Outer Scale Research Articles

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.

Experimental evidence of amplitude modulation in permeable-wall turbulence

The dynamic interplay between surface and subsurface flow in the presence of a permeable boundary was investigated using low and high frame-rate particle-image velocimetry measurements in a refractive-index-matching flow environment. Two idealized permeable wall models were considered. Both models contained five layers of cubically packed spheres, but one exhibited a smooth interface with the flow, while the other embodied a hemispherical surface topography. The relationship between the large-scale turbulent motions overlying the permeable walls and the small-scale turbulence just above, and within, the walls was explored using instantaneous and statistical analyses. Although previous studies have indirectly identified the potential existence of amplitude modulation in permeable-wall turbulence (a phenomenon identified in impermeable-wall turbulence whereby the outer large scales modulate the intensity of the near-wall, small-scale turbulence), the present effort provides direct evidence of its existence in flow over both permeable walls considered. The spatio-temporal signatures of amplitude modulation were also characterized using conditional averaging based on zero-crossing events. This analysis highlights the connection between large-scale regions of high/low streamwise momentum in the surface flow, downwelling/upwelling across the permeable interface and enhancement/suppression of small-scale turbulence, respectively, just above and within the permeable walls. The presence of bed roughness is found to intensify the strength and penetration of flow into the permeable bed modulated by large-scale structures in the surface flow, and linked to possible roughness-formed channelling effects and shedding of smaller-scale flow structures from the roughness elements.

Morphological and molecular characterization of the Colomerus vitis erineum strain (Trombidiformes: Eriophyidae) from grapevine erinea and buds.

The grapevine erineum mite strain (GEM) of Colomerus vitis (Pagenstecher) has spread throughout the main viticultural areas worldwide and was recently demonstrated to be a vector of Grapevine pinot gris virus (GPGV) and Grapevine inner necrosis virus (GINV). Its females mainly overwinter under the outer bud scales as winter morphs (deutogynes). Goals of this study were to characterize the morphology of protogynes (spring-summer morphs) and deutogynes (winter morphs), to confirm their genetic similarity, and to establish the seasonal period of the deutogyne occurrence. Buds or leaves from a single vineyard (cv. Luisa), Bari area, Apulia, Italy, infested with GEM were sampled 6 × from December 2015 to January 2017. Sixty-six traits commonly used for taxonomic identification were analysed on females. The length of the tibial setae l' on leg I and the tarsal setae ft' on leg II, as well as the number of smooth dorsal semiannuli differed significantly between protogynes and deutogynes, and were easier to detect than other significantly distinctive traits. ITS1 was investigated in individuals collected from buds and erinea, and the sequences confirmed that these two morphs have identical ITS1 fragments. The 1-year study demonstrated the simultaneous presence of protogynes and deutogynes in July and September 2016, whereas only protogynes were found in April and May 2016, and only deutogynes in December 2015 and January 2017.

Low nanomolar concentrations of a quercetin oxidation product, which naturally occurs in onion peel, protect cells against oxidative damage

The occurrence of the quercetin oxidation metabolite 2-(3,4-dihydroxybenzoyl)-2,4,6-trihydroxy-3(2H)-benzofuranone (BZF), whose antioxidant potency is notably higher than the antioxidant potency of quercetin, was investigated in twenty quercetin-rich plant foods. BZF was identified (HPLC-DAD-ESI-MS/MS) only in the dry outer scales of onions and shallots. Aqueous extracts of onions (OAE) and shallots (SAE) were evaluated for their antioxidant and cytoprotective properties. OAE, whose potency did not differ from SAE, protected ROS-exposed Caco2 cells against oxidative (78%) and cellular (90%) damage at a 3 µg/L concentration (corresponding to 0.03 nM of BZF). After chromatographic resolution of OAE, the BZF peak accounted fully and exclusively for its antioxidant effect. The antioxidant effects of OAE and of a pure BZF were described by two perfectly overlapping curves whose concentration-dependence was within the 3 × 10−4 to 102 nM BZF range. Such unprecedented low concentrations place BZF-containing plants on the frontier of the search for novel sources of antioxidants.

Remote Sensing of Stable Boundary Layer of Atmosphere

The stability of the atmospheric boundary layer (ABL) has been studied experimentally with a Stream Line coherent Doppler wind lidar and an MTP-5 temperature profilometer. Two-dimensional height-time distributions of the parameters characterizing the ABL temperature regime and wind turbulence, namely, the Richardson number, the dissipation rate of the kinetic energy of turbulence, the variance of fluctuations of the radial velocity, and the outer scale of turbulence, have been obtained. The amplitudes and period of oscillations of wind velocity components during atmospheric waves arising in the stable ABL have been determined.

Effect of SiC and WC additon on Oxidation Behavior of Spark-Plasma-Sintered ZrB<sub>2</sub>

ZrB2 ceramic and ZrB2 ceramic composites with the addition of SiC, WC, and SiC/WC are successfully synthesized by a spark plasma sintering method. During high-temperature oxidation, SiC additive form a SiO2 amorphous outer scale layer and SiC-deplete ZrO2 scale layer, which decrease the oxidation rate. WC addition forms WO3 during the oxidation process to result in a ZrO2/WO3 liquid sintering layer, which is known to improve the antioxidation effect. The addition of SiC and WC to ZrB2 reduces the oxygen effective diffusivity by one-fifth of that of ZrB2. The addition of both SiC and WC shows the formation of a SiO2 outer dense glass layer and ZrO2/WO3 layer so that the anti-oxidation effect is improved three times as much as that of ZrB2. Therefore, SiC- and WC-added ZrB2 has a lower two-order oxygen effective diffusivity than ZrB2; it improves the anti-oxidation performance 3 times as much as that of ZrB2.

Compressible and Incompressible Magnetic Turbulence Observed in the Very Local Interstellar Medium by Voyager 1

Abstract Voyager 1 observed Kolmogorov-like (k −5/3) compressible turbulence just upwind of the heliopause. Subsequent measurements by Voyager 1 further from the heliopause revealed that the observed fluctuations were now fully incompressible, with a k −5/3 spectrum that was essentially identical to that of the earlier compressible spectrum. Zank et al. showed that only compressible fast magnetosonic modes could be transmitted from the inner heliosheath into the very local interstellar medium (VLISM), and could exhibit a k −5/3 spectrum. We show here that the small plasma beta VLISM admits three-wave interactions between a fast magnetosonic mode, a zero-frequency mode, and an Alfvén wave. The fast magnetosonic mode is converted to an incompressible Alfvén (or zero-frequency) mode with wavenumber almost identical to that of the initial compressible fast mode. The initial compressible and generated incompressible spectra are essentially identical. For the wavelength range observed by Voyager 1, we estimate that compressible fast modes are fully mode-converted to incompressible fluctuations within ∼10 au of the heliopause. We suggest that the VLISM magnetic field spectrum is a superposition of a higher amplitude ∼k −5/3 spectrum of heliospheric origin with an estimated correlation length ∼30 au, having a minimum wavenumber ∼(100)−1 (au)−1, and a lower amplitude (possibly local) ISM k −5/3 spectrum, the latter possessing an outer scale ≥2 pc. We suggest that the transmission of compressible turbulence from an inner asterosheath into the local circumstellar interstellar medium surrounding a star, and the subsequent mode conversion to incompressible turbulence, may be a general mechanism by which stars drive turbulence in the interstellar medium.

Palissya – absolutely incomprehensible or surprisingly interpretable: a new morphological model, affiliations and phylogenetic insights

Abstract The morphology of the adaxial structures of cones belonging to Palissya Endlicher 1847 emend. nov. are reinterpreted based on exquisitely preserved permineralised material from the Lower Cretaceous of Queensland. Although the material was not found in situ, it likely derives from the Orallo Formation, which is Valanginian in age. The cones have dual vascular bundles in each bract/scale complex, and the different tissue types in the bract and ovule/scale complex support interpretation of the cone as a compound structure. Since the early twentieth century it has been widely accepted that each ovule is surrounded by a cup-shaped structure, but the detailed morphology of the “cup” has hitherto been unclear. These new three-dimensionally preserved specimens with in situ ovules are described as Palissya tillackiorum sp. nov. This study demonstrates that the “cup” is formed from a pair of thin scales that subtend but are not fused to each ovule; each pair of scales comprises a thicker outer and thinner inner scale. The organographic relationships among ovules and scales in Palissya show a high degree of synorganisation. The adaxial surface of the bract/scale complex has 2–6 pairs of erect (orthotropous) ovules. The ovule/scale units are arranged symmetrically in two parallel rows on either side of the midline of the bract/scale. Individual ovule/scale units are comparable to those seen in extant Podocarpaceae and Taxaceae. The ovules are thin-walled and are interpreted to have a single integument and a non-thickened (non-lignified) micropyle. These new insights allow reinterpretation of material previously referred to Palissya. A new species is described from Yorkshire, England, as P. harrisii C.R. Hill ex Pattemore & Rozefelds sp. nov. All species based on well preserved cones are reconsidered herein: P. sphenolepis (Braun 1843) Nathorst 1908 emend. Florin 1958, P. elegans Parris, Drinnan & Cantrill 1995 emend. nov., P. bartrumii Edwards 1934 emend. nov., P. antarctica Cantrill 2000 and P. hunanensis Wang 2012. Palissya ovalis Parris et al. 1995 differs structurally from Palissya and is transferred to Knezourocarpon Pattemore 2000 emend. nov. Representatives of this genus may superficially resemble those of Palissya in compressions and impressions, and their congeneric status has been previously suggested; hence its inclusion in this study. Knezourocarpon has adaxial processes that are positioned in two parallel rows but it lacks ovules and paired lateral scales that formed a cup-shape, and its processes attach directly to a central vascular trace. The improved understanding of Palissya’s morphology allows for definite separation of these genera, although the higher-order affiliation of Knezourocarpon remains unclear.

Capacity of turbulent ocean links with carrier Bessel-Gaussian localized vortex waves.

Based on the power spectrum of the index fluctuation with the outer scale of seawater turbulence, we develop the channel capacity of oceanic turbulence links with carrier Bessel-Gaussian vortex localized waves. By this capacity model, we investigate the influences of seawater turbulence and carrier parameters on the channel capacity. The results show that a higher rate of dissipation of kinetic energy per unit mass of fluid, larger inner scale, or lower dissipation rate of the mean-squared temperature causes the higher channel capacity; the Bessel-Gaussian localized vortex wave with a larger source transverse size, smaller Bessel cone angle, lower orbital angular momentum quantum number, or broader initial half-pulse width has stronger resistance to oceanic turbulent perturbation. This work provides a theoretical basis for realizing high-capacity oceanic optical communication with carrier Bessel-Gaussian vortex localized waves.

The ameliorative effect of monotropein, astragalin, and spiraeoside on oxidative stress, endoplasmic reticulum stress, and mitochondrial signaling pathway in varicocelized rats

BackgroundMonotropein, astragalin, and spiraeoside (MAS) are active compounds extracted from medicinal herbs; monotropein from Morinda officinalis How (Rubiaceae), astragalin (kaempferol 3-O-glucoside) from Cuscuta chinensis Lamark (Convolvulaceae) and spiraeoside from the outer scales of Allium cepa L. (Liliceae) in a ratio of 6.69:0.41:3.61. Monotropein, astragalin, and spiraeoside are well-known antioxidants, anti-inflammatory, and antinociceptive agents. The current investigation aims to study the molecular mechanism of varicocele-induced male infertility and the underlying pharmacological mechanisms of MAS.MethodsFour groups were included: control (CTR), MAS 200 group (MAS 200 mg/kg), varicocele group (VC), and VC + MAS 200 group (MAS 200 mg/kg). Sprague-Dawley (SD) rats were treated with 200 mg/kg MAS or vehicle once daily for 28 days. The possible signaling mechanism and effects of MAS were measured via histological staining, immunohistochemistry, western blot, and biochemical assays.ResultsParameters such as sperm motility and count, Johnsen’s scores, spermatogenic cell density, serum testosterone, testicular superoxide dismutase (SOD), catalase, glutathione peroxidase (GPx) and expression of the steroidogenic acute regulatory protein (StAR) improved significantly in the VC + MAS 200 group compared with the VC group. MAS treatment of varicocele-induced group significantly decreased the levels of serum luteinizing hormone (LH) and follicle-stimulating hormone (FSH), as well as testicular interleukin-6 (IL6), tumor necrosis factor-α (TNF-α), ROS/RNS, and malondialdehyde (MDA). It also decreased the apoptotic index and reduced the expression of endoplasmic reticulum (ER) protein levels (Grp78, p-IRE1α, and p-JNK) and apoptotic markers such as cleaved caspase-3 and Bax/Bcl2 ratio.ConclusionThis study suggests that the crosstalk between oxidative stress, ER stress, and mitochondrial pathway mediates varicocele-induced testicular germ cell apoptosis. MAS promotes spermatogenesis in varicocele-induced SD rat, probably by decreasing cytokines (IL-6, TNF-α) levels, regulating abnormal sex hormones, and decreasing oxidative stress, ER stress, and apoptosis.

The minimum of the time-delay wavefront error in Adaptive Optics

Abstract An analytical expression is given for the minimum of the time-delay induced wavefront error (also known as the servo-lag error) in Adaptive Optics systems under temporal prediction filtering. The analysis is based on the von Kármán model for the spectral density of refractive index fluctuations and the hypothesis of frozen flow. An optimal, temporal predictor can achieve up to a factor 1.77 more reduction of the wavefront phase variance compared to the zero-order prediction strategy, which is commonly used in Adaptive Optics systems. Alternatively, an optimal predictor can allow for a 1.41 times longer time-delay to arrive at the same residual phase variance. Generally, the performance of the optimal, temporal predictor depends on the very product of time-delay, wind speed and the reciprocal of turbulence outer scale.

Turbulence-induced changes in the state of polarization of partially polarized, partially coherent pulsed electromagnetic beams propagating through anisotropic turbulence

The changes in the state of polarization of partially polarized, partially coherent pulsed electromagnetic beams propagating along a horizontal path through anisotropic turbulence are investigated. Unpolarized and partially polarized, partially coherent pulsed electromagnetic Gaussian Schell-model beams are compared in terms of the turbulence-induced changes in the spectral degree of polarization. Our analysis is focused on models pertaining to electromagnetic Gaussian Schell-model pulsed beams but can either be readily reduced to scalar or be readily generalized to other beam classes. Within the framework of the anisotropic generalized exponential spectrum, considering simultaneously the finite inner and outer scales of turbulence and the asymmetric property of turbulence eddies in the orthogonal x y -plane throughout the propagation path, we derive analytical expressions for the cross-spectral density matrix, spectral degree of polarization, orientation angle, and degree of ellipticity. Finally, we study the effects of the anisotropic turbulence parameter on the spectral degree of polarization, orientation angle, and degree of ellipticity of the beams. Our results can be useful for applications involving partially polarized, partially coherent pulsed beams propagating through atmospheric turbulence.

Transmittance of finite-energy frozen beams in oceanic turbulence

Frozen waves have the good characteristic for resisting the diffraction and absorption in absorbing medium, which can solve the low transmittance of light waves in seawater. By the turbulence spectrum of seawater and the theory of frozen waves, we develop a frozen wave theory for random field and establish a transmittance model for finite energy frozen beams and analyze the diffracting- and absorption-resistance of finite energy frozen waves from the beam transmission wavelength, beam waist, beam orbital angular momentum quantum number, inner scale of turbulence, outer scale of turbulence, the “temperature structure” constant and the ratio of temperature and salinity. The transmittance of for finite energy frozen waves decreases as the propagation distance increases, and by designing longitudinal profile we can compensate the attenuation loss of the transmittance. We derive that the frozen wave has an optimal wavelength window in “seawater transmission window”. Our results theoretically provide a feasible basis for the establishment of underwater multipoint base station optical communication network.

Randomized spectral sampling for efficient simulation of laser propagation through optical turbulence

We present a new method for the generation of atmospheric turbulence phase screens based on the frequency shift property of the Fourier transform. This method produces low spatial frequency distortions without additional computation time penalties associated with methods using subharmonic subgrids. It is demonstrated that for simulations of atmospheric turbulence with finite outer scales, the performance of our method with respect to the statistical phase structure function of the screen meets or exceeds other methods with respect to agreement with theory. We outline small-scale accuracy issues associated with modelling non-Kolmogorov spectral power laws using existing techniques, and propose a solution. For simulations of long-range propagation through atmospheric optical turbulence, our method provides various advantages over standard methods.

The role of the critical layer in the channel flow transition revisited

The focus of this paper is on the development of a novel and simple linear modeling to interpret the (asymptotic) instability conditions for laminar channel (Poiseuille) flow, thereby giving insight on the major length and time scales of the subsequent mean turbulent regime. Although this is an old problem, recently there has been a renewed effort to understand how information on the wall turbulence scalings can be obtained by studying the flow linear dynamics, among other approaches by using the resolvent analysis. Here the classic asymptotic stability analysis is reformulated by means of a pseudo two-fluid model, a central inviscid flow motion, and a wall viscous one, forcing each other on their common interface streamline. The best agreement with the results of the celebrated Orr–Sommerfeld equation is obtained for the interface located around the elevation of the base flow average value, equal to 2/3 times the maximum velocity (frequency scale). It is argued that, in the early stage of perturbations growth, while the mechanism leading to instability (and that is related to the extraction of energy from the base flow via the Reynolds stress), is located near the wall in the critical layer region (already known result for inner length scale), the central region around the flow average velocity (i.e., the outer length scale is of order $${\mathcal {O}}(h)$$, with h being the channel half-height) is also deeply involved in the onset of the instability. The initial linear amplification of the wall viscous modes of the present analysis agrees with the major features of the wall functions driving the full turbulent profile, found by means of the resolvent analysis, in the subsequent nonlinear stage.

X-ray phase contrast imaging of Vitis spp. buds shows freezing pattern and correlation between volume and cold hardiness

Grapevine (Vitis spp.) buds must survive winter temperatures in order to resume growth when suitable conditions return in spring. They do so by developing cold hardiness through deep supercooling, but the mechanistic process of supercooling in buds remains largely unknown. Here we use synchrotron X-ray phase contrast imaging to study cold hardiness-related characteristics of V. amurensis, V. riparia, and V. vinifera buds: time-resolved 2D imaging was used to visualize freezing; and microtomography was used to evaluate morphological changes during deacclimation. Bud cold hardiness was determined (low temperature exotherms; LTEs) using needle thermocouples during 2D imaging as buds were cooled with a N2 gas cryostream. Resolution in 2D imaging did not allow for ice crystal identification, but freezing was assessed by movement of tissues coinciding with LTE values. Freezing was observed to propagate from the center of the bud toward the outer bud scales. The freezing events observed lasted several minutes. Additionally, loss of supercooling ability appears to be correlated with increases in bud tissue volume during the process of deacclimation, but major increases in volume occur after most of the supercooling ability is lost, suggesting growth resumption processes are limited by deacclimation state.

Modelling the Gravitational Effects of Random Underground Density Variations

A mathematical model for small-scale spatial variations in gravity above the Earth’s surface is presented. Gravity variations are treated as a Gaussian random process arising from underground density variations which are assumed to be a Gaussian random process. Expressions for two-point spatial statistics are calculated for both the vertical component of gravity and the vertical gradient of the vertical component. Results are given for two models of density variations: a delta-correlated model and a fractal model. The effect of an outer scale in the fractal model is investigated. It is shown how the results can be used to numerically generate realisations of gravity variations with fractal properties. Such numerical modelling could be useful for investigating the feasibility of using gravity surveys to locate and characterise underground structures; this is explored through the simple example of a tunnel detection scenario.

<p><strong>Notes on Indian <em>Neolitsea </em>(Lauraceae)—two new varietal combinations under <em>N. cassia </em>and <em>N. foliosa </em>and typification of five names</strong></p>

During the course of revision of the genus Neolitsea (Bentham 1880: 161) Merrill (1906: 56) for India and adjoining countries it was found that N. foliosa (Nees 1831: 64) Gamble (1925a: 1240) and N. cassia (Linnaeus 1753: 369) Kostermans (1952: 85) are two closely related species, the former differing from the latter “by having much broader, coriaceous leaves with a pronounced areolation, the completely glabrous terminal buds and branches, and the glabrous outer bud scales of the flower umbels.” (Kostermans 1995: 169). Further, both these species have two types of fruits, mostly globose to subglobose but occasionally oblong, oblong-ellipsoid to ovoid-oblong. The present study revealed that these two forms of fruits merit recognition as distinct varieties in each species, having no intergradations. The variety of N. cassia, characterized by such oblong fruits has been described previously as Litsea zeylanica (Nees & T. Nees 1823: 58, pl. 5) var. rigescens Meissner (1864: 226), which therefore is transferred to N. cassia here with designation of a lectotype. In N. foliosa, an isolectotype (G00694474: image!) bears oblong to oblong-ellipsoid fruits but the common form with globose to subglobose fruits has been described previously as Litsea scrobiculata (Meissner 1864: 223), treated in Indian Floras (e.g. Gamble 1925a, Saldanha & Ramesh 1984, Vajravelu 1990, Mohanan & Henry 1994) as Neolitsea scrobiculata (Meisn.) Gamble (1925a: 1240), eventually reduced to a synonym of N. foliosa by Kostermans (1995: 168–169). Hence Litsea scrobiculata is reinstated here and treated as a distinct variety of N. foliosa with designation of a lecotype. Furthermore, lectotypes are also designated for the names Tetradenia foliosa Nees (1831: 64), basionym of Neolitsea foliosa, N. fischeri Gamble (1925b: 132) and Tetradenia umbrosa Nees (1831: 64), basionym of Neolitsea umbrosa (Nees) Gamble (1914: 79).

A universal velocity profile for smooth wall pipe flow

The most important unanswered questions in turbulence regard the nature of turbulent flow in the limit of infinite Reynolds number. The Princeton superpipe (PSP) data comprise 26 velocity profiles that cover three orders of magnitude in the Reynolds number from $Re=19\,639$, to $Re=20\,088\,000$ based on pipe radius and pipe centreline velocity. In this paper classical mixing length theory is combined with a new mixing length model of the turbulent shear stress to solve the streamwise momentum equation and the solution is used to approximate the PSP velocity profiles. The model velocity profile is uniformly valid from the wall to the pipe centreline and comprises five free parameters that are selected through a minimization process to provide an accurate approximation to each of the 26 profiles. The model profile is grounded in the momentum equation and allows the velocity derivative, Reynolds shear stress and turbulent kinetic energy production to be studied. The results support the conclusion that logarithmic velocity behaviour near the wall is not present in the data below a pipe Reynolds number somewhere between $Re=59\,872$, and $Re=87\,150$. Above $Re=87\,150$, the data show a very clear, nearly logarithmic, region. But even at the highest Reynolds numbers there is still a weak algebraic dependence of the intermediate portion of the velocity profile on both the near-wall and outer flow length scales. One of the five parameters in the model profile is equivalent to the well-known Kármán constant, $k$. The parameter $k$ increases almost monotonically from $k=0.4034$ at $Re=87\,150$ to $k=0.4190$ at $Re=20\,088\,000$, with an average value, $k=0.4092$. The variation of the remaining four model parameters is relatively small and, with all five parameters fixed at average values, the model profile reproduces the entire velocity data set and the wall friction reasonably well. With optimal values of the parameters used for each model profile, the fit to the PSP survey data is very good. Transforming the model velocity profile using the group, $u/u_{0}\rightarrow ku/u_{0}$, $y^{+}\rightarrow ky^{+}$ and $R_{\unicode[STIX]{x1D70F}}\rightarrow kR_{\unicode[STIX]{x1D70F}}$ where $R_{\unicode[STIX]{x1D70F}}$ is the friction Reynolds number, leads to a reduced expression for the velocity profile. When the reduced profile is cast in outer variables, the physical velocity profile is expressed in terms of $\ln (y/\unicode[STIX]{x1D6FF})$ and a new shape function $\unicode[STIX]{x1D719}(y/\unicode[STIX]{x1D6FF})$. In the limit of infinite Reynolds number, the velocity profile asymptotes to plug flow with a vanishingly thin viscous wall layer and a continuous derivative everywhere. The shape function evaluated at the pipe centreline is used to produce a new friction law with an additive constant that depends on the Kármán constant and a wall damping length scale.

Dependence of 3D Self-correlation Level Contours on the Scales in the Inertial Range of Solar Wind Turbulence

Abstract The self-correlation level contours at the 1010 cm scale reveal a 3D isotropic feature in the slow solar wind and a quasi-anisotropic feature in the fast solar wind. However, the 1010 cm scale is approximately near the low-frequency break (outer scale of turbulence cascade), especially in the fast wind. How the self-correlation level contours behave with dependence on the scales in the inertial range of solar wind turbulence remains unknown. Here we present the 3D self-correlation function level contours and their dependence on the scales in the inertial range for the first time. We use data at 1 au from instruments on the Wind spacecraft in the period 2005–2018. We show the 3D isotropic self-correlation level contours of the magnetic field in the inertial range of both slow and fast solar wind turbulence. We also find that the self-correlation level contours of the velocity in the inertial range present 2D anisotropy with an elongation in the perpendicular direction and 2D isotropy in the plane perpendicular to the mean magnetic field. These results indicate differences between the magnetic field and the velocity, providing new clues to interpret the solar wind turbulence on the inertial scale.