the sonic boom decreased in 59 % of the cases and increased in 41 % of the cases. Thus, homogeneous atmospheric turbulence seems to favor a decrease, rather than an increase, in boom overpressure. In addition, we found that turbulence has a small effect on the propagation path from the flight altitude to the ground. Nonetheless, this small change in the propagation path may result in a variability, of the point at which the sonic boom reaches the ground, of up to 1820 ft in the north-south direction (flight direction) and 115 ft in the east-west direction.

Numerical study of wake vortex decay and descent in homogeneous atmospheric turbulence

Numerical study of wake vortex decay and descent in homogeneous atmospheric turbulence

Probability distribution of irradiance for the onset of strong scintillation

We calculated the probability distribution function (PDF) from simulations for an initially spherical wave propagated through homogeneous atmospheric turbulence. The onset of strong scintillation was calculated. By onset of strong scintillation, we mean conditions of weak scintillation changing to the condition of strong focusing. In addition, one case in the saturation regime was calculated. The simulations’ PDF’s are compared with several heuristic models of the PDF and are seen to progress from close to log normal for the cases of weakest scintillation to close to the log normally modulated exponential PDF (LNME PDF) for the cases of strong scintillation. The simulations’ PDF’s are not in agreement with the K PDF for any of the calculated cases. The best agreement was obtained in comparison with Beckmann’s PDF [P. Beckmann, Probability in Communication Engineering (Harcourt, Brace, & World, 1967)]. Beckmann’s PDF varies from being the log-normal PDF for weak scintillation to being the LNME PDF for strong scintillation and progresses further to the theoretically expected exponential PDF in the limit of saturated scintillation. We recommend that simulation be used to predict the irradiance PDF for plane and diverged waves in homogeneous turbulence in preference to using heuristic models. More complicated propagation cases remain in the domain of heuristic argumentation.

Two-point coherence in the atmospheric surface layer

Two-point, one-dimensional coherence in horizontally homogeneous atmospheric turbulence is studied, both by experiment and analysis. Measurements are carried out using horizontally spaced sensors with the separation perpendicular to the mean velocity. Two-dimensional spectral models and three-dimensional inertial-range spectral tensors are used in the coherence calculations. The one-dimensional coherence for both velocity and scalar fluctuations is found to roll off at a wavenumber much smaller than we would expect from the classical notion of eddy correlation. This is a consequence of the cancellation of Fourier components aliased from the direction of the sensor separation into the streamwise direction. However, the coherence for the three velocity components behaves somewhat differently, reflecting the relative orientations of the velocity component, sensor separation and the mean velocity. These features are well predicted by the calculation. The analysis is also extended to calculate the two-point scalar-vertical velocity cospectrum and the results are in good agreement with our experimental data. The ratio of two- to one-point cospectra decreases at slightly larger wavenumber than the two-point scalar coherence does.

Connection between structural and statistical models of atmospheric turbulence

A structural model of isotropic homogeneous atmospheric turbulence is presented, in which the turbulence is described as an ensemble of individual localized quasistatic eddies or turbules. Turbules of different sizes a are assumed self‐similar with respect to their temperature and flow velocity fields, and randomly positioned and oriented with no correlations. It is shown that, in order to obtain agreement with the Kolmogorov acoustical scattering spectrum, the usual relation between turbule flow speed v and size, v∝a1/3, must be assumed, and, in addition, (i) turbule number densities must be proportional to a−3, and (ii) turbule sizes must be in a geometric sequence, from the outer scale to the inner. It is also shown that the Kolmogorov spectrum is insensitive to the turbule morphology, and that the extent of the ‘‘inertial range’’ is influenced only weakly by the morphology. Expressions for CT2 and Cv2, and for the boundaries of the inertial range, are derived in terms of the structural parameters.

Variance of focal-plane centroids

The variance of the unbiased focal-plane estimates of image centroids from a point source is derived for arbitrary strength of scattering by using path-integral methods. The Markov approximation and narrow angular scattering are assumed. Results are presented for an ideal focusing telescope with an aperture transmission that produces no phase errors. Calculations of the leading term are performed for a circular telescope aperture and the case of homogeneous atmospheric turbulence described by the Hill spectrum [ J. Fluid Mech.88, 541– 562 ( 1978)]. When there are irradiance fluctuations, the variance of the unbiased estimate of image centroids depends on the choice of the origin of the weighting vector. The variance of the centroid of a single image depends on three physical parameters related to the Fresnel scale, the inner scale, and the strength of scattering. The variance of the separation between two images from two separated telescope apertures depends on the same parameters in addition to the normalized separation of the apertures. The important contributions from propagation distance and spectral wave number are identified for the different parameter regimes. The magnitude of centroid motion compared to the average image size is also discussed.