Fluctuating Velocity Field Research Articles

Temperature anisotropy instabilities driven by intermittent velocity shears in the solar wind

Where and under what conditions the transfer of energy between electromagnetic fields and particles takes place in the solar wind remains an open question. We investigate the conditions that promote the growth of kinetic instabilities predicted by linear theory to infer how turbulence and temperature-anisotropy-driven instabilities are interrelated. Using a large dataset from Solar Orbiter, we introduce the radial rate of strain, a novel measure computed from single-spacecraft data, which we interpret as a proxy for the double-adiabatic strain rate. The solar wind exhibits high absolute values of the radial rate of strain at locations with large temperature anisotropy. We measure the kurtosis and skewness of the radial rate of strain from the statistical moments to show that it is non-Gaussian for unstable intervals and increasingly intermittent at smaller scales with a power-law scaling. We conclude that the velocity field fluctuations in the solar wind contribute to the presence of temperature anisotropy sufficient to create potentially unstable conditions.

Kinetic Alfvén wave cascade in sub-ion range plasma turbulence

Kinetic Alfvén waves (KAWs) are simulated with a 3D particle-in-cell (PIC) code by using the eigenvector relations of density, velocity, electric, and magnetic field fluctuations derived from a two-fluid KAW model. Similar simulations are also performed with a whistler waves setup. The 2D two-fluid eigenvector relations are converted into 3D by using rotation of the reference frame. The initial condition for the simulations is a superposition of several waves at scales slightly larger than the ion skin depth. The nonlinear interactions produce a transfer of energy to smaller scales. The magnetic field perturbation ratios, velocity perturbation, and density perturbation ratios are calculated from the simulation at higher wavenumbers and compared with the analytically expected ratios for KAWs and whistler waves. We find that in both types of simulations, initialized either with an ensemble of KAWs or with whistlers, the observed polarization relations at later times match better with the KAW relations compared to whistlers. This indicates a preference for excitation of KAW fluctuations at smaller scales. The power spectrum in the perpendicular direction is calculated, and it shows similar indices as measured in the solar wind power spectrum in the transition (sub-ion) region. The power law extends to smaller scales when a higher ion-to-electron mass ratio is taken. The 2D magnetic power spectrum in magnetic field parallel and perpendicular directions shows typical anisotropy where the power spreads more in the perpendicular direction than in the parallel direction. This study shows that KAWs can explain features of the sub-ion range plasma turbulence in the solar wind.

Superresolution and analysis of three-dimensional velocity fields of underexpanded jets in different screech modes

Time-resolved (TR), three-dimensional (3D) velocity fields of screeching, underexpanded jets are estimated using non-time-resolved particle image velocimetry and simultaneous TR microphone measurements. Specifically, we aim to reconstruct TR 3D velocity fluctuation fields associated with the A2, B, and C modes of a screeching jet using a linear regression model and to analyze screech dynamics of these modes. The linear regression model is constructed on the basis of a linear relationship between the velocity and acoustic fields. Three nozzle pressure ratios (NPRs) of 2.30, 2.97, and 3.40 are employed. The dominant azimuthal modes for three cases are investigated using azimuthal Fourier coefficients of the acoustic data obtained by the azimuthal array of eight microphones placed near the nozzle exit. The dominant azimuthal modes at NPRs of 2.30, 2.97, and 3.40 are m=0, 1, and 1, respectively. The first two proper orthogonal decomposition (POD) modes in these azimuthal modes are dominant at all NPRs and are associated with screech. 3D velocity fluctuation fields associated with screech are reconstructed from these leading POD modes of the acoustic data. The reconstructed 3D velocity fluctuation fields at NPRs of 2.97 and 3.40 exhibit two helical structures with opposite rotation directions. The present results demonstrate that, in the B mode, the flapping structure exhibits random clockwise and counterclockwise rotations over an extended time domain, while maintaining a consistent direction within short time domains. In addition, in the C mode, two helical structures with opposite rotation directions, as well as the flapping structure, are observed. Published by the American Physical Society 2024

Estimation of Turbulent Mixing Factor and Study of Turbulent Flow Structures in Pressurized Water Reactor Sub Channel by Direct Numerical Simulation

Abstract Subchannel analysis codes are presently a requirement for design and safety analysis of nuclear reactors. Among the crucial inputs for these codes, the turbulent mixing factor holds particular significance. However, acquiring this factor through experimental means proves to be a challenging endeavor, primarily due to the necessity for precise pressure equilibrium between subchannels. Consequently, this requirement leads to the undertaking of expensive and intricate experiments for each new reactor or in cases where there are modifications in fuel bundle design. The need for direct numerical simulation (DNS) stems from the challenges and costs involved in experimental techniques, and the uncertainties due to empiricism in computational fluid dynamics (CFD) models. In this study, DNS has been conducted across six Reynolds numbers, ranging from 17,640 to 1.176 × 105, in the geometry of a pressurized water reactor (PWR) subchannel. The resulting turbulent flow structures have been computed and their dynamics are examined. Furthermore, this paper presents a methodology for directly calculating the turbulent mixing factor from the fluctuating velocity field obtained from DNS data. The turbulent mixing process has been scrutinized in-depth, and a correlation for the turbulent mixing factor is developed. It is noted that most of the mixing occurs in the near-wall region. The study suggests different mixing factors for mass and momentum mixing. This paper aims to provide a comprehensive insight into the turbulent mixing phenomenon.

Integrating Flow Field Dynamics and Chemical Atmosphere Predictions for Enhanced Sulfur Corrosion Risk Assessment in Power Boilers.

In this work, we attempt to explain the phenomenon of sulfur corrosion of power boiler water walls under the conditions of large fluctuations in carbon monoxide concentrations. To assess the conditions required for corrosion formation, a criterion based on the chemical and flow field parameters of the flue gas is proposed. The formulated sulfur corrosion criterion is based on the mixture fraction variance and the turbulence time scale. Numerical modeling of coal combustion in a 250 MW power boiler is performed using ANSYS. Two cases of combustion in a boiler are analyzed, with the first simulating the boiler operated using classic high-swirl burners and the second one accounting for boiler operation with modified low-swirl burners. Calculations of pulverized coal combustion are performed using the standard k-ε turbulence model and the combustion described by the mixture fraction. The simulation results reveal that the low-swirl burner is characterized by higher values of the mixture fraction variance and a higher frequency of fluctuation of the velocity field, which is strongly related to an increased corrosion rate. The study outcomes show the validity of using the criterion of the mixture fraction variance and velocity field fluctuations to determine the areas at risk of sulfur corrosion.

Simultaneous measurement of the distributed longitudinal strain and velocity field for a cantilevered cylinder exposed to turbulent cross flow

The structural response of a cantilevered cylinder under free-stream conditions both with low and high turbulence intensity generated by turbulence-generating grids is analysed with concurrent measurements of the velocity field and the distributed strain. The thin-walled cylinder, with a diameter (D) of 50 mm, is mounted in a water flume as a cantilevered beam supported at one end, with 95% of its body submerged and exposed to cross flow yielding a Reynolds number of Re = 25000. We employ a novel combination of simultaneous particle image velocimetry and distributed strain measurements using Rayleigh backscattering fibre optic sensors. These sensors are embedded onto the surface of the cylinder to measure the experienced strain (ε\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varepsilon $$\\end{document}) of the structure along its spanwise direction, covering both the windward and leeward faces of the cylinder. The sensors fine spatial resolution allows us to discern the influence of the flow on the structural response of the cylinder in two distinct regions of the structure: upstream and downstream of the mean separation location. This differentiation allows us to isolate the local effects introduced by the free-stream conditions on the loading events over the body from the global force generated by the vortex shedding and other coherent motions present within the flow. Distinguishing between these direct and indirect effects helps determine which is more relevant for fatigue-life cycle analysis. The cross power spectral density between the fluctuating velocity field and the strain reveals that the load is dominated by the vortex shedding, and this relationship is intensified with the introduction of free-stream turbulence. It also helps to discern the different dynamics imposed by the two free-stream turbulence conditions.

Anisotropy of Density Fluctuations in the Solar Wind at 1 au

A well-known property of solar wind plasma turbulence is the observed anisotropy of the autocorrelations, or equivalently the spectra, of velocity and magnetic field fluctuations. Here we explore the related but apparently not well-studied issue of the anisotropy of plasma density fluctuations in the energy-containing and inertial ranges of solar wind turbulence. Using 10 yr (1998–2008) of in situ data from the Advanced Composition Explorer mission, we find that for all but the fastest wind category, the density correlation scale is slightly larger in directions quasi-parallel to the large-scale mean magnetic field as compared to quasi-perpendicular directions. The correlation scale in fast wind is consistent with isotropic. The anisotropy as a function of the level of correlation is also explored. We find at small correlation levels, i.e., at energy-containing scales and larger, the density fluctuations are close to isotropy for fast wind, and slightly favor more rapid decorrelation in perpendicular directions for slow and medium winds. At relatively smaller (inertial range) scales where the correlation values are larger, the sense of anisotropy is reversed in all speed ranges, implying a more “slablike” structure, especially prominent in the fast wind samples. We contrast this finding with published results on velocity and magnetic field correlations.

Characterization of Turbulent Fluctuations in the Sub-Alfvénic Solar Wind

Parker Solar Probe (PSP) observed sub-Alfvénic solar wind intervals during encounters 8–14, and low-frequency magnetohydrodynamic (MHD) turbulence in these regions may differ from that in super-Alfvénic wind. We apply a new mode decomposition analysis to the sub-Alfvénic flow observed by PSP on 2021 April 28, identifying and characterizing entropy, magnetic islands, forward and backward Alfvén waves, including weakly/nonpropagating Alfvén vortices, forward and backward fast and slow magnetosonic (MS) modes. Density fluctuations are primarily and almost equally entropy- and backward-propagating slow MS modes. The mode decomposition provides phase information (frequency and wavenumber k) for each mode. Entropy density fluctuations have a wavenumber anisotropy of k ∥ ≫ k ⊥, whereas slow-mode density fluctuations have k ⊥ > k ∥. Magnetic field fluctuations are primarily magnetic island modes (δ B i ) with an O(1) smaller contribution from unidirectionally propagating Alfvén waves (δ B A+) giving a variance anisotropy of 〈δBi2〉/〈δBA2〉=4.1 . Incompressible magnetic fluctuations dominate compressible contributions from fast and slow MS modes. The magnetic island spectrum is Kolmogorov-like k⊥−1.6 in perpendicular wavenumber, and the unidirectional Alfvén wave spectra are k∥−1.6 and k⊥−1.5 . Fast MS modes propagate at essentially the Alfvén speed with anticorrelated transverse velocity and magnetic field fluctuations and are almost exclusively magnetic due to β p ≪ 1. Transverse velocity fluctuations are the dominant velocity component in fast MS modes, and longitudinal fluctuations dominate in slow modes. Mode decomposition is an effective tool in identifying the basic building blocks of MHD turbulence and provides detailed phase information about each of the modes.

Total and static temperature statistics in compressible turbulent plane channel flow

The paper studies the statistics of total and static temperature (total $h_t$ and static $h$ enthalpy) in compressible turbulent plane channel flow using direct numerical simulations (DNS) data covering the range of centreline Mach numbers $0.3\lessapprox \bar {M}_{{{CL}}_x} \lessapprox 2.5$ and Huang–Coleman–Bradshaw friction Reynolds numbers $100\lessapprox Re_{\tau ^\star }\lessapprox 1000$ . For this class of very-cold-wall flows, the DNS data for correlation coefficients and joint probability density functions (p.d.f.s) show that $h_t'$ is invariably very strongly correlated with the streamwise velocity fluctuation $u'$ , in contrast to static temperature (static enthalpy $h'$ ) whose correlation with $u'$ weakens rapidly with increasing wall distance. We study various correlations and joint p.d.f.s of $h_t'$ and $h'$ in relation to the fluctuating velocity field, including the turbulent Prandtl number $Pr_{{T}}$ , and discuss the predictions of Reynolds analogy. The scaling of the mean enthalpy and the fluctuating enthalpy variance and fluxes with respect to inner and outer velocity scales is investigated. The complex behaviour and scaling of different terms in the transport equations for the enthalpy variance and fluxes are discussed.

Estimation of 2D profile dynamics of electrostatic potential fluctuations using multi-scale deep learning

Abstract Dynamics in magnetically confined plasmas are dominated by turbulence driven by spatial inhomogeneities in density and temperature. Simultaneous measurement of velocity field and density fluctuations is necessary to observe the particle transport, but the measurement of the velocity field fluctuations is often challenging. Here, we propose a method to estimation velocity field fluctuations from density fluctuations by using plasma turbulence simulations and a deep technique learning. In order to take multi-scale characteristics into account, the several number of spatial filters are used in the convolutional neural network. The velocity field fluctuations are successfully predicted, and the particle transport estimated from the predicted velocity field fluctuations is within 93.1% accuracy. The deep learning could be used for the prediction of physical variables which are difficult to be measured.

A Joint Multifractal Approach to Solar Wind Turbulence

Previous studies have shown that solar wind, a plasma medium with turbulent dynamics, exhibits anomalous scaling features, i.e., intermittency, in the inertial domain. This intermittent nature has primarily been investigated through the study of the scaling features of the structure functions of single quantities. We use a novel approach based on joint multifractal analysis in this study to simultaneously investigate the scaling characteristics of both the magnetic field and the plasma velocity in solar wind turbulence. Specifically, we focus on the joint multifractal behavior of magnetic and velocity field fluctuations in both fast and slow solar wind streams observed by the ESA-Ulysses satellite, with the goal of identifying any differences in their joint multifractal characteristics.

Anomalous crystalline ordering of particles in a viscoelastic fluid under high shear

Addition of particles to a viscoelastic suspension dramatically alters the properties of the mixture, particularly when it is sheared or otherwise processed. Shear-induced stretching of the polymers results in elastic stress that causes a substantial increase in measured viscosity with increasing shear, and an attractive interaction between particles, leading to their chaining. At even higher shear rates, the flow becomes unstable, even in the absence of particles. This instability makes it very difficult to determine the properties of a particle suspension. Here, we use a fully immersed parallel plate geometry to measure the high-shear-rate behavior of a suspension of particles in a viscoelastic fluid. We find an unexpected separation of the particles within the suspension resulting in the formation of a layer of particles in the center of the cell. Remarkably, monodisperse particles form a crystalline layer which dramatically alters the shear instability. By combining measurements of the velocity field and torque fluctuations, we show that this solid layer disrupts the flow instability and introduces a single-frequency component to the torque fluctuations that reflects a dominant velocity pattern in the flow. These results highlight the interplay between particles and a suspending viscoelastic fluid at very high shear rates.

Synthetic eddy generation and modelling of turbine operation in a turbulent tidal flow

In the operation of hydrokinetic turbines in tidal sites, the effect of onset flow turbulence on device performance and reliability deserves particular attention. Computational Fluid Dynamics (CFD) models capable to describe this complex phenomenology are necessary to predict harmful operating conditions and to implement design strategies to mitigate the impacts. Similarly, the description of the interaction between turbine wakes and eddies in the onset turbulent flow is important in the study of tidal arrays.
 An original CFD methodology to simulate the operation of a tidal turbine in an arbitrary turbulent flow is presented. The methodology falls within the class of Synthetic Methods (SM). A randomly fluctuating velocity field is generated by a volume force distribution acting as forcing term in the Navier-Stokes equations. With respect to existing volume-force SM, an original definition of the forcing terms, and a control strategy to enforce a prescribed turbulence metrics are proposed. Volume force terms are imposed in a thin layer in the upstream region of the computational domain by a sinusoidal distribution with random variation of both intensity and phase. A Proportional-Integral-Derivative (PID) control is applied to minimize the difference between the intensity of the generated flow turbulence and the prescribed conditions.
 In [1] the model was applied to describe a turbulent stream in an unbounded flow by Detached Eddy Simulation (DES). The capability to generate eddies that evolve into a homogeneous, isotropic turbulent flow was demonstrated. Here, the model is applied to analyze the interaction between the generated onset turbulent flow and a tidal turbine. A computationally efficient approach is used here in which the turbine is described by a volume force method, in a similar fashion as turbulence generation is modelled. Specifically, a hybrid viscous/inviscid methodology is applied in which the DES solver is strongly coupled with a Boundary Integral Equation Method (BIEM) solver. At each time step, the blade load distribution is calculated by a time-accurate BIEM solution and recasts as volume force terms that are plugged into the DES solution. Examples of BIEM validation studies are given in [2, 3, 4] and in the results of a recent blind-test benchmark to be presented at the EWTEC 2023 Conference [5].
 The numerical application described here deals with a 3-bladed horizontal-axis tidal turbine in a 16% intensity, isotropic turbulent onset flow. In the full paper, the overall methodology is described, and numerical results are presented and discussed. Particular attention is given to characterize the generated turbulent stream in terms of key metric quantities like turbulence intensity, Power Spectral Density (PSD), time and spatial scales, isotropy, Probability Density Function (PDF). The results are analyzed to discuss the capability of the methodology to render a physically-consistent description of the phenomenology governing turbine operation in a real tidal flow.
 
 Gregori, M. et al., Mar. Sci. Eng. 2022. (https://doi.org/10.3390/jmse10101332)
 Sarichloo, Z. et al., Marine Energy Journal, 2022. (https://doi.org/10.36688/imej.5.77-90)
 Dubbioso, G.A. et al., Proceedings of EWTEC 2019.
 Salvatore, F. et al., Mar. Sci. Eng. 2018, 6, 53. (https://doi.org/10.3390/jmse6020053)
 Willden, R. et al., Submitted to EWTEC 2023.

Lagrangian and Eulerian Supersaturation Statistics in Turbulent Cloudy Rayleigh–Bénard Convection: Applications for LES Subgrid Modeling

Abstract Turbulent fluctuations of scalar and velocity fields are critical for cloud microphysical processes, e.g., droplet activation and size distribution evolution, and can therefore influence cloud radiative forcing and precipitation formation. Lagrangian and Eulerian water vapor, temperature, and supersaturation statistics are investigated in direct numerical simulations (DNS) of turbulent Rayleigh–Bénard convection in the Pi Convection Cloud Chamber to provide a foundation for parameterizing subgrid-scale fluctuations in atmospheric models. A subgrid model for water vapor and temperature variances and covariance and supersaturation variance is proposed, valid for both clear and cloudy conditions. Evaluation of phase change contributions through an a priori test using DNS data shows good performance of the model. Supersaturation is a nonlinear function of temperature and water vapor, and relative external fluxes of water vapor and heat (e.g., during entrainment-mixing and phase change) influence turbulent supersaturation fluctuations. Although supersaturation has autocorrelation and structure functions similar to the independent scalars (temperature and water vapor), the autocorrelation time scale of supersaturation differs. Relative scalar fluxes in DNS without cloud make supersaturation PDFs less skewed than the adiabatic case, where they are highly negatively skewed. However, droplet condensation changes the PDF shape response: it becomes positively skewed for the adiabatic case and negatively skewed when the sidewall relative fluxes are large. Condensation also increases correlations between water vapor and temperature in the presence of relative scalar fluxes but decreases correlations for the adiabatic case. These changes in correlation suppress supersaturation variability for the nonadiabatic cases and increase it for the adiabatic case. Implications of this work for subgrid microphysics modeling using a Lagrangian stochastic scheme are also discussed.

Linear Mode Decomposition in Magnetohydrodynamics Revisited

Small-amplitude fluctuations in the magnetized solar wind are measured typically by a single spacecraft. In the magnetohydrodynamics (MHD) description, fluctuations are typically expressed in terms of the fundamental modes admitted by the system. An important question is how to resolve an observed set of fluctuations, typically plasma moments such as the density, velocity, pressure, and magnetic field fluctuations, into their constituent fundamental MHD modal components. Despite its importance in understanding the basic elements of waves and turbulence in the solar wind, this problem has not yet been fully resolved. Here, we introduce a new method that identifies between wave modes and advected structures such as magnetic islands or entropy modes and computes the phase information associated with the eligible MHD modes. The mode-decomposition method developed here identifies the admissible modes in an MHD plasma from a set of plasma and magnetic field fluctuations measured by a single spacecraft at a specific frequency and an inferred wavenumber k m . We present data from three typical intervals measured by the Wind and Solar Orbiter spacecraft at ∼1 au and show how the new method identifies both propagating (wave) and nonpropagating (structures) modes, including entropy and magnetic island modes. This allows us to identify and characterize the separate MHD modes in an observed plasma parcel and to derive wavenumber spectra of entropic density, fast and slow magnetosonic, Alfvénic, and magnetic island fluctuations for the first time. These results help identify the fundamental building blocks of turbulence in the magnetized solar wind.

Toward the use of LES for industrial complex geometries. Part II: Reduce the time-to-solution by using a linearised implicit time advancement

The strong increase in computational power observed during the last few years has allowed to use Large Eddy Simulation (LES) for industrial configurations. Nevertheless, the time-to-solution is still too large for a daily use in the design phases. The objective of this work is to develop a new time integration method to reduce the time-to-solution of LES of incompressible flows by allowing the use of larger time step. The projection method, probably the most commonly used method in the context of LES of incompressible flow, is generally applied using explicit time advancement which constrains the time-step value for stability reasons (CFL and Fourier constraints). The time step can then be small with respect to the physical characteristic times of the studied flow. In this case, an implicit time advancement method, which is unconditionally stable, can be used. However, this leads to non-linear resolution of momentum equation which can strongly increase time-to-solution because of non-linear iterations inside a physical iteration. To relax the stability constraints while minimising the computational cost of an iteration, a linearised implicit time advancement based on Backward Differentiation Formula (BDF) scheme is proposed in this work. The linearisation is performed using an extrapolated velocity field based on the previous fields. This time integration is first evaluated on a turbulent pipe test case. It is observed a time-to-solution up to five times lower than the explicit time integration while keeping the same accuracy in terms of mean and fluctuating velocity fields. To incorporate this new time advancement method in the automatic mesh convergence developed in Part I, a time-step control method based on the local truncation error is used. The resulting automatic time-step and mesh procedure is evaluated on a turbulent round jet case and on PRECCINSTA configuration, a swirl burner which is a representative case of an industrial aeronautical injection system. This new procedure leads to a time-to-solution up to three times lower than the previous procedure, presented in Part I.

Cascade-Net for predicting cylinder wake at Reynolds numbers ranging from subcritical to supercritical regime

The application of machine learning techniques embedded with fluid mechanics has gained significant attention due to their exceptional ability to tackle intricate flow dynamics problems. In this study, an energy-cascade-conceptualized network termed Cascade-Net is proposed. This model is grounded in generative adversarial networks to predict the spatiotemporal fluctuating velocity in the near-wall wake of a circular cylinder in a physics-informed manner. A comprehensive dataset is obtained by wind tunnel testing, comprising the near-wake velocity field and wall pressure of a rough circular cylinder with Reynolds numbers from subcritical to supercritical regimes. By leveraging convolutional neural networks, the Cascade-Net utilizes the pressure data, Reynolds numbers, and a few of velocity measured in the wake field to predict the spatiotemporal fluctuating velocity. The velocity fluctuations are predicted hierarchically at different resolved scales, ensuring that the energy cascade in turbulence is accurately simulated. The results show that the Cascade-Net presents good generalization performance and is capable of accurately predicting fluctuating velocity fields and the second-order moments in both extrapolation and interpolation cases at various Reynolds numbers. The mechanism of Cascade-Net in prediction is also investigated by parametric analysis in the convolutional layer and spatial attention gate, manifesting that the Cascade-Net is heavily dependent on the velocity characteristics of the larger resolved scale adjacent to target smaller scales to prediction, which interprets the success of Cascade-Net in capturing the intricate physics of the cylinder wake.

Reduced-order representation of superstructures in a turbulent boundary layer

The present work is devoted to a low-dimensional characterization of superstructures (SS) in a turbulent boundary layer (TBL). The main purpose is to provide new insight on the spatial correlation between SS and large-scale motion (LSM) with the help of reduced-order analysis via proper orthogonal decomposition (POD). A dataset of three-dimensional streamwise fluctuating velocity fields of a TBL with Reτ=1817, obtained by direct numerical simulation, is decomposed by POD into cross-sectional POD eigenmodes and streamwise-varying mode coefficients. The spatial pattern of the POD eigenmodes of leading-order POD modes, their characteristic length scales, as well as their geometric similarity are analyzed in detail. A conditional-average method is further proposed to yield a reduced-order representation of typical local geometric patterns of the SS, which are mainly contributed to by one particular observation mode. It is found that large-scale motion-like structures constitute the core region of SS. These conditional-averaged structures are treated as elementary cells, which jointly form the skeleton of SS, i.e., uSK which is low dimensionally reconstructed by the first six POD modes. It is found that uSK presents quasi-Gaussian behavior, suggesting a quasi-equilibrium state of elementary SS cells. Finally, ⟨uSK2⟩(y) presents a log-law scaling with the decaying slope of A1SK=1.49, but the log-law region is apparently higher than that of the original velocity field, i.e., ⟨u2⟩(y).

Effects of mean shear on the vortex identification and the orientation statistics

This work compares the threshold applied to the swirling strength as well as the vortex orientation statistics in the total and fluctuating velocity fields using direct numerical simulations of compressible and incompressible turbulent channel flows. It is concluded that the difference in the swirling strength for vortex identification is minimal in the logarithmic region such that these two situations share the same threshold. Regarding the vortex orientation, the inclination angle remains similar. However, as the wall-normal distance increases, a more and more obvious distinction is noticed for its orientation with respect to the spanwise (z) direction. It is mainly due to their intrinsic differences and attendant contrasting preference for the vortex identification, i.e., vortices rotating in the −z direction for the total velocity field and in the z direction for the fluctuating one. These observations function as a reasonable explanation for various remarks in previous studies.

Coronal Loop Heating by Nearly Incompressible Magnetohydrodynamic and Reduced Magnetohydrodynamic Turbulence Models

The transport of waves and turbulence beyond the photosphere is central to the coronal heating problem. Turbulence in the quiet solar corona has been modeled on the basis of the nearly incompressible magnetohydrodynamic (NI MHD) theory to describe the transport of low-frequency turbulence in open magnetic field regions. It describes the evolution of the coupled majority quasi-2D and minority slab component, driven by the magnetic carpet and advected by a subsonic, sub-Alfvénic flow from the lower corona. In this paper, we couple the NI MHD turbulence transport model with an MHD model of the solar corona to study the heating problem in a coronal loop. In a realistic benchmark coronal loop problem, we find that a loop can be heated to ∼1.5 million K by transport and dissipation of MHD turbulence described by the NI MHD model. We also find that the majority 2D component is as important as the minority slab component in the heating of the coronal loop. We compare our coupled MHD/NI MHD model results with a reduced MHD (RMHD) model. An important distinction between these models is that RMHD solves for small-scale velocity and magnetic field fluctuations and obtains the actual viscous/resistive dissipation associated with their evolution whereas NI MHD evolves scalar moments of the fluctuating velocity and magnetic fields and approximates dissipation using an MHD turbulence phenomenology. Despite the basic differences between the models, their simulation results match remarkably well, yielding almost identical heating rates inside the corona.