Fluctuations Of Total Energy Research Articles

Influence of time-varying flow on dynamic flame characteristics in VCE: Numerical and experimental study

Afterburner shows obvious transient characteristics in variable cycle engines (VCEs), herein, a compact flame holder and injection device with well performance coordinating a rear variable bypass injector (RVABI) were designed and investigated under variable inlet conditions. Inlet aerodynamic parameters were dynamically simulated and adjusted from small to large to investigate the matching law of bypass ratio and guiding angle, flow structure, and combustion characteristics. A typical case was experimentally verified well, and the coherent modes of the transient velocity field were identified using snapshot proper orthogonal decomposition(POD). It is found from POD that the first modes contributing to the total fluctuation energy are decreased by 15% when the guiding angle increased to 31.92°. The inlet conditions have little effect on the vortex structure near the pilot, while the red-blue alternating vortex structures in the rear of the strut are mainly influenced by the coupling of back pressure between the strut and the pilot. The air entrainment strength guided by RVABI will affect the three-dimensional vortex system built by the flame holder, and cause flow separation or local flameout when the velocity distortion is out of 0.5–1.2. Increased air-entrainment strength generates high turbulent energy, which can improve flow separation and increase radial flame development's instability. Moreover, a guiding angle of nearly 5° has the same effect on air entrainment strength as a bypass ratio of 0.2.

Passive Flow Control Application Using Single and Double Vortex Generator on S809 Wind Turbine Airfoil

The current study is aimed at investigating the influences of vortex generator (VG) applications mounted to the suction and pressure surfaces of the S809 wind turbine airfoil at low Reynolds number flow conditions. Both single and double VG applications were investigated to provide technological advancement in wind turbine blades by optimizing their exact positions on the surface of the airfoil. The results of the smoke-wire experiment for the uncontrolled case reveal that a laminar separation bubble formed near the trailing edge of the suction surface, and it was moved towards the leading edge as expected when the angle of attack was increased, resulting in bubble burst and leading-edge flow separation at α = 12°. The u/U∞, laminar kinetic energy and total fluctuation energy contours obtained from the numerical study clearly show that both the single and double VG applications produced small eddies, and those eddies in the double VG case led the flow to be reattached at the trailing edge of the suction surface and to gain more momentum by energizing. This situation was clearly supported by the results of aerodynamic force; the double VG application caused the lift coefficient to increase, resulting in an enhancement of the aerodynamic performance. A novel finding is that the VG at the pressure surface caused the flow at the wake region to gain more energy and momentum, resulting in a reattached and steadier flow condition.

Experimental mode decomposition investigation on 3-stage axial flow compressor stall phenomena using aeroacoustics measurements

Safely operating compressors is quite critical. Rotating stall is highly undesirable and affects negatively the performance and stability of aero-engine compressors. It is important to identify a precursor of such rotating stalling phenomena observed on the compressor. In this work, we conduct experimental measurements on a 3-stage axial flow compressor by using 8 acoustic pressure sensors. Emphasis is being placed on applying different mode decomposition methods such as Proper Orthogonal Decomposition (POD) and Empirical Mode Decomposition (EMD) on these acoustics data to shed lights on the stall phenomena. Comparison is then made between these methods and conventional means like continuous wavelet (CWA), and PSD (Power Spectrum Density) analyses to achieve a timely detection of stall inception and the energy distribution before and after stall occurred. It is found from POD that the dominant acoustic modes contributing to more than 90% of the total fluctuation energy are changed from 3 to 4, when the stall occurred. The EMD investigation shows that the compressor stall is associated with a few low-frequency IMFs (intrinsic mode function). Time evolutions of such IMFs are observed to grow from negligible amplitude disturbances into limit cycles. Additionally, applying CWA reveals that the stall cell is originated from the first stage and then propagates circumferentially and axially to the second and third stage. Finally, PSD analysis shows that the stall frequency related to the spike-type stall cell exists only on the first stage. This is different from the blade passing frequency as observed on all stages of the compressor. In summary, the present work offers alternative acoustic measurements to examine the dynamic instability of a compressor stall with advanced signal-processing techniques applied.

Chromium ditelluride monolayer: A novel promising 2H phase thermoelectric material with direct bandgap and ultralow lattice thermal conductivity

Inspired by the groundbreaking discoveries of the transition metal dichalcogenides materials (TMDCs) with 2H- and 1T- phases, the crystal structure, electronic and phonon thermal transport, and thermoelectric properties of novel 2H-phase CrTe2 monolayer are theoretically evaluated by the first-principles calculation and Boltzmann transport theory. The 2H-CrTe2 monolayer is a direct semiconductor with a bandgap of ∼ 0.93 eV. The elastic modulus and phonon dispersion calculations demonstrate that the 2H-CrTe2 monolayer is mechanically and dynamically stable due to the absence of negative value in elastic constant and frequency. Ab initio molecular dynamics (AIMD) simulations demonstrate the thermal stability of the 2H-CrTe2 monolayer at high temperature, as evidenced by slight fluctuations in total energy. In combination with the small group velocity, large Grüneisen parameter, and strong anharmonic scattering, the ultralow lattice thermal conductivity is predicated for the 2H-CrTe2 monolayer (∼ 0.21 W/mK @ 300 K). The optimal dimensionless figure of merit (ZT) values for the p- and n-type 2H-CrTe2 monolayers are ∼ 4.05 and ∼ 3.08 at 900 K, respectively. Our present results would not only provide a fundamental understanding of electronic transport and thermoelectric properties of the 2H-CrTe2 monolayer, but also shed some light on the theoretical design of low dimensional nanomaterials with high thermoelectric applications.

Energy fluctuations in one dimensional Zhang sandpile model

We consider the Zhang sandpile model in one-dimension (1D) with locally conservative (or dissipative) dynamics and examine its total energy fluctuations at the external drive time scale. The bulk-driven system leads to Lorentzian spectra, with a cutoff time T growing linearly with the system size L. The fluctuations show 1/f α behavior with α ∼ 1 for the boundary drive, and the cutoff time varies non-linearly. For conservative local dynamics, the cutoff time shows a power-law growth T ∼ L λ that differs from an exponential form ∼exp(μL) observed for the nonconservative case. We suggest that the local dissipation is not a necessary ingredient of the system in 1D to get the 1/f noise, and the cutoff time can reveal the distinct nature of the local dynamics. We also discuss the energy fluctuations for locally nonconservative dynamics with random dissipation.

Three new C[sbnd]N compounds in orthorhombic symmetry: Theoretical investigations

Three CN compounds Cmcm C3N2, Pmna-I CN and Pmna-II CN are predicted in this work and their physical properties are systematically investigated by first-principles calculations. Each of the proposed CN compounds is in orthorhombic symmetry and has superhard characteristics. The phonon dispersion spectra, relative enthalpies, total energy fluctuations and elastic constants indicate that the proposed three CN compounds are dynamically, thermodynamically, thermally and mechanically stable at ambient pressure, respectively. The elastic anisotropy properties of Cmcm C3N2 as well as Pmna-I CN and Pmna-II CN are examined by illustrating the three-dimensional surface constructions of Young's modulus, shear modulus, and Poisson's ratio. Moreover, the Heyd-Scuseria-Ernzerhof (HSE06) hybrid functional is utilized to depict the electronic band structures of Cmcm C3N2, Pmna-I CN and Pmna-II CN, and it is found that Cmcm C3N2 and Pmna-II CN are indirect gap semiconductor materials with the bandgaps of 4.13 eV and 2.03 eV, respectively, and Pmna-I CN is a direct bandgap semiconductor with the bandgap of 1.86 eV. In addition, the densities of state of the proposed three CN compounds are analyzed elaborately, which reveals that the hardness feature of the materials mainly owing to the strong covalent bond between carbon and nitrogen atoms, and the excellent hardness characteristics make them superhard materials with potential technological and industrial applications.

Analysis of coherence in turbulent stratified wakes using spectral proper orthogonal decomposition

We use spectral proper orthogonal decomposition (SPOD) to extract and analyse coherent structures in the turbulent wake of a disk at Reynolds number $ {\textit {Re}} = 5 \times 10^{4}$ and Froude numbers $ {\textit {Fr}} = 2$ , 10. We find that the SPOD eigenspectra of both wakes exhibit a low-rank behaviour and the relative contribution of low-rank modes to total fluctuation energy increases with $x/D$ . The vortex shedding (VS) mechanism, which corresponds to $ {\textit {St}} \approx 0.11 - 0.13$ in both wakes, is active and dominant throughout the domain in both wakes. The continual downstream decay of the SPOD eigenspectrum peak at the VS mode, which is a prominent feature of the unstratified wake, is inhibited by buoyancy, particularly for $ {\textit {Fr}} = 2$ . The energy at and near the VS frequency is found to appear in the outer region of the wake when the downstream distance exceeds $Nt = Nx/U = 6 - 8$ . Visualizations show that unsteady internal gravity waves (IGWs) emerge at the same $Nt = 6 - 8$ . A causal link between the VS mechanism and the unsteady IGW generation is also established using the SPOD-based reconstruction and analysis of the pressure transport term. These IGWs are also picked up in SPOD analysis as a structural change in the shape of the leading SPOD eigenmode. The $ {\textit {Fr}} = 2$ wake shows layering in the wake core at $Nt > 15$ which is captured by the leading SPOD eigenmodes of the VS frequency at downstream locations $x/D > 30$ . The VS mode of the $ {\textit {Fr}} = 2$ wake is streamwise coherent, consisting of $V$ -shaped structures at $x/D \gtrsim 30$ . Overall, we find that the coherence of wakes, initiated by the VS mode at the body, is prolonged by buoyancy to far downstream. Also, this coherence is spatially modified by buoyancy into horizontal layers and IGWs. Low-order truncations of SPOD modes are shown to efficiently reconstruct important second-order statistics.

Proper orthogonal and dynamic mode decomposition analyses of nonlinear combustion instabilities in a solid-fuel ramjet combustor

In ramjet propulsion systems, syelf-excited combustion instability is highly undesirable. It may lead to violent structural vibration and even mission failure. For this, self-excited combustion instabilities in such SFRJ are investigated numerically by 2D unsteady Reynolds-Average Navier-Stokes (URANS) model and varying the inlet mass flow rate ṁair. When combustion instability occurs, large-amplitude temperature, velocity, and reacting species wavy motions are observed along the axial flow direction. To shed light on the flow features and the energy distribution among the unstable eigenmodes, proper orthogonal (POD) and dynamic mode decomposition (DMD) analyses of nonlinear combustion instabilities in a solid-fuel Ramjet (SFRJ) combustor are conducted. The POD studies reveal that the fluctuation energy of the first six modes contributes to 99% of the total fluctuation energy of all modes. It means that the main features of the SFRJ combustors could be captured by using the first six modes. Unlike POD studies, DMD analysis captures the frequency information and spatial structures in the entire flow field. Examining the DMD growth rate reveals that all dominant DMD eigenmodes are marginally stable (growth rate = 0) or unstable (positive growth rate). And the frequency of each dominant mode could be enhanced by 3–10 Hz as theṁair is increased by 0.2 kg/s. The mode energy decreases with the increase of the mode order, with the decrease up to around 90%. The DMD analysis on velocity field indicated that the flow separation could be observed near the backward facing step. And the DMD mode structure of the temperature field can significantly affect the mode structures of Mach number and YCO2 field. In general, the present work provides detailed analyses of the SFRJ flow field in the presence of self-excited combustion instability by using POD and DMD approaches.

Experimental investigation on axial compressor stall phenomena using aeroacoustics measurements via empirical mode and proper orthogonal decomposition methods

In this work, we conduct experimental investigations on a single-stage axial compressor to shed lights on the dynamic stall phenomena via aeroacoustic measurements. For this, 8 acoustic pressure sensors are installed equally around the circumference of the compressor intake. The acoustic pressure data are simultaneously logged in real-time. Classical and conventional Fourier-transform based methods reveal that the compressor stall will occur beyond a critical pressure ratio or a flow coefficient as illustrated on a compressor map. However, there is no warning precursor obtained from the conventional signal analysis methods. Further investigations are conducted using a number of advanced signal processing techniques, such as empirical mode decomposition (EMD) and proper orthogonal decomposition (POD) and continuous wavelet (CW) methods. EMD analysis reveals that the compressor stall is corresponding to a low-frequency intrinsic mode function (IMF). It is growing rapidly from negligible amplitude random disturbances to limit cycle oscillations. POD shows that the number of the dominant acoustic modes contributing to more than 98.5% of the total fluctuation energy is changed from 3 to 7, when the stall occurs. This is insightful for low-order modeling of the compressor stall phenomena. Finally, applying CW transform could provide a warning of 0.05 s precursor on the tested axial compressor. In general, the present work opens up an alternative approach to study the dynamic physics of a compressor stall by applying an array of acoustic sensors with proper advanced data-processing methods implemented.

Optimal disturbances and large-scale energetic motions in turbulent boundary layers

We examine disturbances leading to optimal energy growth in a spatially developing, zero-pressure-gradient turbulent boundary layer. The slow development of the turbulent mean flow in the streamwise direction is modelled through a parabolized formulation to enable a spatial marching procedure. In the present framework, conventional spatial optimal disturbances arise naturally as the homogeneous solution to the linearized equations subject to a turbulent forcing at particular wavenumber combinations. A wave-like decomposition for the disturbance is considered to incorporate both conventional stationary modes as well as propagating modes formed by non-zero frequency/streamwise wavenumber and representative of convective structures naturally observed in wall turbulence. The optimal streamwise wavenumber, which varies with the spatial development of the turbulent mean flow, is computed locally via an auxiliary optimization constraint. The present approach can then be considered, in part, as an extension of the resolvent-based analyses for slowly developing flows. Optimization results reveal highly amplified disturbances for both stationary and propagating modes. Stationary modes identify peak amplification of structures residing near the centre of the logarithmic layer of the turbulent mean flow. Inner-scaled disturbances reminiscent of near wall streaks, and amplified over short streamwise distances, are identified in the computed streamwise energy spectra. In all cases, however, propagating modes surpass their stationary counterpart in both energy amplification and relative contribution to total fluctuation energy. We identify two classes of large-scale energetic modes associated with the logarithmic and wake layers of the turbulent mean flow. The outer-scaled wake modes agree well with the large-scale motions that populate the wake layer. For high Reynolds numbers, the log modes increasingly dominate the energy spectra with the predicted streamwise and wall-normal scales in agreement with superstructures observed in turbulent boundary layers.

Lattice models for granular-like velocity fields: finite-size effects

Long-range spatial correlations in the velocity and energy fields of a granular fluid are discussed in the framework of a 1d lattice model. The dynamics of the velocity field occurs through nearest-neighbour inelastic collisions that conserve momentum but dissipate energy. A set of equations for the fluctuating hydrodynamics of the velocity and energy mesoscopic fields give a first approximation for (i) the velocity structure factor and (ii) the finite-size correction to the Haff law, both in the homogeneous cooling regime. At a more refined level, we have derived the equations for the two-site velocity correlations and the total energy fluctuations. First, we seek a perturbative solution thereof, in powers of the inverse of system size. On the one hand, when scaled with the granular temperature, the velocity correlations tend to a stationary value in the long time limit. On the other hand, the scaled standard deviation of the total energy diverges, that is, the system shows multiscaling. Second, we find an exact solution for the velocity correlations in terms of the spectrum of eigenvalues of a certain matrix. The results of numerical simulations of the microscopic model confirm our theoretical results, including the above described multiscaling phenomenon.

PIV measurement of mildly controlled flow over a straight-wing model

This paper follows our previous work [Tang et al. Exp. Therm. Fluid Sci. 57:1–10 (2014)] to further demonstrate the effectiveness of a newly developed synthetic-jet (SJ) array in flow separation control over a straight-wing model using tomographic particle image velocimetry (Tomo-PIV) measurements. The wing model is tested in a wind tunnel at a fixed angle of attack 19° and chord Reynolds number 1.2×105, with the SJ array operating with a momentum coefficient of 4.2×10−5 and a reduced frequency of 7.2. Different from all existing SJ-based flow separation control, the present control is so mild that the controlled flow sometimes attaches to and sometimes separates from the wing surface. Both time-averaged and phase-locked flow fields are presented and analyzed. It is found that the control effect reaches its maximum at the nominal phase angle 180°, which is close to the instant when the SJ array achieves its maximum blowing. Significant reduction of the shape factor confirms the effectiveness of the current SJ array in overcoming flow separation. The proper orthogonal decomposition (POD) analysis reveals that, no matter whether the SJ array is actuated or not, the first mode consists of a 2D plane jet-like flow over the wing surface, carrying more than 70% of the total fluctuation energy. Although not strong enough to change this dominant mode, the present mild SJ control significantly increases the occurrence rate of flow attachment. The conditional turbulent kinematic energy (TKE) is also analyzed. It is found that while the introduction of the SJs has little influence on the conditional TKE for the separated flows, it reduces the thickness of the wall-attached layer of high TKE values for the attached flows.

KINETIC EVOLUTION OF CORONAL HOLE PROTONS BY IMBALANCED ION-CYCLOTRON WAVES: IMPLICATIONS FOR MEASUREMENTS BY SOLAR PROBE PLUS

We extend the kinetic guiding-center model of collisionless coronal hole protons presented in Isenberg and Vasquez to consider driving by imbalanced spectra of obliquely propagating ion-cyclotron waves. These waves are assumed to be a small by-product of the imbalanced turbulent cascade to high perpendicular wavenumber, and their total intensity is taken to be 1% of the total fluctuation energy. We also extend the kinetic solutions for the proton distribution function in the resulting fast solar wind to heliocentric distances of 20 solar radii, which will be attainable by the Solar Probe Plus spacecraft. We consider three ratios of outward-propagating to inward-propagating resonant intensities: 1, 4, and 9. The self-consistent bulk flow speed reaches fast solar wind values in all cases, and these speeds are basically independent of the intensity ratio. The steady-state proton distribution is highly organized into nested constant-density shells by the resonant wave-particle interaction. The radial evolution of this kinetic distribution as the coronal hole plasma flows outward is understood as a competition between the inward- and outward-directed large-scale forces, causing an effective circulation of particles through the (v{sub ∥}, v{sub ⊥}) phase space and a characteristic asymmetric shape to the distribution. These asymmetries are substantial and persistmore » to the outer limit of the model computation, where they should be observable by the Solar Probe Plus instruments.« less

A factor involved in efficient breakdown of supersonic streamwise vortices

Spatially developing processes in supersonic streamwise vortices were numerically simulated at Mach number 5.0. The vortex evolution largely depended on the azimuthal vorticity thickness of the vortices, which governs the negative helicity profile. Large vorticity thickness greatly enhanced the centrifugal instability, with consequent development of perturbations with competing wavenumbers outside the vortex core. During the transition process, supersonic streamwise vortices could generate large-scale spiral structures and a number of hairpin like vortices. Remarkably, the transition caused a dramatic increase in the total fluctuation energy of hypersonic flows, because the negative helicity profile destabilizes the flows due to helicity instability. Unstable growth might also relate to the correlation length between the axial and azimuthal vorticities of the streamwise vortices. The knowledge gained in this study is important for realizing effective fuel-oxidizer mixing in supersonic combustion engines.

Shearing instability of a dilute granular mixture

The shearing instability of a dilute granular mixture composed of smooth inelastic hard spheres or disks is investigated. By using the Navier-Stokes hydrodynamic equations, it is shown that the scaled transversal velocity mode exhibits a divergent behavior, similarly to what happens in one-component systems. The theoretical prediction for the critical size is compared with direct Monte Carlo simulations of the Boltzmann equations describing the system, and a good agreement is found. The total energy fluctuations in the vicinity of the transition are shown to scale with the second moment of the distribution. The scaling distribution function is the same as found in other equilibrium and nonequilibrium phase transitions, suggesting the existence of some kind of universality.

Proper orthogonal decomposition of wall-pressure fluctuations under the constrained wake of a square cylinder

The proper orthogonal decomposition (POD) analysis of the wall-pressure fluctuations below the constrained wake of a two-dimensional square cylinder in proximity to a plane wall was made on two systems, i.e., G/ D = 0.25 and 0.5, which corresponds to the wakes with and without suppression of the vortex shedding, respectively. Here, G is the gap distance and D is the width of the square cylinder. Synchronized measurements of wall-pressure fluctuations were made using a microphone array. For the system G/ D = 0.5, the first two energetic modes contribute 34.7% and 23.4% to the total fluctuation energy, respectively; however, the fluctuation energy corresponding to the third mode are relatively small and less than 10%. This sharp variation in eigenvalue is due to the presence and dominance of the Karman-like vortex shedding. However, for the system G/ D = 0.25, the considerable reduction in the eigenvalues of the first several modes is due to the suppression of the Karman-like vortex shedding. The spatial wavy pattern of the first several energetic eigenmodes was shown to be a good reflection of convective vortices superimposed in the wakes. The spectra of the POD coefficients determined the frequency of the dominant structures. Based on the coherence of the POD coefficients, an effective method of determining the number of POD modes for reconstruction of the low-order wall-pressure field was proposed. Accordingly, the low-order wall-pressure fluctuations in the systems G/ D = 0.5 and 0.25 were reconstructed by using the first four and five POD modes, respectively. The coherence and cross-correlation analysis of the reconstructed wall-pressure fluctuations, which excluded the influence of the small-scale structures and background ‘noise’, gave an insight view of the footprints of the dominant flow structures, which otherwise could not be effectively captured by using the original wall-pressure fluctuations.

Thermal Properties for Bulk Silicon Based on the Determination of Relaxation Times Using Molecular Dynamics

Molecular dynamics simulations are performed to estimate acoustical and optical phonon relaxation times, dispersion relations, group velocities, and specific heat of silicon needed to solve the Boltzmann transport equation (BTE) at 300 K and 1000 K. The relaxation times are calculated from the temporal decay of the autocorrelation function of the fluctuation of total energy of each normal mode in the ⟨100⟩ family of directions, where the total energy of each mode is obtained from the normal mode decomposition of the motion of the silicon atoms over a period of time. Additionally, silicon dispersion relations are directly determined from the equipartition theorem obtained from the normal mode decomposition. The impact of the anharmonic nature of the potential energy function on the thermal expansion of the crystal is determined by computing the lattice parameter at the cited temperatures using a NPT (i.e., constant number of atoms, pressure, and temperature) ensemble, and are compared with experimental values reported in the literature and with those computed analytically using the quasiharmonic approximation. The dependence of the relaxation times with respect to the frequency is identified with two functions that follow the functional form of the relaxation time expressions reported in the literature. From these functions a simplified version of relaxation times for each normal mode is extracted. Properties, such as group and phase velocities, thermal conductivity, and mean free path, needed to further develop a methodology for the thermal analysis of electronic devices (i.e., from nano- to macroscales) are determined once the relaxation times and dispersion relations are obtained. The thermal properties are validated by comparing the BTE-based thermal conductivity against the predictions obtained from the Green–Kubo method. It is found that the relaxation times closely resemble the ones obtained from perturbation theory at high temperatures; the contribution to the thermal conductivity of the transverse acoustic, longitudinal acoustic, and longitudinal optical modes being approximately 30%, 60%, and 10%, respectively, and the contribution of the transverse optical mode negligible.

Statistical isotropy in three-dimensional magnetohydrodynamic turbulence

Direct numerical simulation (DNS) of decaying isotropic three-dimensional (3D) magnetohydrodynamic (MHD) turbulence based on the 10243-modes in a periodic box is used for studying the statistical properties of turbulence. In this paper, the presence of intermittency in MHD turbulence is investigated through the analysis of the probability distribution function (PDF) for Elsässer fields and total energy fluctuations. We observe that the PDFs of the Elsässer fields fluctuations display strong non-Gaussian behavior at small scale, which can be ascribed to multifractality feature, while the PDFs of the total energy fluctuations have the same shape over all observed scales and are monofractal. The PDFs have stretched exponential tail and satisfy the function P(∣δX∣)∼exp (−A∣δX∣μ). Numerically, we extract the exponent μ and find that it is constant for monofractal behavior as the length scale varies. To check the notion of self-similarity in the respective fluctuations, we apply the compensated structure functions which could be a reliable way in turbulence.

Fractality feature in incompressible three-dimensional magnetohydrodynamic turbulence

High-resolution direct numerical simulation data for three-dimensional magnetohydrodynamic (MHD) turbulence based on the 10243-modes in a periodic box are used to study the statistical properties of turbulence. In this paper, the presence of intermittency in MHD turbulence is investigated through the analysis of the Probability Distribution Function (PDF) for Elsässer fields and total energy fluctuations. The energy PDFs exhibit similarity over all scales of the turbulent system since they show no substantial qualitative change in shape as the scale of the fluctuations varies. This is in sharp and surprising contrast to the well-known behavior of PDFs of turbulent field fluctuations of, for example, velocity, and magnetic and Elsässer fields. The PDFs have exponential tails and satisfy the function P(| δX |) ~ exp(–A | δX | μ). Numerically, we extract the exponent μ and find that it is constant for monofractal behavior as the scale of length varies. The compensated structure functions exhibit self-similarity for the respective fluctuations, and it is a reliable way in turbulence. PACS Nos.: 52.30.–q , 52.30.Cv , 52.35.Ra , 52.65.–y

Fractality feature in incompressible three-dimensional magnetohydrodynamic turbulence

Abstract Direct Numerical Simulation (DNS) of decaying isotropic 3D magnetohydrodynamic (MHD) turbulence based on the 10243-modes in a periodic box is used to study the statistical properties of turbulence. In this paper, the presence of intermittency in MHD turbulence is investigated through the analysis of the Probability Distribution Function (PDF) for Elsässer fields and total energy fluctuations. We observe that the PDFs of the Elsässer fields fluctuations display a strong non-Gaussian behavior at small scale, which can be ascribed to multifractality feature, while the PDFs of the total energy fluctuations have the same shape over all observed scales and are monofractal. The PDFs have stretched exponential tail and satisfy the function P(|δX|) ∼ exp(−A|δX|μ). Numerically, we extract the exponent μ and find that it is constant for monofractal behavior as the length scale varies. To check the notion of self-similarity in the respective fluctuation, we apply the compensated structure functions.