Properties Of Turbulence Research Articles

Investigation of properties of superfluid He4 turbulence using a hot-wire signal

We report hot-wire measurements performed in two very different, co- and counter-rotating flows, in normal and superfluid helium at 1.6 K, 2 K, and 2.3 K. As recently reported, the power spectrum of the hot-wire signal in superfluid flows exhibits a significant bump at high frequency (Diribarne et al. [1]). We confirm that the bump frequency does not depend significantly on the temperature and further extend the previous analysis of the velocity dependence of the bump, over more than one decade of velocity. The main result is that the bump frequency depends on the turbulence intensity of the flow, and that using the turbulent Reynolds number rather than the velocity as a control parameter collapses results from both co- and counter-rotating flows. The vortex shedding model previously proposed, in its current form, does not account for this observation. This suggests that the physical origin of the bump is related to the small scale turbulence properties of the flow. We finally propose some qualitative physical mechanism by which the smallest structures of the flow, at intervortex distance, could affect the heat flux of the hot-wire.

Statistical properties of two-dimensional elastic turbulence.

We numerically investigate the spatial and temporal statistical properties of a dilute polymer solution in the elastic turbulence regime, i.e., in the chaotic flow state occurring at vanishing Reynolds and high Weissenberg numbers. We aim at elucidating the relations between measurements of flow properties performed in the spatial domain with the ones taken in the temporal domain, which is a key point for the interpretation of experimental results on elastic turbulence and to discuss the validity of Taylor's hypothesis. To this end, we carry out extensive direct numerical simulations of the two-dimensional Kolmogorov flow of an Oldroyd-B viscoelastic fluid. Static pointlike numerical probes are placed at different locations in the flow, particularly at the extrema of mean flow amplitude. The results in the fully developed elastic turbulence regime reveal large velocity fluctuations, as compared to the mean flow, leading to a partial breakdown of Taylor's frozen-field hypothesis. While second-order statistics, probed by spectra and structure functions, display consistent scaling behaviors in the spatial and temporal domains, the third-order statistics highlight robust differences. In particular the temporal analysis fails to capture the skewness of streamwise longitudinal velocity increments. Finally, we assess both the degree of statistical inhomogeneity and isotropy of the flow turbulent fluctuations as a function of scale. While the system is only weakly nonhomogenous in the cross-stream direction, it is found to be highly anisotropic at all scales.

TRAO Survey of the Nearby Filamentary Molecular Clouds, the Universal Nursery of Stars (TRAO FUNS). II. Filaments and Dense Cores in IC 5146

Abstract We present the results on the physical properties of filaments and dense cores in IC 5146, as a part of the TRAO FUNS project. We carried out on-the-fly mapping observations using the Taeduk Radio Astronomy Observatory (TRAO) 14 m telescope covering about 1 square degree of the area of IC 5146 using various molecular lines. We identified 14 filaments (24 in total, including sub-filaments) from the C18O (1–0) data cube and 22 dense cores from the N2H+ (1–0) data. We examined the filaments’ gravitational criticality, turbulence properties, accretion rate from filaments to dense cores, and relative evolutionary stages of cores. Most filaments in IC 5146 are gravitationally supercritical within the uncertainty, and most dense cores are formed in them. We found that dense cores in the hubs show a systemic velocity shift of ∼0.3 km s−1 between the N2H+ and C18O gas. Besides, these cores are subsonic or transonic, while the surrounding filament gas is transonic or supersonic, indicating that the cores in the hubs are likely formed by the dissipation of turbulence in the colliding turbulent filaments and the merging is still ongoing. We estimated a mass accretion rate of 15–35 M ⊙ Myr−1 from the filaments to the dense cores, and the required timescales to collect the current core mass are consistent with the lifetime of the dense cores. The structures of filaments and dense cores in the hub can form from a collision of turbulent converging flows, and mass flow along the filaments to the dense cores may play an important role in forming dense cores.

Turbulence Properties of a Deep‐Sea Hydrothermal Plume in a Time‐Variable Cross‐Flow: Field and Model Comparisons for Dante in the Main Endeavour Field

AbstractA large eddy simulation is used to study a high temperature hydrothermal vent plume in a stratified and tidally modulated crossflow, in order to identify its turbulence and mixing characteristics. The model parameters and source conditions that are comparable to the vertical velocity and refractive index fluctuations measured 20 m above the Dante sulfide mound in the Main Endeavour vent Field are a heat transport of 50 MW over a cross‐sectional area of 4 × 4.5 m2. With these model source conditions and output results taken at 20 m above the source with 1 Hz sampling, the shear production of turbulent kinetic energy (TKE), the vertical transport of TKE, and the buoyancy production/dissipation are quantified showing that shear production dominates. Similarly, thermal variance production, and its vertical transport, is also quantified showing that the advective term dominates. Because of enhanced entrainment of ambient water into the plume during strong crossflows, all mean and turbulent quantities show tidally modulated values. Assuming steady state, the dissipation rates are evaluated. During strong crossflows, the tilting of the vertical velocity contours and isotherms plays a critical role in the stability of the plume and in creating high shear and thermal gradients on the upstream side of the plume center axis. These dissipation rates are used to quantify the refractive index fluctuations, and given the high thermal dissipation quantity it is the main contributing factor in acoustic forward scatter.

Reduced-model scrape-off layer turbulence (nSOLT) simulations comparing three fueling scenarios

The 2D scrape-off-layer turbulence code (nSOLT) includes 1D Boltzmann neutral–plasma interactions, a model of divertor recycling (introduced here), and a fixed source of plasma concentrated at the core-side boundary. Three fueling methods are considered herein: (1) neutral injection in the far-SOL is accomplished by specifying the density of Franck–Condon distributed neutrals streaming in from the boundary. (2) Divertor recycling is modeled by injecting a fraction of the particle parallel flux in the scrape-off layer (SOL) back into the edge region as a source of plasma. (3) A constant source fuels the edge plasma from the core-side boundary to model pellet injection. For machine parameters (B, Rm, and L//) illustrative of the MAST-U device, and for a deuterium plasma, turbulent equilibria are obtained that share the same plasma fueling rate for each of the three fueling methods, with only one of the sources on in each case. In the presence of self-consistent turbulence, quasi-steady plasma and neutral (deuterium) profiles, fueling efficiencies, SOL transparencies, and heat flux widths are compared. Characteristics of the turbulent fluctuations, including skewness, cross-phases, and power spectra, are described. The calculated fueling efficiencies, SOL transparencies to neutral penetration, and many of the turbulent properties are remarkably similar for all three fueling methods despite significant differences in the plasma profiles. The nonlinear states of the three cases are dominated by separatrix-spanning vortex cells that control particle and heat losses into the SOL.

Bifurcation structure of unstable periodic orbits in plane Couette flow with the Smagorinsky model

To study the dynamical properties of plane Couette turbulence, this paper describes unstable periodic orbits (UPOs) in a large eddy simulation (LES) system with a Smagorinsky-type eddy viscosity model. At a moderately high Reynolds number, the UPO of the present study possesses spanwise vortices in the central region of the channel, which seem to be caused by a streak instability. These stretched vortices are shown to enhance transfer of the streamwise turbulent momentum, as in developed near-wall turbulence.

Turbulence and capillary waves on bubbles.

We present a link between the theory of deep water waves and that of bubble surface perturbations. Theory correspondence is shown analytically for small wavelengths in the linear regime and investigated numerically in the nonlinear regime. To do so, we develop the second-order spatial perturbation equations for the Rayleigh-Plesset equation and solve them numerically. Our code is publicly available. Studying capillary waves on stable bubbles, we recreate the Kolmogorov-Zakharov spectrum predicted by weak turbulence theory, putting wave turbulence theory to use for bubbles. In this investigation, it seems that curvature does not affect turbulent properties. The calculated bubble surface responds qualitatively to low gravity experiments. The link demonstrated opens new possibilities for studying several bubble phenomena, including sonoluminescence and cavitation, using the extensive tools developed in the wave turbulence framework.

Energy spectra of Sub-Surface Velocity Fields Beneath Faraday Waves

Faraday waves form on the surface of a fluid which is subject to vertical forcing, and are researched in a large range of applications. Some examples are the formation of ordered wave patterns and the controlled walking or orbiting of droplets (Couder et al. (2005); Saylor and Kinard (2005)). Moreover, recent studies discovered the existence of a horizontal velocity field at the fluid surface, called Faraday flow, which was shown to exhibit an inverse energy cascade and thus properties of two-dimensional turbulence (von Kameke et al., 2011, 2013; Francois et al., 2013). Additionally, three-dimensionality effects have been part of recent investigations in quasi-2D flows (both electromagnetically-driven (Kelley and Ouellette, 2011; Martell et al., 2019) or produced by parametrically-excited waves (Francois et al., 2014; Xia and Francois, 2017)). Furthermore, the occurrence of an inverse cascade in thick layers is also subject of current studies on the coexistence of 2D and 3D turbulence (Biferale et al., 2012; Kokot et al., 2017; Biferale et al., 2017). By performing 2D PIV measurements at horizontal planes beneath the Faraday waves, we recently showed that pronounced three dimensional flows occur in the bulk, with much larger spatial and temporal scales than those on the surface (Colombi et al., 2021), when the system is not shallow in comparison to typical length scales of the surface flow (fluid thickness exceeding half the Faraday wavelength λF). This in turn reveals that an inverse energy cascade and aspects of a confined 2D turbulence can coexist with a three dimensional bulk flow. In this work, 2D PIV measurements of the velocity fields are carried out at a vertical cross-section xz-plane and at four distinct horizontal xy-planes at different depths in Faraday waves. The results reveal that small and fast vertical jets penetrate from the surface into the bulk with fast accelerating bursts and strong momentum transport in the z−direction. Furthermore, the fraction of flow kinetic energy in the vertical direction is found to peak inside a layer of approximately 10 mm (one Faraday wavelength) below the fluid surface.

Turbulence transport in the solar corona: Theory, modeling, and Parker Solar Probe

A primary goal of the Parker Solar Probe (PSP) Mission is to answer the outstanding question of how the solar corona plasma is heated to the high temperatures needed for the acceleration of the solar wind. Various heating mechanisms have been suggested, but one that is gaining increasing credence is associated with the dissipation of low frequency magnetohyrodynamic (MHD) turbulence. However, the MHD turbulence models come in several flavors: one in which outwardly propagating Alfvén waves experience reflection from the large-scale flow and density gradients associated with the solar corona, and the resulting counterpropagating Alfvén waves couple nonlinearly to produce quasi-2D turbulence that dissipates and heats the corona, thereby driving the solar wind. The second approach eschews a dominant outward flux of Alfvén waves but argues instead that quasi-2D turbulence dominates the lower coronal plasma and is generated in the constantly upwelling magnetic carpet, experiencing dissipation as it is advected through the corona and into the solar wind, yielding temperatures in the corona that exceed a million degrees. We review the two turbulence models, describe the modeling that has been done, and relate PSP observations to the basic predictions of both models. Although PSP measurements are made in the super-Alfvénic solar wind, the observations are close to the coronal region, thus providing a glimpse into the likely properties of coronal turbulence. Observations of low-frequency MHD turbulence by PSP in the super-Alfvénic solar wind allow us to place constraints on models of the turbulently heated solar corona that drive the supersonic solar wind.

Statistical Properties of Small-scale Linear Magnetic Holes in the Martian Magnetosheath

Abstract The small-scale linear magnetic hole (LMH) is a magnetic dip with a size less than or on the order of ρ i (proton gyroradius), which may contribute to turbulence properties in the solar wind and other astrophysical plasmas. Based on one-month measurements of the Mars Atmosphere and Volatile EvolutioN mission, 174 small-scale LMH events in the Martian magnetosheath are used to investigate their statistical properties in this study. Our results show that small-scale linear LMHs are ubiquitous in the Martian magnetosheath, and their occurrence rate is estimated to be approximately 1.5 events per hour based on one-month observations. Compared with the ambient plasma, the averaged magnitude of the magnetic field in these holes can decrease from 6.8–3.5 nT. Nearly 66% of events have a B min/B value in the range of (0.45, 0.75). The duration of small-scale MHs is mainly less than 0.4 s. For 90% of the events, the size along the solar wind flow is less than ρ i . As the rotation angle increases, the occurrence rate of small-scale LMHs decrease. However, the B min/B, size, and duration of small-scale LMHs have no obvious dependence on their rotation angle.

Liquid hydrodynamics in a gas-liquid vortex reactor

A gas–liquid vortex reactor (GLVR) is considered one of the promising Process-Intensified Equipment for applications that require high mixing and mass transfer efficiency. To gain understanding of the fundamentals of GLVR operation, the gas–liquid hydrodynamics in the GLVR has been investigated by high-speed imaging, digital images analysis and cross correlation. Gas bubbles and liquid ligaments are observed in the GLVR over a wide operating window. The dynamic liquid layer thickness in the GLVR chamber varies in the range of 26–36 mm. The instantaneous and time-average velocity fields of the liquid phase are obtained with a guaranteed high signal-to-noise ratio (cross correlation peak ratio higher than 10), allowing the analysis of liquid turbulent properties including the turbulent kinetic energy and its dissipation rate. Results show that the high turbulent kinetic energy dissipation rate ranging from 23 to 114 m2/s3 contributes to a high mixing and mass transfer efficiency in the GLVR.

Coupled and decoupled stratocumulus-topped boundary layers: turbulence properties

Abstract. 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.

How close are shell models to the 3D Navier–Stokes equations?

Shell models have found wide application in the study of hydrodynamic turbulence because they are easily solved numerically even at very large Reynolds numbers. Although bereft of spatial variation, they accurately reproduce the main statistical properties of fully-developed homogeneous and isotropic turbulence. Moreover, they enjoy regularity properties which still remain open for the three-dimensional (3D) Navier–Stokes equations (NSEs). The goal of this study is to make a rigorous comparison between shell models and the NSEs. It turns out that only the estimate of the mean energy dissipation rate is the same in both systems. The estimates of the velocity and its higher-order derivatives display a weaker Reynolds number dependence for shell models than for the 3D NSEs. Indeed, the velocity-derivative estimates for shell models are found to be equivalent to those corresponding to a velocity gradient averaged version of the 3D Navier–Stokes equations (VGA-NSEs), while the velocity estimates are even milder. Numerical simulations over a wide range of Reynolds numbers confirm the estimates for shell models.

Review and Comparison of Numerical Simulations of Secondary Flow in River Confluences

River confluences are a common feature in natural water resources. The flow characteristics in confluences are complicated, especially at junction areas between tributaries and the main river. One of the typical characteristics of confluences is secondary flow, which plays an important role in mixing, velocity, sediment transport, and pollutant dispersion. In addition to the experimental and field studies that have been conducted in this area, the development of computational fluid dynamics has allowed researchers in this field to use different numerical models to simulate turbulence properties in rivers, especially secondary flows. Nowadays, the hydrodynamics of flows in confluences are widely simulated by using three-dimensional models in order to fully capture the flow structures, as the flow characteristics are considered to be turbulent and three-dimensional at river junctions. Several numerical models have been recommended for this purpose, and various turbulence models have been used to simulate the flows at confluences. To assess the accuracy of turbulence models, flows have been predicted by applying different turbulence models in the numerical model and the results have been compared with other data, such as field, laboratory, and experimental data. The purpose behind these investigations was to find the suitable model for each case of turbulent flow and for different types of confluences. In this study, the performances of turbulence models for confluences are reviewed for different numerical simulation strategies.

A Comparative Study between Sand- and Gravel-Bed Open Channel Flows in the Wake Region of a Bed-Mounted Horizontal Cylinder

In nature, environmental and geophysical flows frequently encounter submerged cylindrical bodies on a rough bed. The flows around the cylindrical bodies on the rough bed are very complicated as the flow field in these cases will be a function of bed roughness apart from the diameter of the cylinder and the flow velocity. In addition, the sand-bed roughness has different effects on the flow compared to the gravel-bed roughness due to differences in the roughness heights. Therefore, the main objective of this article is to compare the mean velocities and turbulent flow properties in the wake region of a horizontal bed-mounted cylinder over the sand-bed with that over the gravel-bed. Three experimental runs, two for the sand-bed and one for the gravel-bed with similar physical and hydraulic conditions, were recorded to fulfil this purpose. The Acoustic Doppler Velocimetry (ADV) probe was used for measuring the three-dimensional (3D) instantaneous velocity data. This comparative study shows that the magnitude of mean streamwise flow velocity, streamwise Reynolds normal stress, and Reynolds shear stress are reduced on the gravel-bed compared to the sand-bed. Conversely, the vertical velocities and vertical Reynolds normal stress are higher on the gravel-bed than the sand-bed.

Convective and Turbulent Motions in Nonprecipitating Cu. Part I: Method of Separation of Convective and Turbulent Motions

AbstractAtmospheric motions in clouds and cloud surroundings have a wide range of scales, from several kilometers to centimeters. These motions have different impacts on cloud dynamics and microphysics. Larger-scale motions (hereafter referred to as convective motions) are responsible for mass transport over distances comparable with cloud scale, while motions of smaller scales (hereafter referred to as turbulent motions) are stochastic and responsible for mixing and cloud dilution. This distinction substantially simplifies the analysis of dynamic and microphysical processes in clouds. The present research is Part I of the study aimed at describing the method for separating the motion scale into a convective component and a turbulent component. An idealized flow is constructed, which is a sum of an initially prescribed field of the convective velocity with updrafts in the cloud core and downdrafts outside the core, and a stochastic turbulent velocity field obeying the turbulent properties, including the −5/3 law and the 2/3 structure function law. A wavelet method is developed allowing separation of the velocity field into the convective and turbulent components, with parameter values being in a good agreement with those prescribed initially. The efficiency of the method is demonstrated by an example of a vertical velocity field of a cumulus cloud simulated using the System for Atmospheric Modeling (SAM) with bin microphysics and resolution of 10 m. It is shown that vertical velocity in clouds indeed can be represented as a sum of convective velocity (forming zone of cloud updrafts and subsiding shell) and a stochastic velocity obeying laws of homogeneous and isotropic turbulence.

Experimental and numerical study on the heat transfer to supercritical water in an inclined smooth tube

Heat transfer to supercritical water in a smooth tube with an inclined angle of 25° was investigated experimentally and numerically. Experimental results show that the increase of mass flux improves the heat transfer. As the pressure increases, influence of physical property variation to the heat transfer becomes gentle. Thereby, the increase of pressure reduces the heat transfer under an enhanced condition. Dimensionless buoyancy parameters Grq*/Grqth and Gr‾/Re2.7 are compared on the basis of experimental results. The evaluated result shows that Grq*/Grqth is applicable to the inclined tube flow. Base on the supercritical data, a new heat transfer correlation is proposed. Numerical analysis was completed with the shear stress transport k-ω model. Corresponding results show that the influence of variable mass flux and pressure on supercritical heat transfer is realized by changing radial distributing characteristics of turbulence and physical property. The increase of mass flux improves the radial turbulence and heat-absorbing capacity of the boundary fluid, so the supercritical heat transfer is enhanced. At a low mass flux condition where heat transfer reduction occurs, the increase of pressure improves the heat transfer. At a high mass flux condition where heat transfer enhancement occurs, the increase of pressure reduces the heat transfer. Influence of natural convection caused by the buoyancy leads to the occurrence of heat transfer disparity between top and bottom sides of the inclined tube. The increase of mass flux weakens the influence of natural convection and improves local heat transfer at the top side. At the low mass flux condition, the increase of pressure conducts the same effect with the increase of mass flux. At the high mass flux condition, the increase of pressure reduces the local heat transfer at the top side.

Multiscale energy budget of inertially driven turbulence in normal and superfluid helium

In this paper we present a novel hydrodynamic experiment using liquid $^4$He. The flow is forced inertially by a canonical oscillating grid using either its normal (He~I) or superfluid (He~II) phase, generating a statistically stationary turbulence. We characterise the turbulent properties of the flow using 2D Lagrangian Particle tracking on hollow glass micro-spheres. As expected for tracer particles, the Vorono\"{i} tessellation on particle positions does not show a significant departure from a random Poisson process neither in He~I nor He~II phase. Particles' positions are tracked with high temporal resolution, allowing to resolve velocity fluctuations at integral and inertial scales while properly assessing the noise contribution. Additionally, we differentiate the particles' positions (by convolution with Gaussian kernels) in order to access small scale quantities like acceleration. Using these measured quantities and the formalism of classical Homogeneous Isotropic Turbulence (HIT) to perform an energy budget across scales we extract the energy injection rate at the large scale, the energy flux cascading through inertial scales, down to small scales at which it is dissipated. We found that in such inertially driven turbulence, regardless of the normal or superfluid state of the fluid, estimates of energy at the different scales are compatible with each other and consistent with oscillating grid turbulence results reported for normal fluids in the literature. The largest discrepancy shows up at small scales where the signal to noise ratio is harder to control and where the 2D measurement is contaminated by the 3D nature of the flow. This motivates to focus future experimental projects towards small scales, low noise and 3D measurements.

Spectrum of kinetic plasma turbulence at 0.3-0.9 astronomical units from the Sun.

We investigate spectral properties of turbulence in the solar wind that is a weakly collisional astrophysical plasma, accessible to in situ observations. Using the Helios search coil magnetometer measurements in the fast solar wind, in the inner heliosphere, we focus on properties of the turbulent magnetic fluctuations at scales smaller than the ion characteristic scales, the so-called kinetic plasma turbulence. At such small scales, we show that magnetic power spectra between 0.3 and 0.9 AU from the Sun have a generic shape ∼f^{-8/3}exp(-f/f_{d}), where the dissipation frequency f_{d} is correlated with the Doppler shifted frequency f_{ρe} of the electron Larmor radius. This behavior is statistically significant: all the observed kinetic spectra are well described by this model, with f_{d}=f_{ρe}/1.8. Our results indicate that the electron gyroradius plays the role of the dissipation scale and marks the end of the electromagnetic cascade in the solar wind.

The near-Sun streamer belt solar wind: turbulence and solar wind acceleration

The fourth orbit of Parker Solar Probe (PSP) reached heliocentric distances down to 27.9R⊙, allowing solar wind turbulence and acceleration mechanisms to be studied in situ closer to the Sun than previously possible. The turbulence properties were found to be significantly different in the inbound and outbound portions of PSP’s fourth solar encounter, which was likely due to the proximity to the heliospheric current sheet (HCS) in the outbound period. Near the HCS, in the streamer belt wind, the turbulence was found to have lower amplitudes, higher magnetic compressibility, a steeper magnetic field spectrum (with a spectral index close to –5/3 rather than –3/2), a lower Alfvénicity, and a ‘1∕f’ break at much lower frequencies. These are also features of slow wind at 1 au, suggesting the near-Sun streamer belt wind to be the prototypical slow solar wind. The transition in properties occurs at a predicted angular distance of ≈4° from the HCS, suggesting ≈8° as the full-width of the streamer belt wind at these distances. While the majority of the Alfvénic turbulence energy fluxes measured by PSP are consistent with those required for reflection-driven turbulence models of solar wind acceleration, the fluxes in the streamer belt are significantly lower than the model predictions, suggesting that additional mechanisms are necessary to explain the acceleration of the streamer belt solar wind.