Low-frequency Turbulence Research Articles

Investigation of electromagnetic fluctuations in a magnetically screened high beta plasma

We report low-frequency electromagnetic turbulence in large-volume plasma devices in a region that receives magnetically screened plasma. The magnetic screen is produced by the activation of a large solenoid that generates a strong magnetic field ( BEEF ) transverse to the background axial magnetic field ( Bz ). The magnetic field strength variation in BEEF controls the plasma diffusion and is responsible for parametric profile modifications in large volume plasma devices. The turbulence is characterized by the observed features of an electromagnetic mode having frequency ordering in the lower hybrid range (f ci < f < f LH). The free energy source for the excited turbulence is believed to be the prevalent finite radial pressure gradient in the system. The excited electromagnetic mode shows typical scales for the wave number, k⊥ ∼ 0.13 cm−1 and frequency f ∼ 6 kHz and propagates with phase velocity comparable to ion acoustic velocity, C s in electron diamagnetic drift direction. It is believed that the low-frequency pressure gradient-driven electromagnetic mode exhibits coupling with the lower hybrid or whistler wave.

GX: a GPU-native gyrokinetic turbulence code for tokamak and stellarator design

GX is a code designed to solve the nonlinear gyrokinetic system for low-frequency turbulence in magnetized plasmas, particularly tokamaks and stellarators. In GX, our primary motivation and target is a fast gyrokinetic solver that can be used for fusion reactor design and optimization along with wide-ranging physics exploration. This has led to several code and algorithm design decisions, specifically chosen to prioritize time to solution. First, we have used a discretization algorithm that is pseudospectral in the entire phase space, including a Laguerre–Hermite pseudospectral formulation of velocity space, which allows for smooth interpolation between coarse gyrofluid-like resolutions and finer conventional gyrokinetic resolutions and efficient evaluation of a model collision operator. Additionally, we have built GX to natively target graphics processors (GPUs), which are among the fastest computational platforms available today. Finally, we have taken advantage of the reactor-relevant limit of small $\rho _*$ by using the radially local flux-tube approach. In this paper we present details about the gyrokinetic system and the numerical algorithms used in GX to solve the system. We then present several numerical benchmarks against established gyrokinetic codes in both tokamak and stellarator magnetic geometries to verify that GX correctly simulates gyrokinetic turbulence in the small $\rho _*$ limit. Moreover, we show that the convergence properties of the Laguerre–Hermite spectral velocity formulation are quite favourable for nonlinear problems of interest. Coupled with GPU acceleration, which we also investigate with scaling studies, this enables GX to be able to produce useful turbulence simulations in minutes on one (or a few) GPUs and higher fidelity results in a few hours using several GPUs. GX is open-source software that is ready for fusion reactor design studies.

Scaling effects on peak wind load estimation for low-rise buildings: An experimental and analytical study

Though scaling effects on estimation of peak wind loads are extensively documented in the literature, there is a lack of systematic comparison of such scaling effects across different model scales tested in wind tunnels. Moreover, the limited studies on large-scale physical models accepted the inadequacy of simulating the large turbulent eddies rather than addressing the missing low-frequency turbulence simulation inherent in such large-scale testing. This study provides an in-depth comparison of estimates of peak wind loads obtained using a range of experimental scaled models (1:100 and 1:6 model scales) of the Wind Engineering Research Field Laboratory (WERFL) building while applying a Partial Turbulence Simulation (PTS) methodology to incorporate the effects of turbulence. Large-scale wind tunnel testing of structures provides the advantage of achieving an improved Reynolds number (Re) similarity, more accurate geometric similarity, and enhanced resolution of flow details such as corner vortices, than is possible with the use of smaller model scales. However, as the model scale increases, achieving turbulence similarity becomes challenging due to limitations in simulating the low-frequency turbulent eddies in the wind tunnel. The PTS method has been used in the recent past to account for the low-frequency turbulence effects in the peak wind load estimation. The method is referred to as 1DPTS when considering longitudinal turbulence components only and 2DPTS when considering both longitudinal and lateral turbulence components in the analysis. The computationally intensive 2DPTS can be further simplified by using a weighted average method as described in this paper as “weighted average PTS.” The current study explores the effect of scaling on peak wind load estimation by using the 1DPTS, 2DPTS, and weighted average PTS methods. Results from the multi-scale experimental tests demonstrate that using larger model scales and compensating for the low-frequency turbulence deficit in the post-test analysis significantly improve the agreement with the prototype data owing to the simulation of a higher Reynolds number. Furthermore, comparing the results of the proposed weighted average method with full-scale data reveals its potential as a substitute for the original 2DPTS method, offering enhanced accuracy, particularly at the roof corner for oblique wind directions. While the effects of Re are well known, the findings of this study explore its impact in conjunction with the application of the PTS methods on peak Cp estimation across five different model scales with Re ranging from 3.65 × 104 to 2.43 × 106, the latter being closest to the full-scale (field) Re. The findings provide new insights into how large-scale physical model testing in high Re flows, supported by analytical PTS-based compensation, can enhance the accuracy of peak wind load estimations for critical scenarios including cornering winds that generate conical vortices.

Simulating low-frequency wind fluctuations

Abstract. Large-scale flow structures are vital in influencing the dynamic response of floating wind turbines and wake meandering behind large offshore wind turbines. It is imperative that we develop an inflow wind turbulence model capable of replicating the large-scale and low-frequency wind fluctuations occurring in the marine atmosphere since the current turbulence models do not account well for this phenomenon. Here, we present a method to simulate low-frequency wind fluctuations. This method employs the two-dimensional (2D) spectral tensor for low-frequency, anisotropic wind fluctuations presented by Syed and Mann (2024) to generate stochastic wind fields. The simulation method generates large-scale 2D spatial wind fields for the longitudinal u and lateral v wind components, which can be converted into a frequency domain using Taylor's frozen turbulence hypothesis. The low-frequency wind turbulence is assumed to be independent of the high-frequency turbulence; thus, a broad spectral representation can be obtained just by superposing the two turbulent wind fields. The method is tested by comparing the simulated and theoretical spectra and co-coherences of the combined low- and high-frequency fluctuations. Furthermore, the low-frequency wind fluctuations can also be subjected to anisotropy. The resulting wind fields from this method can be used to analyze the impact of low-frequency wind fluctuations on wind turbine loads and dynamic response and to study the wake meandering behind large offshore wind farms.

Impact of low-frequency fluctuations on loads of a fixed-bottom offshore reference wind turbine

Marine atmospheric turbulence is predominantly characterized by large-scale structures associated with low-frequency wind turbulence. However, conventional turbulence models for assessing wind turbine loads often fall short of adequately integrating these low-frequency wind fluctuations. In this study, we used a model for low-frequency wind fluctuations to generate wind fields representative of offshore wind conditions in the North Sea. The IEA 15 MW reference wind turbine was subjected to three distinct incoming wind fields: high-frequency (3D) turbulence, low-frequency (2D) turbulence combined with high-frequency (3D) turbulence, and 3D turbulence scaled by target or measured standard deviation of wind components. We found that increased damage equivalent loads by incorporating the low-frequency wind fields are only significant for the tower base fore-aft and blade root fore-aft moments. The impact of low-frequency wind turbulence on the damage equivalent loads was more pronounced for below-rated wind speeds. The scaled 3D turbulence yielded the highest lifetime damage equivalent loads, i.e., in the range of 8-18% more than the unscaled 3D turbulence and combined 2D +3D turbulence. This method leads to an overestimation of loads and, hence, more expensive turbines. Incorporating 2D+3D turbulence in wind fields resulted in a 3.8% increase in lifetime damage equivalent loads for the tower base fore-aft and blade root flapwise moments compared to unscaled 3D turbulence. These findings underscore the importance of considering low-frequency wind fluctuations in the turbine design process, especially for a more accurate estimation of loads.

A Tempered Fractional Kinetic Transport Theory for Energetic Particle Interaction with Quasi-two-dimensional Turbulence in the Large-scale Solar Wind

Observational evidence is accumulating that turbulence in the solar wind is intermittent (non-Gaussian) because of the strong presence of a quasi-two-dimensional (quasi-2D), low-frequency turbulence component containing nonpropagating, closed, small-scale magnetic flux ropes with open meandering field lines in between. le Roux & Zank showed how one can derive fractional focused and Parker-type transport equations that model large-scale anomalous transport in the solar wind as the outcome of energetic particle interaction with quasi-2D turbulence. In this follow-up paper this theory is developed further to address certain limitations. (i) The second moment of the Lévy probability distribution function (PDF) specified in the theory for the particle step size is infinite, indicating unphysical transport. (ii) The expected transition of energetic particle transport from anomalous to normal diffusion beyond a certain critical transport distance was not included. (iii) The competition between anomalous diffusion and advection is not properly sustained at late times. Shortcomings (i) and (ii) are addressed by introducing an exponentially truncated Lévy PDF for the energetic particle step size in the theory, resulting in revised tempered fractional focused and Parker-type transport equations featuring tempered fractional derivatives that enable modeling of tempered Lévy flights. Furthermore, these equations are cast in a tempered fractional telegrapher form to investigate whether the fractional wave equation part of the equation can restore causality in unscattered particle transport during early times and in Lévy flights during intermediate times (Lévy walks). They are also transformed into a tempered fractional Fokker–Planck form to overcome limitation (iii).

Characterization of SOL profiles and turbulence in ICRF-heated plasmas in EAST

Scrape-off layer (SOL) profiles and turbulence in ion cyclotron range of frequency (ICRF)-heated plasmas are investigated by the reciprocating probe diagnostic system (FRPs) and gas puff imaging (GPI) diagnostic in EAST. A radio-frequency (RF) sheath potential reaching up to 100 V is identified proximate to the ICRF antennas. Notably, the amplitude of this RF sheath potential escalates in response to rising ICRF power and inversely with plasma density. When a RF sheath is present in the far SOL, a pronounced density ‘shoulder’ forms in front of the ICRF antennas, while the ‘shoulder’ fade away as the antenna and associated RF sheath shift outwards. A strong E r shear is revealed by measurements from both FRPs and GPI. Analysis of the poloidal wave number-frequency spectrum reveals suppression of high-frequency turbulence in the far SOL due to the RF sheath. This effect is manifested in the reduced autocorrelation time τ c and reduced average blob size δ blob of the SOL plasma. Intriguingly, the poloidal propagation direction of the low-frequency turbulence reverses from the electron to the ion diamagnetic drift direction at the RF sheath location. A surge of tungsten impurity is potentially attributed to the heightened interaction between the SOL plasmas and the wall material. Shifting the ICRF antennas outward, to alleviate heat spots, results in the relocation of the RF sheath to the shaded region of the main limiter. This shift amplifies the radial velocity of blobs in the far SOL and concurrently diminishes the SOL density when compared to conditions without ICRF injection. The properties of ion saturation current fluctuations are consistent with the stochastic model predictions.

Review of recent analytical advances in the spectroscopy of hydrogenic lines in plasmas

Abstract Broadening of hydrogenic spectral lines is an important tool in spectroscopic diagnostics of various laboratory and astrophysical plasmas. We review recent analytical advances in three areas. First, we review the analytical solution for the splitting of hydrogenic lines under the combination of a circularly polarized electromagnetic wave with a strong magnetic field. Practical applications of this solution relate to the spectroscopic diagnostic of the electron cyclotron waves and to the relativistic laser–plasma interactions. Second, we review analytical results concerning the Stark–Zeeman broadening of the Lyman-alpha (Ly-alpha) line in plasmas. These results allow for the Stark width of the Ly-alpha π-component to be used for the experimental determination of the ion density or of the root-mean-square field of a low-frequency electrostatic plasma turbulence in the situation where the Zeeman effect dominates over the Stark effects. Third, we review recent analytical advances in the area of the intra-Stark spectroscopy: three different new methods, based on the emergent phenomenon of the Langmuir-wave-caused structures (“L-dips”) in the line profiles, for measuring super-strong magnetic fields of the GigaGauss range developing during relativistic laser–plasma interactions. We also review the rich physics behind the L-dips phenomenon – because there was a confusion in the literature in this regard.

Electrostatic Wave Decay in the Randomly Inhomogeneous Solar Wind

Despite a few space observations where Langmuir and ion acoustic waves are expected to participate in the mechanism of electrostatic decay, this is to date believed to be the main and fastest nonlinear wave process in the solar wind. However, in such a plasma where random density fluctuations are ubiquitous, the question of whether nonlinear wave processes play a significant role in Langmuir wave turbulence generated by electron beams associated with type III solar radio bursts remains still open. This paper provides several answers by studying, owing to two-dimensional challenging particle-in-cell simulations, the dynamics and the properties of the ion acoustic waves excited by such Langmuir wave turbulence and the role they play in the electrostatic decay. The impact on this process of plasma background density fluctuations and electron-to-ion temperature ratio is studied. Moreover, it is shown that, for a typical solar wind plasma with an average level of density fluctuations of a few percent of the ambient density and a temperature ratio of the order of 1, nonlinear induced scattering off ions occurs, with small intensity low-frequency quasi-modes and only in localized plasma regions where density is depleted or weakly perturbed by low-frequency turbulence.

Experimental and numerical investigation of ICRF induced low-frequency turbulence reduction across the scrape-off layer on the EAST tokamak

In magnetic confinement fusion devices, the plasma particle and energy transport depend on the turbulence transport. Ion cyclotron range of frequency (ICRF) wave heating can interact with the turbulence in the plasma edge and change the turbulence transport. To understand their interaction/correlation, the radial modification of turbulence by ICRF in the scrape-off layer (SOL) was investigated using midplane reciprocating Langmuir probe, reflectometry, Doppler reflectometry, and Divertor probes on the EAST tokamak. We showed a first demonstration that this interaction occurs at all radii and affects the turbulence across the whole SOL. It was observed that ICRF attenuates the large-scale turbulence structures (usually in the form of blobs) by breaking them into smaller ones, leading to a suppression of low-frequency turbulence in the whole SOL. Moreover, this turbulence reduction is accompanied by an increase in the high-frequency turbulence fluctuations and an increase in the poloidal velocity in the SOL. This poloidal velocity is generated by the radial electric field during ICRF. Following this, BOUT++ simulations were conducted, and the simulations results are in line with the experimental results. They show that the RF-sheath induced radial electric field can explain the increase in high-frequency fluctuations and suppression of turbulence in the SOL.

The temporal and latitudinal dependences of turbulence driven by pickup ions in the outer heliosphere

The distribution of turbulence in the heliosphere remains a mystery, due to the complexity in not only modeling the turbulence transport equations but also identifying the drivers of turbulence that vary with time and spatial location. Beyond the ionization cavity (a few astronomical units (AU) from the Sun), the turbulence is driven predominantly by freshly created pickup ions (PUIs), in contrast to the driving by stream shear and compression. Understanding the source characteristics is necessary to refine turbulence transport models and interpret measurements of turbulence and solar wind temperature in the outer heliosphere. Using a recent latitude-dependent solar wind speed model and the ionization rate of neutral interstellar hydrogen (H), we investigate the temporal and spatial variation in the strength of low-frequency turbulence driven by PUIs from 1998 to 2020. We find that the driving rate is stronger during periods of high solar activity and at lower latitudes in the outer heliosphere. The driving rates for parallel and anti-parallel propagating (relative to the background magnetic field) slab turbulence have different spatial and latitude dependences. The calculated generation rate of turbulence by PUIs is an essential ingredient to investigate the latitude dependence of turbulence in the outer heliosphere, which is important to understand the heating of the distant solar wind and the modulation of cosmic rays.

Low-frequency turbulence suppression by amplification of synchronized zonal flow with energetic particle driven modes

We investigate the suppression of the turbulent transport associated to the emergence of spontaneous internal transport barriers, due to the combined collective effects played by trapped electrons and energetic passing ions. Numerical experiments performed with a ‘particle mode’ model based on a double gyro-average over the fast cyclotron phase and over the bounce (or transit) phases are used to show the role played by energetic particles in the suppression of the ion-temperature-gradient driven turbulence. We show this occur via phase locking in a Kuramoto-type synchronization process.

Observation of turbulence energy transfer in a cylindrical laboratory plasma device

We report the experimental results on the turbulence energy transfer in a cylindrical laboratory plasma based on the data obtained by a set of quadruple Langmuir probe on Zheda plasma experiment device. The turbulence energy transfer is directly embodied in the alternating change in the fluctuation amplitudes between the low frequency turbulence at ∼0.1–0.2 kHz and the drift wave (DW) turbulence at ∼1–2 kHz. The estimation of the radial electric field and the bispectral analysis of the experiments suggest that the DW turbulence gains the energy from the low frequency turbulence with the magnetic field increase. The energy transport due to the interaction between the low frequency turbulence and the DW turbulence is a possible reason to drive the turbulence energy transfer associated with the magnetic field increase in the laboratory plasma.

A novel Doppler backscattering (DBS) system to simultaneously measure radio frequency plasma fluctuations and low frequency turbulence.

A novel quadrature Doppler Backscattering (DBS) system has been developed and optimized for the E-band (60-90GHz) frequency range using either O-mode or X-mode polarization in DIII-D plasmas. In general, DBS measures the amplitude of density fluctuations and their velocity in the lab frame. The system can simultaneously monitor both low-frequency turbulence (f < 10MHz) and radiofrequency plasma density fluctuations over a selectable frequency range (20-500MHz). Detection of high-frequency fluctuations has been demonstrated for low harmonics of the ion cyclotron frequency (e.g., 2fci ∼ 23MHz) and externally driven high-frequency helicon waves (f = 476MHz) using an adjustable frequency down conversion system. Importantly, this extends the application of DBS to a high-frequency spectral domain while maintaining important turbulence and flow measurement capabilities. This unique system has low phase noise, good temporal resolution (sub-millisecond), and excellent wavenumber coverage (kθ ∼ 1-20cm-1 and kr ≲ 30cm-1). As a demonstration, localized internal DIII-D plasma measurements are presented from turbulence (f ≤ 5MHz), Alfvenic waves (f ∼ 6.5MHz), ion cyclotron waves (f ≥ 20MHz), as well as fluctuations around 476MHz driven by an external high-power 476MHz helicon wave antenna. In the future, helicon measurements will be used to validate GENRAY and AORSA modeling tools for prediction of helicon wave propagation, absorption, and current drive location for the newly installed helicon current drive system on DIII-D.

Water surface response to turbulent flow over a backward-facing step

The water surface response to subcritical turbulent flow over a backward-facing step (BFS) is studied via high-resolution large-eddy simulation (LES). The LES method is validated first using data of previously reported experiments. The LES-predicted water surface is decomposed into different types of gravity waves as well as turbulence-driven forced waves. Analysis of the LES data reveals the interplay between low-frequency large-scale turbulence structures, which are the result of flow separation from the step and reattachment behind the step, and the dynamics of the water surface. The water surface deformation is mainly the result of freely propagating gravity waves and forced waves, owing to turbulence in the form of rollers and/or hairpin vortices. Gravity waves with zero group velocity define the characteristic spatial and temporal scales of the surface deformations at higher frequencies, while large eddies determine their low-frequency modulation. These deformations are mainly confined in lateral bands that propagate downstream following the advection of the near-surface streamwise vortices (rollers) that are shed from the step. Steeper surface waves are observed in regions of negative perturbation velocity gradient and down-welling, downstream of the larger rollers, and are associated with thin isolated regions of high vorticity near the surface. The investigation of such a complex flow has shown that the decomposition of the water surface fluctuations into its different physical components may be used to identify the dynamics of the underlying flow structure.

Slowly drifting radio fibres

ABSTRACT The fine structure in the continuum radiation of type IV solar radio bursts is very rich in various structures (zebra structure, fibres, pulsations, spikes, etc.). So far, however, no attention has been paid to the isolated fibres that occasionally appear in the metre and decimetre ranges. Here we give and discuss examples of the dynamic spectra of such bursts obtained many years ago (in the metre waveband from 1969) as well in recent years (in the decimetre and microwave wavebands from 2003–2013). Isolated fibres are observed mostly in the decimetre range (although there are examples in both the metre and microwave ranges), and they reveal a number of features of classical fibre bursts. As a generation mechanism for such fibres, the process of interaction of whistlers with Langmuir plasmons was suggested. An analysis of conditions for the realization of this process in solar magnetic arch structures and its efficiency was carried out. Estimates of the intensity of low-frequency turbulence (whistlers) and magnetic field strength in the solar corona were obtained using the data of radio fibres.

Estimation of Turbulent Proton and Electron Heating Rates via Landau Damping Constrained by Parker Solar Probe Observations

The heating of ions and electrons due to turbulent dissipation plays a crucial role in the thermodynamics of the solar wind and other plasma environments. Using magnetic field and thermal plasma observations from the first two perihelia of the Parker Solar Probe, we model the relative heating rates as a function of the radial distance, magnetic spectra, and plasma conditions, enabling us to better characterize the thermodynamics of the inner heliosphere. We employ the Howes et al. steady-state cascade model, which considers the behavior of turbulent, low-frequency, wavevector-anisotropic, critically balanced Alfvénic fluctuations that dissipate via Landau damping to determine proton-to-electron heating rates Q p /Q e . We distinguish ion cyclotron frequency circularly polarized waves from low-frequency turbulence and constrain the cascade model using spectra constructed from the latter. We find that the model accurately describes the observed energy spectrum from over 39.4% of the intervals from Encounters 1 and 2, indicating the possibility for Landau damping to heat the young solar wind. The ability of the model to describe the observed turbulent spectra increases with the ratio of thermal-to-magnetic pressure, β p , indicating that the model contains the necessary physics at higher β p . We estimate high magnitudes for the Kolmogorov constant which is inversely proportional to the nonlinear energy cascade rate. We verify the expected strong dependency of Q p /Q e on β p and the consistency of the critical balance assumption.

Edge turbulence transport during ELM suppression with n = 4 resonant magnetic perturbation on EAST

The edge turbulence characteristics and the induced radial transport have been investigated in edge localized mode (ELM) suppression by using the 4 resonant magnetic perturbation coils on EAST, with 3.6 and the electron collisionality 0.5. During ELM suppression, the edge turbulence is enhanced dramatically, as measured by the reciprocating probe and the poloidal correlation reflectometry. In the near SOL, the low frequency turbulence (<30 kHz) has a large fluctuation level and propagates along the ion diamagnetic drift direction with a speed of 0.35 km s−1 in the plasma frame; an electromagnetic mode around 120 kHz with a small (∼0.15 cm−1) appears when the ELM is suppressed; weak broadband turbulence between 40–120 kHz propagates in the electron diamagnetic drift direction with a velocity of 3.4 km s−1 in the plasma frame. During the ELM suppression, the radial turbulent particle flux, calculated in both the time and frequency domains, is much higher (can be up to five times) than that in the inter-ELM phase. Furthermore, the low frequency turbulence (<30 kHz) dominates the cross-field particle transport. The 120 kHz electromagnetic mode also contributes to outward particle flux, which is relatively small. A set of CGYRO simulations are performed to illustrate the nature of the 120 kHz electromagnetic mode and the low frequency turbulence, suggesting that the former is the micro-tearing mode and the latter is the ion temperature gradient mode. The bispectral analysis suggests a strong three-wave coupling between the low frequency and high frequency turbulence (>250 kHz), which could be beneficial to form the observed turbulent transport. The estimated upstream cross-field particle flux is consistent with the total particle flux deposited on divertor targets, demonstrating that the enhanced radial turbulent particle transport is an important mechanism for particle exhaust in ELM suppression.

Analysis of Plasma Emission Experiments and ‘Dips’

It has been claimed that recent experiments using high-powered lasers have identified dip structures in spectral line profiles in plasmas and that these were successfully used to reliably infer both plasma parameters and information on high and low-frequency turbulence. The analysis of those experiments relies on a flawed theory. In the present work, we computed the line spectra correctly using the parameters inferred in the original papers. The results bear little resemblance to the experimental profiles. The only way to reconcile the parameters deduced in these experiments is to invoke very broadband turbulence, with the relevant distribution functions that are neither known nor measured playing critical roles. Furthermore, the dip positions are shown to be sensitive to details such as field directionality and variations in the frequency and field amplitude. Hence, dips cannot be used to reliably diagnose such plasmas.

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.