Inertial-range Magnetic-fluctuation Anisotropy Observed from Parker Solar Probe’s First Seven Orbits

Solar wind turbulence is anisotropic with respect to the mean magnetic field. Anisotropy leads to ambiguity when interpreting in situ turbulence observations in the solar wind because an apparent change in the measurements could be due to either the change of intrinsic turbulence properties or to a simple change of the spacecraft sampling direction. We demonstrate the ambiguity using the spectral index and magnetic compressibility in the inertial range observed by the Parker Solar Probe during its first seven orbits ranging from 0.1 to 0.6 au. To unravel the effects of the sampling direction, we assess whether the wave-vector anisotropy is consistent with a two-dimensional (2D) plus slab turbulence transport model and determine the fraction of power in the 2D versus slab component. Our results confirm that the 2D plus slab model is consistent with the data and the power ratio between 2D and slab components depends on radial distance, with the relative power in 2D fluctuations becoming smaller closer to the Sun.

Relative dispersion with finite inertial ranges

Relative dispersion experiments are often analysed using theoretical predictions from two- and three-dimensional turbulence. These apply to infinite inertial ranges, assuming the same dispersive behaviour over all scales. With finite inertial ranges, the metrics are less conclusive. We examine this using pair separation probability density functions (PDFs), obtained by integrating a Fokker–Planck equation with different diffusivity profiles. We consider time-based metrics, such as the relative dispersion, and separation-based metrics, such as the finite scale Lyapunov exponent (FSLE). As the latter cannot be calculated from a PDF, we introduce a new measure, the cumulative inverse separation time (CIST), which can. This behaves like the FSLE, but advantageously has analytical solutions in the inertial ranges. This allows the establishment of consistency between the time- and space-based metrics, something which has been lacking previously. We focus on three dispersion regimes: non-local spreading (as in a two-dimensional enstrophy inertial range), Richardson dispersion (as in an energy inertial range) and diffusion (for uncorrelated pair motion). The time-based metrics are more successful with non-local dispersion, as the corresponding PDF applies from the initial time. Richardson dispersion is barely observed, because the self-similar PDF applies only asymptotically in time. In contrast, the separation-based CIST correctly captures the dependencies, even with a short (one decade) inertial range, and is superior to the traditional FSLE at large scales. Nevertheless, it is advantageous to use all measures together, to seek consistent indications of the dispersion.

Non-local dispersion and the reassessment of Richardson's t3-scaling law

The Richardson-scaling law states that the mean square separation of a fluid particle pair grows according to t3 within the inertial range and at intermediate times. The theories predicting this scaling regime assume that the pair separation is within the inertial range and that the dispersion is local, which means that only eddies at the scale of the separation contribute. These assumptions ignore the structural organization of the turbulent flow into large-scale shear layers, where the intense small-scale motions are bounded by the large-scale energetic motions. Therefore, the large scales contribute to the velocity difference across the small-scale structures. It is shown that, indeed, the pair dispersion inside these layers is highly non-local and approaches Taylor dispersion in a way that is fundamentally different from the Richardson-scaling law. Also, the layer's contribution to the overall mean square separation remains significant as the Reynolds number increases. This calls into question the validity of the theoretical assumptions. Moreover, a literature survey reveals that, so far, t3 scaling is not observed for initial separations within the inertial range. We propose that the intermediate pair dispersion regime is a transition region that connects the initial Batchelor- with the final Taylor-dispersion regime. Such a simple interpretation is shown to be consistent with observations and is able to explain why t3 scaling is found only for one specific initial separation outside the inertial range. Moreover, the model incorporates the observed non-local contribution to the dispersion, because it requires only small-time-scale properties and large-scale properties.

Geometry of Magnetic Fluctuations near the Sun from the Parker Solar Probe

Solar wind magnetic fluctuations exhibit anisotropy due to the presence of a mean magnetic field in the form of the Parker spiral. Close to the Sun, direct measurements were not available until the recently launched Parker Solar Probe (PSP) mission. The nature of the anisotropy and geometry of the magnetic fluctuations play a fundamental role in dissipation processes and in the transport of energetic particles in space. Using PSP data, we present measurements of the geometry and anisotropy of the inner heliosphere magnetic fluctuations, from fluid to kinetic scales. The results are surprising and different from 1 au observations. We find that fluctuations evolve characteristically with size scale. However, unlike 1 au solar wind, at the outer scale, the fluctuations are dominated by wavevectors quasi-parallel to the local magnetic field. In the inertial range, average wavevectors become less field aligned, but still remain more field aligned than near-Earth solar wind. In the dissipation range, the wavevectors become almost perpendicular to the local magnetic field in the dissipation range, to a much higher degree than those indicated by 1 au observations. We propose that this reduced degree of anisotropy in the outer scale and inertial range is due to the nature of large-scale forcing outside the solar corona.

Coupled and decoupled stratocumulus-topped boundary layers: turbulence properties

We compare turbulence properties in coupled and decoupled marine stratocumulus-topped boundary layers (STBLs) using high-resolution in situ measurements performed by the helicopter-borne Airborne Cloud Turbulence Observation System (ACTOS) platform in the region of the eastern North Atlantic. The thermodynamically well-mixed coupled STBL was characterized by a comparable latent heat flux at the surface and in the cloud-top region, and substantially smaller sensible heat flux in the entire depth. Turbulence kinetic energy (TKE) was efficiently generated by buoyancy in the cloud and at the surface, and dissipated with comparable rate across the entire depth. Structure functions and power spectra of velocity fluctuations in the inertial range were reasonably consistent with the predictions of Kolmogorov theory. The turbulence was close to isotropic. In the decoupled STBL, decoupling was most obvious in humidity profiles. Heat fluxes and buoyant TKE production at the surface were similar to the coupled case. Around the transition level, latent heat flux decreased to zero and TKE was consumed by weak stability. In the cloud-top region, heat fluxes almost vanished and buoyancy production was significantly smaller than for the coupled case. The TKE dissipation rate inside the decoupled STBL varied between its sublayers. Structure functions and power spectra in the inertial range deviated from Kolmogorov scaling. This was more pronounced in the cloud and subcloud layer in comparison to the surface mixed layer. The turbulence was more anisotropic than in the coupled STBL, with horizontal fluctuations dominating. The degree of anisotropy was largest in the cloud and subcloud layer of the decoupled STBL. Integral length scales, of the order of 100 m in both cases, indicate turbulent eddies smaller than the depth of the coupled STBL or of the sublayers of the decoupled STBL. We hypothesize that turbulence produced in the cloud or close to the surface is redistributed across the entire coupled STBL but rather only inside the sublayers where it was generated in the case of the decoupled STBL. Scattered cumulus convection, developed below the stratocumulus base, may play a role in transport between those sublayers.

Variable Energy Fluxes and Exact Relations in Magnetohydrodynamics Turbulence

In magnetohydrodynamics (MHD), there is a transfer of energy from the velocity field to the magnetic field in the inertial range itself. As a result, the inertial-range energy fluxes of velocity and magnetic fields exhibit significant variations. Still, these variable energy fluxes satisfy several exact relations due to conservation of energy. In this paper, using numerical simulations, we quantify the variable energy fluxes of MHD turbulence, as well as verify several exact relations. We also study the energy fluxes of Elsässer variables that are constant in the inertial range.

How Turbulent is the Magnetically Closed Corona?

We argue that the magnetically closed corona evolves primarily quasi-statically, punctuated by many localized bursts of activity associated with magnetic reconnection at a myriad of small current sheets. The sheets form by various processes that do not involve a traditional turbulent cascade whereby energy flows losslessly through a continuum of spatial scales starting from the large scale of the photospheric driving. If such an inertial range is a defining characteristic of turbulence, then the magnetically closed corona is not a turbulent system. It nonetheless has a complex structure that bears no direct relationship to the pattern of driving.