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Magnetohydrodynamic (MHD) turbulence is a crucial component of the current paradigms of star formation, dynamo theory, particle transport, magnetic reconnection, and evolution of structure in the interstellar medium (ISM) of galaxies. Despite the importance of turbulence to astrophysical fluids, a full theoretical framework based on solutions to the Navier–Stokes equations remains intractable. Observations provide only limited line-of-sight information on densities, temperatures, velocities, and magnetic field strengths, and therefore directly measuring turbulence in the ISM is challenging. A statistical approach has been of great utility in allowing comparisons of observations, simulations, and analytic predictions. In this review article, we address the growing importance of MHD turbulence in many fields of astrophysics and review statistical diagnostics for studying interstellar and interplanetary turbulence. In particular, we will review statistical diagnostics and machine learning algorithms that have been developed for observational data sets in order to obtain information about the turbulence cascade, fluid compressibility (sonic Mach number), and magnetization of fluid (Alfvénic Mach number). These techniques have often been tested on numerical simulations of MHD turbulence, which may include the creation of synthetic observations, and are often formulated on theoretical expectations for compressible magnetized turbulence. We stress the use of multiple techniques, as this can provide a more accurate indication of the turbulence parameters of interest. We conclude by describing several open-source tools for the astrophysical community to use when dealing with turbulence.

The third-order scaling law, Yaglom law, of Elsässer fluctuations in the solar wind is believed to reflect the inertial range energy cascade of the MHD turbulence and provides an approach to evaluate the cascade rate. However, the occurrence ratio with the Yaglom scaling law, the fraction of the intervals where the Yaglom linear scaling is observed, is reported to be low (0.05–0.30) in the high-latitude solar wind observed by the Ulysses spacecraft. Whether the occurrence ratio could be higher in other conditions remains unknown. Here, we analyze the occurrence of the third-order scaling in the inner heliosphere with the first 100 days of observation of the Helios 1 and Helios 2 spacecraft. We investigate 162 intervals in the leading edges and 323 intervals in the trailing edges of the high-speed streams, respectively. All of these intervals have a time duration of 9 hr. We find that in the inner heliosphere the occurrence ratio is relatively high in the leading edges (0.58) and moderate in the trailing edges (0.45). Among the data intervals with the Yaglom scaling in the leading edges, 94.7% of intervals give positive rates, while in the trailing edges 78.6% give negative rates. The variations of the occurrence ratio with various turbulence parameters are shown. The cascade rate is found to be higher than the proton heating rate calculated from the data, which have third-order scaling. These new results raise several questions related to the nature and origin of the third-order scaling law and may initiate new studies on solar wind turbulence.

Several studies of Galactic cosmic-ray (GCR) modulation within the astrospheres of stars deemed to be proxies for the young Sun have concluded that the intensities of these particles would, at early stages of the Sun’s evolution, be negligible at 1 au. These studies, however, do not take into account the varying interstellar conditions the young Sun would have encountered as it traversed its Galactic orbit, nor do they realistically model the transport of GCRs. The present study, for the first time, examines the influence of various interstellar parameters in the Galactic spiral arms on the astrosphere of κ1 Ceti, a young Sun proxy, through magnetohydrodynamic modelling. We demonstrate that these conditions lead to an astrosphere with considerably smaller dimensions than previous estimates. We also model the transport of turbulence parameters within said astrosphere for the first time, demonstrating that turbulence levels could be significantly higher than observed in the heliosphere. Finally, these insights are implemented in a 3D, ab initio GCR transport model to compute GCR intensities at 1 au, demonstrating the importance of drift effects in astrospheric modulation: full drift effects lead to GCR intensities comparable to modern observations, while turbulence-reduced drift coefficients lead to significantly smaller intensities.

Two new five-beam acoustic Doppler current profilers—the Nortek Signature1000 AD2CP and the Teledyne RDI Sentinel V50—are demonstrated to measure turbulence at two energetic tidal channels within Puget Sound, Washington. The quality of the raw data is tested by analyzing the turbulent kinetic energy frequency spectra, the turbulence spatial structure function, the shear in the profiles, and the covariance Reynolds stresses. The five-beam configuration allows for a direct estimation of the Reynolds stresses from along-beam velocity fluctuations. The Nortek’s low Doppler noise and high sampling frequency allow for the observation of the turbulent inertial subrange in both the frequency spectra and the turbulence structure function. The turbulence parameters obtained from the five-beam acoustic Doppler current profilers are validated with turbulence data from simultaneous measurements with acoustic Doppler velocimeters. These combined results are then used to assess a turbulent kinetic energy budget in which depth profiles of the turbulent kinetic energy dissipation and production rates are compared. The associated codes are publicly available on the MATLAB File Exchange website.

Atmospheric turbulence parameters, such as turbulent kinetic energy and dissipation rate, are of great significance in weather prediction, meteorological disasters, and forecasting. Due to the lack of ideal direct detection methods, traditional structure function methods are mainly based on Kolmogorov's assumption of local isotropic turbulence and the well-known -5/3 power law within the inertial subrange, which limits their application. Here, we propose a method for directly measuring atmospheric turbulence parameters using coherent Doppler wind lidar, which can directly obtain atmospheric turbulence parameters and vertical structural features, breaking the limitations of traditional methods. The first published spatiotemporal distribution map of the power-law exponent of the inertial subrange is provided in this study, which indicates the heterogeneity of atmospheric turbulence at different altitudes and also indicates that the power-law exponent at high altitudes does not fully comply with the -5/3 power law, proving the superiority of our method. We analyze the results under different weather conditions, indicating that the method still holds. The turbulent kinetic energy and power-law index obtained by this method are continuously compared with the results obtained with an ultrasonic anemometer for a month-long period. The results of the two have high consistency and correlation, verifying the accuracy and applicability of the proposed method. The proposed method has great significance in studying the vertical structural characteristics of atmospheric turbulence.

Measuring plasma parameters in the upper solar corona and inner heliosphere is challenging because of the region’s weakly emissive nature and inaccessibility for most in situ observations. Radio imaging of broadened and distorted background astronomical radio sources during solar conjunction can provide unique constraints for the coronal material along the line of sight. In this study, we present radio spectral imaging observations of the Crab Nebula (Tau A) from 2024 June 9 to June 22 when it was near the Sun with a projected heliocentric distance of 5–27 solar radii, using the Owens Valley Radio Observatory’s Long Wavelength Array at multiple frequencies in the 30–80 MHz range. The imaging data reveal frequency-dependent broadening and distortion effects caused by anisotropic wave propagation through the turbulent solar corona at different distances. We analyze the brightness, size, and anisotropy of the broadened images. Our results provide detailed observations showing that the eccentricity of the unresolved source increases as the line of sight approaches the Sun, suggesting a higher anisotropic ratio of the plasma turbulence closer to the Sun. In addition, the major axis of the elongated source is consistently oriented in the direction perpendicular to the radial direction, suggesting that the turbulence-induced scattering effect is more pronounced in the direction transverse to the coronal magnetic field. Lastly, when the source undergoes large-scale refraction as the line of sight passes through a streamer, the apparent source exhibits substructures at lower frequencies. This study demonstrates that observations of celestial radio sources with lines of sight near the Sun provide a promising method for measuring turbulence parameters in the inner heliosphere.

The method and results of lidar studies of spatiotemporal variability of wind turbulence in the atmospheric boundary layer are reported. The measurements were conducted by a Stream Line pulsed coherent Doppler lidar (PCDL) with the use of conical scanning by a probing beam around the vertical axis. Lidar data are used to estimate the kinetic energy of turbulence, turbulent energy dissipation rate, integral scale of turbulence, and momentum fluxes. The dissipation rate was determined from the azimuth structure function of radial velocity within the inertial subrange of turbulence. When estimating the kinetic energy of turbulence from lidar data, we took into account the averaging of radial velocity over the sensing volume. The integral scale of turbulence was determined on the assumption that the structure of random irregularities of the wind field is described by the von Kármán model. The domain of applicability of the used method and the accuracy of the estimation of turbulence parameters were determined. Turbulence parameters estimated from Stream Line lidar measurement data and from data of a sonic anemometer were compared.

The arrival directions of TeV-PeV cosmic rays are remarkably uniform due to the isotropization of their directions by scattering on turbulent magnetic fields. Small anisotropies can exist in standard diffusion models, however, only on the largest angular scales. Yet, high-statistics observatories like IceCube and High-Altitude Water Cherenkov Observatory have found significant deviations from isotropy down to small angular scales. Here, we explain the formation of small-scale anisotropies by considering pairs of cosmic rays that get correlated by their transport through the same realization of the turbulent magnetic field. We argue that the formation of small-scale anisotropies is the reflection of the particular realization of the turbulent magnetic field experienced by cosmic rays on timescales intermediate between the early, ballistic regime and the late, diffusive regime. We approach this problem in two different ways: First, we run test particle simulations in synthetic turbulence, covering for the first time the TV rigidities of observations with realistic turbulence parameters. Second, we extend the recently introduced mixing matrix approach and determine the steady-state angular power spectrum. Throughout, we adopt magneto-static, slab-like turbulence. We find excellent agreement between the predicted angular power spectra in both approaches over a large range of rigidities. In the future, measurements of small-scale anisotropies will be valuable in constraining the nature of the turbulent magnetic field in our Galactic neighborhood.

We investigate the role of interplanetary (IP) shocks in solar wind turbulence using observations of Solar Orbiter, Parker Solar Probe, and Wind. Employing statistical analysis of quasi-perpendicular fast forward (FF) and fast reverse (FR) shocks, we revisit evolution of magnetic field turbulence across IP shocks. Our previous work indicates that the spectral properties of magnetic fluctuations are statistically conserved across different types of IP shocks, except FR shocks in the transition range of frequencies. We focus on the spectral index in the transition range ( αtr ) using 1 minute sliding windows at 10 s intervals to probe the turbulent dissipation near shocks. We address the influence of key turbulence parameters, particularly cross helicity (σc) and fluctuation amplitude (σB), on αtr . Our results demonstrate (1) an immediate change in αtr across the shock with no evidence for further gradual or asymptotic evolution over extended intervals, and this implies that shock universally serves as a thin boundary separating two turbulence states; (2) the dominant factor forming the steepness of αtr is σc, rather than σB; and (3) the statistically shallower downstream αtr of FR shocks results from a systematic reduction in σc across shocks. These findings suggest that the observed spectral modification is primarily governed by changes in turbulence Alfvénicity, not directly by dissipation processes related to the shock, and can be commonly observed toward extensive heliospheric distances.

The performance of ground-based astronomical observations and free-space optical communication (FSOC) systems suffers from atmospheric turbulence and meteorological conditions. The a priori knowledge of atmospheric conditions several hours before observations allows the programming of astronomical observations (flexible scheduling) to be optimized. In this paper, we present a prediction study based on the Weather Research and Forecasting (WRF) model. It allows the prediction and characterization of a useful set of meteorological parameters relevant to atmospheric physics (e.g., pressure, temperature, relative humidity, wind speed, and direction). Predicted parameters are then injected into an optical turbulence (OT) model to compute the refractive index structure constant C n 2 . We performed sets of simulations for Cerro Pachon Observatory in Chile, using the data from the National Centers for Environmental Prediction (NCEP) Climate Forecast System Reanalysis (CFSR). The main goal is to quantify how accurately numerical weather prediction models can reproduce conditions over the complex terrain of the Cerro Pachon area. In order to produce a reliable forecast, meteorological prognostic skills need accurate representations of the physical parameterization options. Three widely used Planetary Boundary Layer (PBL) schemes and two Land Surface Models (LSM) were tested, analyzed, and compared in order to find the optimal WRF configuration. Predictions are compared to in situ measurements coming from balloon-borne radiosoundings. It is determined that the predicted C n 2 are in good agreement with the radiosoundings measurements with a mean relative error (MRE) under 6.4% at all altitudes when using balloon measurements to deduce some parameters such as the outer scale of turbulence L 0 , which is used in the OT model. For a fully operational prediction, the MREs between the predictions and the measurements range from 1.4% to 8% according to the different ways to estimate the L 0 profiles. Seasonal statistics are also presented for different meteorological and turbulence parameters.