Small Outer Scale Research Articles

The Evolution and Role of Solar Wind Turbulence in the Inner Heliosphere

Abstract The first two orbits of the Parker Solar Probe spacecraft have enabled the first in situ measurements of the solar wind down to a heliocentric distance of 0.17 au (or 36 ). Here, we present an analysis of this data to study solar wind turbulence at 0.17 au and its evolution out to 1 au. While many features remain similar, key differences at 0.17 au include increased turbulence energy levels by more than an order of magnitude, a magnetic field spectral index of −3/2 matching that of the velocity and both Elsasser fields, a lower magnetic compressibility consistent with a smaller slow-mode kinetic energy fraction, and a much smaller outer scale that has had time for substantial nonlinear processing. There is also an overall increase in the dominance of outward-propagating Alfvénic fluctuations compared to inward-propagating ones, and the radial variation of the inward component is consistent with its generation by reflection from the large-scale gradient in Alfvén speed. The energy flux in this turbulence at 0.17 au was found to be ∼10% of that in the bulk solar wind kinetic energy, becoming ∼40% when extrapolated to the Alfvén point, and both the fraction and rate of increase of this flux toward the Sun are consistent with turbulence-driven models in which the solar wind is powered by this flux.

Lommel-Gaussian Pulsed Beams Carrying Orbital Angular Momentum Propagation in Asymmetric Oceanic Turbulence

By developing the complex phase perturbation for vortex pulsed beams in asymmetric oceanic turbulence and the spatiotemporal orthogonal basis for Lommel-Gaussian pulsed beam, we establish the received probability model of orbital angular momentum (OAM) modes for vortex pulsed beams propagating through asymmetric oceanic turbulence. Using this new model, we investigate the received probability and the pulse broadening of OAM modes of Lommel-Gaussian pulsed beam in asymmetric oceanic turbulence. Numerical simulation results show that Lommel-Gaussian pulsed beam causes a smaller pulse broadening when it propagates through oceanic turbulence with higher asymmetric factor, lower temperature structure constant, smaller inner scale and outer scale. In addition, Lommel-Gaussian pulsed beam with lower carrier frequency propagates through the oceanic turbulence with higher asymmetric factor, larger inner scale, smaller outer scale and smaller temperature structure constant, which obtains a higher received probability of signal OAM modes. For Lommel-Gaussian pulsed beams, the change of OAM quantum number has a week effect on the pulse broadening and the received probability.

RELAY PROPAGATION OF PARTIALLY COHERENT COSH-GAUSSIAN BEAMS IN NON-KOLMOGOROV TURBULENCE

The analytical formulas for the average intensity and power in the bucket of the relay propagation of partially coherent cosh-Gaussian (ChG) beams in non-Kolmogorov turbulence have been derived based on the extended Huygens-Fresnel principle. The in∞uences of the beam parameters, relay system parameters and the non-Kolmogorov turbulence parameters on relay propagation are investigated by numerical examples. Numerical results reveal that the relay propagation of the beam is difierent from that in the case of Kolmogorov turbulence. It is shown that the relay propagation has advantages over direct propagation, and the relay propagation of partially coherent ChG beams depends greatly on the beam parameters, relay system and the generalized exponent fi. The focusability of the beam at the target in non-Kolmogorov turbulence increases with larger inner scale, larger relay system radius, smaller outer scale, and smaller generalized structure constant. The results are useful for the practical applications of relay propagation, i.e., free- space communication.

Atmospheric image blur with finite outer scale or partial adaptive correction

Seeing-limited resolution in large telescopes working over wide wavelength range depends substantially on the turbulence outer scale and cannot be adequately described by one "seeing" value. We attempt to clarify frequent confusions on this matter. We study the effects of finite turbulence outer scale and partial adaptive corrections by means of analytical calculations and numerical simulations. If a von Karman turbulence model is adopted, a simple approximate formula captures the dependence of atmospheric long-exposure resolution on the outer scale over the entire practically interesting range of telescope diameters and wavelengths. In the infrared (IR), the difference with the standard Kolmogorov seeing formula can exceed a factor of two. We find that low-order adaptive turbulence correction produces residual wave-fronts with effectively small outer scale, so even very low compensation order leads to a substantial improvement in resolution over seeing, compared to the standard theory. Seeing-limited resolution of large telescopes, especially in the IR, is currently under-estimated by not accounting for the outer scale. On the other hand, adaptive-optics systems designed for diffraction-limited imaging in the IR can improve the resolution in the visible by as much as two times.

First statistics of the turbulence outer scale at Dome C

Context. The outer scale of wavefronts is of interest for the dimensioning and the optimisation of the High Angular Resolution techniques such as Interferometry and Adaptive Optics, particularly for the new generation of telescopes such as the Extremely Large Telescopes (ELT). Aims. We aim to provide the first statistics of the outer scale at Dome C site in Antarctica to finalize the characterization of this site. Methods. A new version of the Generalized Seeing Monitor has been developed for extremely cold conditions. Two DIMMs (Differential Image Motion Monitor) were coupled to extract Angle-of-Arrival (AA) fluctuations using CCD detectors. Correlations of these AA fluctuations for different baselines lead to outer scale estimations. Results. For the first time, statistics of the outer scale at Dome C are provided leading to small values in the surface layer at Dome C. These small outer scale values compared to temperate sites considerably reduce the fringe excursion of interferometers and the low orders of the normalized amplitude of atmospheric Zernike coefficients, particularly the tip-tilt. Conclusions. The Dome C small outer scale combined with the large coherence time and large isoplanatic angle are very useful for the development of Adaptive Optics systems and long-baseline interferometers.

Propagation of partially coherent flat-topped beams through a turbulent atmosphere

Based on the modified beam model for flat-topped beams and the Schell model for partially coherent light, an expression for partially coherent flat-topped (PCFT) beams has been proposed. The propagation characteristics of PCFT beams with circular symmetry through a turbulent atmosphere have been studied. By using the generalized Huygens-Fresnel integral and Fourier transform method, the expressions for the cross-spectral density function and the average intensity have been given and the analytical expression for the root-mean-square width has been derived. The effects of the beam order, the spatial coherence, and the turbulent parameter on the intensity distributions and beam spreading have been discussed in detail. Our results show that the on-axis intensity of the beams decreases with increasing turbulence and decreasing coherence of the source, whereas the on-axis intensity of the beams in the far field decreases slightly with increasing beam order. The relative spreading of PCFT beams is smaller for beams with a higher order, a lower degree of global coherence of the source, a larger inner scale, and a smaller outer scale of the turbulence.

The Outer Scale of Turbulence in the Magnetoionized Galactic Interstellar Medium

We analyze Faraday rotation and depolarization of extragalactic radio point sources in the direction of the inner Galactic plane to determine the outer scale and amplitude of the rotation measure power spectrum. Structure functions of rotation measure show lower amplitudes than expected when extrapolating electron density fluctuations to large scales assuming a Kolmogorov spectral index. This implies an outer scale of those fluctuations on the order of a parsec, much smaller than commonly assumed. Analysis of the partial depolarization of point sources independently indicates a small outer scale of a Kolmogorov power spectrum. In the Galaxy's spiral arms, no rotation measure fluctuations on scales above a few parsecs are measured. In the interarm regions fluctuations on larger scales than in spiral arms are present, and show power-law behavior with a shallow spectrum. These results suggest that in the spiral arms stellar sources such as stellar winds or protostellar outflows dominate the energy injection for the turbulent energy cascade on parsec scales, while in the interarm regions supernova and superbubble explosions are the main sources of energy on scales on the order of 100 pc.

Atmospheric Turbulence Measurements with the Palomar Testbed Interferometer

Data from the Palomar Testbed Interferometer, with a baseline length of 110 and an observing wavelength of $2.2 \mu{\rm m}$, were used to derive information on atmospheric turbulence on 64 nights in 1999. The measured two-aperture variance coherence times at $2.2 \mu{\rm m}$ ranged from 25 msec to 415 msec (the lower value was set by instrumental limitations---the interferometer could not operate when the coherence time was lower than this). On all nights, the spectrum of the short time scale ($<600$ msec) delay fluctuations had a shallower spectrum than the theoretical Kolmogorov value of 5/3. On most nights, the mean value of the power law slope was between 1.40 and 1.50. Such a sub-Kolmogorov slope will result in the seeing improving as the $\approx 0.4$ power of wavelength, rather than the slower 0.2 power predicted by Kolmogorov theory. On four nights, the combination of delay and angle tracking measurements allowed a derivation of the (multiple) wind velocities of the turbulent layers, for a frozen-flow model. The derived wind velocities were all $\le 4 {\rm m s^{-1}}$, except for a small $10 {\rm s^{-1}}$ component on one night. The combination of measured coherence time, turbulence spectral slope, and wind velocity for the turbulent layer(s) allowed a robust solution for the outer scale size (beyond which the fluctuations do not increase). On the four nights with angle tracking data, the outer scale varied from 6 to 54 m, with most values in the 10-25 range. Such small outer scale values cause some components of visibility and astrometric errors to average down rapidly.