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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Turbulent impurity transport simulations in Wendelstein 7-X plasmas

A study of turbulent impurity transport by means of quasilinear and nonlinear gyrokinetic simulations is presented for Wendelstein 7-X (W7-X). The calculations have been carried out with the recently developed gyrokinetic code stella. Different impurity species are considered in the presence of various types of background instabilities: ion temperature gradient (ITG), trapped electron mode (TEM) and electron temperature gradient (ETG) modes for the quasilinear part of the work; ITG and TEM for the nonlinear results. While the quasilinear approach allows one to draw qualitative conclusions about the sign or relative importance of the various contributions to the flux, the nonlinear simulations quantitatively determine the size of the turbulent flux and check the extent to which the quasilinear conclusions hold. Although the bulk of the nonlinear simulations are performed at trace impurity concentration, nonlinear simulations are also carried out at realistic effective charge values, in order to know to what degree the conclusions based on the simulations performed for trace impurities can be extrapolated to realistic impurity concentrations. The presented results conclude that the turbulent radial impurity transport in W7-X is mainly dominated by ordinary diffusion, which is close to that measured during the recent W7-X experimental campaigns. Finally, it is also confirmed that thermodiffusion adds a weak inward flux contribution and that, in the absence of impurity temperature and density gradients, ITG- and TEM-driven turbulence push the impurities inwards and outwards, respectively.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Toward the core-edge coupling of delta-f and total-f gyrokinetic models

The coupling of core reduced delta-f and edge total-f gyrokinetic models could enable a significant speed-up of the whole device modeling simulations. It is thus interesting to compare these models in the core where they will be coupled. The main difference between these models is the presence of the zeroth order term on the right-hand side of the total-f gyrokinetic equation. This term is responsible for driving a radial electric field that is also associated with Geodesic acoustic mode-like oscillations. To investigate the coupling between these models, the subsequent large-scale gyrokinetic 3D turbulence simulations have been performed starting from an already saturated gyrokinetic axisymmetric equilibria (collisions are not included). This work has also been extended to couple different axisymmetric and turbulent models available in XGC. It is shown that the radial electric field and its drive have to be taken care of consistently while coupling different models together.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Characterizing Turbulence at a Forest Edge: Comparing Sub-Filter Scale Turbulence Models in Simulations of Flow over a Canopy

In wildfires, atmospheric turbulence plays a major role in the transfer of turbulent kinetic energy. Understanding how turbulence feeds back into a dynamical system is important, down to the varying small scales of fuel structures (i.e. pine needles, grass). Large eddy simulations (LES) are a common way of numerically representing turbulence. The Smagorinsky model (1963) serves as one of the most studied sub-grid scale representations in LES. In this investigation, the Smagorinsky model was implemented in HIGRAD/FIRETEC, LANL’s coupled fire-atmosphere model. This study was motivated by the need to quantitatively investigate the vorticity budget equation in HIGRAD/FIRETEC. The Smagorinsky turbulent kinetic energy (TKE) was compared to FIRETEC’s 1.5-order TKE eddy-viscosity subgrid-scale model, known as the Linn turbulence model. This was done in simulations of flow over flat terrain with a homogeneous, cuboidal canopy in the center of the domain. Examinations of the modeled vertical TKE profile and turbulent statistics at the leading edge, and throughout the canopy, show that the Smagorinsky model provides comparable results to that of the original closure model posed in FIRETEC.

58 GEOSCIENCES↗
DOE OSTI2023

High-resolution simulations of a turbulent boundary layer impacting two obstacles in tandem

High-fidelity large-eddy simulations of the flow around two rectangular obstacles are carried out at a Reynolds number of 10 000 based on the freestream velocity and the obstacle height. The incoming flow is a developed turbulent boundary layer. Mean-velocity components, turbulence fluctuations, and the terms of the turbulent-kinetic-energy budget are analyzed for three flow regimes: skimming flow, wake interference, and isolated roughness. Three regions are identified where the flow undergoes the most significant changes: the first obstacle’s wake, the region in front of the second obstacle, and the region around the second obstacle. In the skimming-flow case, turbulence activity in the cavity between the obstacles is limited and mainly occurs in a small region in front of the second obstacle. In the wake-interference case, there is a strong interaction between the freestream flow that penetrates the cavity and the wake of the first obstacle. Furthermore, this interaction results in more intense turbulent fluctuations between the obstacles. In the isolated-roughness case, the wake of the first obstacle is in good agreement with that of an isolated obstacle. Separation bubbles with strong turbulent fluctuations appear around the second obstacle.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Direct numerical simulations of activation and deactivation in turbulent atmospheric clouds

Significant knowledge gaps remain in our understanding of turbulence–cloud–aerosol interactions in the Earth's atmosphere, and direct numerical simulation (DNS) has increasingly become an indispensable tool to fill such critical knowledge gaps. Here, this study is an extension of our previous DNS model [Gao et al., J. Geophys. Res.: Atmos., 123(4), 2194–2214 (2018)], with a focus on the activation of aerosol particles into cloud droplets and deactivation of cloud droplets into aerosol particles in a microscale cloud environment. The effects of turbulence intensity, particle curvature, and solute, as well as the initial distributions of the aerosol particles (monodisperse or polydisperse) are investigated. The governing equations for the flow of air, temperature, and water vapor mixing ratio are solved numerically in the Eulerian fashion, assuming homogeneous and isotropic turbulence. The dynamics of the aerosol and cloud particles are calculated with the Lagrangian particle tracking method. The results show that the deviations of the thermodynamic variables from their respective means are significantly reduced, the activation process appears to be delayed, and the deactivation process occurs more rapidly, as the turbulence intensity is increased. The inclusion of particle curvature and solute effects, as well as polydispersity, tends to retard the activation of aerosols into cloud droplets. It is also observed that fluctuations in supersaturation broaden the spread of particle radii, and the broadening is followed by a narrowing as turbulent homogenization reduces thermodynamic fluctuations over time.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Impact of pedestal density gradient and collisionality on ELM dynamics

BOUT++ turbulence simulations are conducted to capture the underlying physics of small ELM characteristics achieved by increasing separatrix density via controlling strike points from vertical to horizontal divertor plates for three EAST discharges. BOUT++ linear simulations show that the most unstable modes change from high-n ideal ballooning modes to intermediate-n peeling–ballooning modes and eventually to peeling–ballooning stable plasmas in the pedestal. Nonlinear simulations show that the fluctuation is saturated at a high level for the lowest separatrix density. The ELM size decreases with increasing separatrix density, until the fraction of this energy lost during the ELM crash becomes less than 1% of the pedestal stored energy, leading to small ELMs. Simulations indicate that small ELMs can be triggered either by the marginally peeling–ballooning instability near the peak pressure gradient position inside the pedestal or by a local instability in the pedestal foot with a larger separatrix density gradient. The pedestal collisionality scan for type-I ELMs with steep pedestal density gradient shows that both linear growth rate and ELM size decrease with increasing collisionality. On the contrary, the pedestal collisionality and pedestal density width scan with a weak pedestal density gradient indicate small ELMs can either be triggered by a high-n ballooning mode or by a low-n peeling mode in a low collisionality region 0.04–0.1. We report the simulations indicate the weaker the linear unstable modes near marginal stability with small linear growth rate, the lower nonlinearly saturated fluctuation intensity and the smaller turbulence spreading from the linear unstable zone to stable zone in the nonlinear saturation phase, leading to small ELMs.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Spatiotemporal Energy Cascade in Three-Dimensional Magnetohydrodynamic Turbulence

We present a new scale decomposition method to investigate turbulence in wavenumber-frequency space. Using 3D magnetohydrodynamic turbulence simulations, we show that magnetic fluctuations with time scales longer than the nonlinear time exhibit an inverse cascade toward even smaller frequencies. Low frequency magnetic fluctuations support turbulence, acting as an energy reservoir that is converted into plasma kinetic energy, the latter cascading toward large wavenumbers and frequencies, where it is dissipated. Our results shed new light on the spatiotemporal properties of turbulence, potentially explaining the origin and role of low frequency turbulent fluctuations in the solar wind.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Characteristics of grassy ELMs and their impact on the divertor heat flux width

We report BOUT++ turbulence simulations are conducted for a 60 s steady-state long pulse high β p EAST grassy ELM discharge. BOUT++ linear simulations show that the unstable mode spectrum covers a range of toroidal mode numbers from low-n (n = 10–15) peeling–ballooning modes (P–B) to high-n (n = 40–80) drift-Alfvén instabilities. Nonlinear simulations show that the ELM crash is triggered by low-n peeling modes and fluctuation is generated at the peak pressure gradient position and radially spread outward into the scrape-off-layer, even though the drift-Alfvén instabilities dominate the linear growth phase. However, drift-Alfvén turbulence delays the onset of the grassy ELM and enhances the energy loss with the fluctuation extending to pedestal top region. Simulations further show that if the peeling drive is removed, the fluctuation amplitude drops by an order of magnitude and the ELM crashes disappear. The divertor heat flux width is ~2 times larger than the estimates based on the HD model and the Eich's ITPA multi-tokamak scaling (or empirical Eich scaling) due to the strong radial turbulence transport.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Low-Reynolds-number oscillating boundary layers on adiabatic slopes

We investigate the instabilities and transition mechanisms of Boussinesq stratified boundary layers on sloping boundaries when subjected to oscillatory body forcing parallel to the slope. We examine idealized forms of boundary layers on hydraulically smooth abyssal slopes in tranquil mid- to low-latitude regions, where low-wavenumber internal tides gently heave isopycnals up and down adiabatic slopes in the absence of mean flows, high-wavenumber internal tides, shelf breaks, resonant tide–bathymetry interactions (critical slopes) and other phenomena associated with turbulence ‘hot spots’. In non-rotating low-Reynolds-number flow, increased stratification on the downslope phase has a relaminarizing effect, while on the upslope phase we find transition-to-turbulence pathways arise from shear production triggered by gravitational instabilities. When rotation is significant (low slope Burger numbers) we find that boundary layer turbulence is sustained throughout the oscillation period, resembling stratified Stokes–Ekman layer turbulence. Simulation results suggest that oscillating boundary layers on smooth slopes at low Reynolds number ($Re\leqslant 840$), unity Prandtl number and slope Burger numbers greater than unity do not cause significant irreversible turbulent buoyancy flux (mixing), and that flat-bottom dissipation rate models derived from the tide amplitude are accurate within an order of magnitude.

42 ENGINEERING↗
DOE OSTI2024

Accuracy of kinetic equilibrium reconstruction of NSTX and NSTX-U plasmas and its impact on the transport and stability analysis

An accurate magnetohydrodynamic (MHD) equilibrium reconstruction is an essential starting point for stability and transport plasma analysis. Herein this work describes an approach for obtaining kinetic equilibrium reconstructions using the OMFIT framework, which has been applied for the first time to spherical tokamak data from NSTX and NSTX-U. The EFIT equilibrium solver is integrated with experimental data analysis procedures and subsequent TRANSP transport simulations to enhance the accuracy of the reconstruction, in particular, at the edge region, by adding constraints on the total pressure and current density profiles, based on the transport code solution. The accuracy of the equilibrium reconstruction depends on the uncertainty and number of constraints, as well as the choice of basis functions to represent the pressure and current density profiles. Improved fidelity of the equilibrium reconstruction is demonstrated by reducing the variability of the magnetic axis and boundary locations from several centimeters, for reconstructions based on magnetic and experimental pressure constraints, to only several millimeters, for kinetic reconstructions based on transport code constraints, when different representations of basis functions were tested. The variability of the safety factor on axis was reduced ten times in the same sensitivity study. The accuracy of the equilibrium reconstruction and subsequent mapping of the experimental kinetic profile data have a significant impact on the trapped gyro Landau fluid and linear CGYRO turbulence simulations, which predict different spectra of unstable modes and turbulent fluxes for cases with different numbers of constraints in the equilibrium reconstruction. Conversely, the stability analysis performed using the GATO code shows plasmas that are stable to n = 1 MHD modes in both equilibria using magnetic and experimental pressure constraints as well as the transport code constrained equilibrium. However, a scan of parameters away from these conditions shows considerable deviation in the threshold of unstable modes between these reconstructions. Therefore, for reliable plasma analysis and use in turbulence and stability calculations, a high-fidelity equilibrium reconstruction with accurate kinetic constraints based on transport code solutions is necessary.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Three-Dimensional Aerodynamics and Vortex-Shedding Characteristics of Wind Turbine Airfoils over 360-Degree Angles of Attack

In this work, we present the first three-dimensional (3D) computational investigation of wind turbine airfoils over 360° angles of attack to predict unsteady aerodynamic loads and vortex-shedding characteristics. To this end, static–airfoil simulations are performed for the FFA-W3 airfoil family at a Reynolds number of 107 with the Improved Delayed Detached Eddy Simulation turbulence model. Aerodynamic forces reveal that the onset of boundary-layer instabilities and flow separation does not necessarily coincide with the onset of stall. In addition, a comparison with two-dimensional simulation data and flat plate theory extension of airfoil polars, suggest that, in the deep stall regime, 3D effects remain critical for predicting both the unsteady loads and the vortex-shedding dynamics. For all airfoils, the vortex-shedding frequencies are found to be inversely proportional to the wake width. In the case of slender airfoils, the frequencies are nearly independent of the airfoil thickness, and their corresponding Strouhal number St is approximately 0.15. Based on the calculated St, the potential for shedding frequencies to coincide with the natural frequencies of the International Energy Agency 15 MW reference wind turbine blades is investigated. The analysis shows that vortex-induced vibrations occur primarily at angles of attack of around ±90° for all airfoils.

17 WIND ENERGY↗
DOE OSTI2024

Direct Numerical Simulation of Involute Channel Turbulence

A direct numerical simulation (DNS) study was performed on turbulent flow in the high flux isotope reactor involute channel geometry to develop a numerical database and determine the differences compared with a flat parallel channel. The varying channel curvature along the walls was studied for differences in mean profiles. Parameters of interest include streamwise velocity, turbulent kinetic energy (TKE), and turbulence dissipation rate, as well as Reynolds stresses and turbulence transport terms. Profile sampling was carried out at 10 locations along the span of the involute. Additional DNS studies were performed on smaller domains of comparable curvature to the involute domain: a high curvature channel (high circular), a low curvature channel (low circular), and a flat channel (flat). Here, each of these four cases was compared against each other and to other DNS studies performed on parallel flows. The results indicate that the bulk involute channel flow does not differ significantly from a flat parallel channel flow and that the curvature of the walls does not significantly alter the mean flow parameters. However, the regions of the involute channel near the side walls exhibit relatively low magnitude twin recirculation structures driven toward the side walls from the centerline of the channel, which warrants further study.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2022

Aircraft Observations of Turbulence in Cloudy and Cloud-Free Boundary Layers Over the Western North Atlantic Ocean From ACTIVATE and Implications for the Earth System Model Evaluation and Development

This study examines boundary layer turbulence derived from high temporal resolution meteorological measurements from 40 research flights over the western North Atlantic Ocean during the 2020 deployments of ACTIVATE. Frequency distributions of various turbulent quantities reveal stronger turbulence during the winter deployment than in summer and for cloud‐topped than in cloud‐free boundary layers during the summer deployment. Maximum turbulence kinetic energy (TKE) is most often within cloud from observations in winter and summer, whereas it is mostly below cloud in both seasons by a global model turbulence parameterization. Further, bivariate frequency distributions are consistent with the bivariate Gaussian probability distribution functions assumed for the closure of higher‐order turbulence/shallow convection parameterizations used by some global models. Turbulence simulated by the Community Atmosphere Model version 6 and the Energy Exascale Earth System Model Atmosphere Model version 2 using such parameterizations is not as strong as observed, with more TKE going into vertical wind perturbations rather than into zonal wind perturbations as observed, suggesting that the treatment of turbulence in Earth system models still needs to be further improved.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

High Fidelity CFD Simulations Supporting the KP-FHR

Kairos Power, LLC, is developing its version of the Fluoride-cooled High-temperature Reactor, the KP-FHR. The design uses a pebble bed core with fluoride salt as a coolant. The pebbles used in the KP-FHR have a diameter of 4 cm, with a shell fuel region where TRISO particles are embedded. A Pebble bed core design is adopted by several Gen IV reactors, They boast many benefits, such as fuel integrity, highly efficient heat transfer, and passive safety. However, it is challenging to accurately predict temperature and flow inside a pebble bed. Traditional approaches use the porous media model, which regards the pebble bed as a continuous medium, but with different temperature fields representing different levels, such as the fluid temperature, pebble surface temperature, and pebble center temperature. Empirical heat transfer correlations are adopted to calculate the heat transfer coefficient between different phases. However, empirical correlations are usually validated with experimental data, which usually lacks detail inside the pebble bed. The available experimental data is also generally at a high Reynolds number, which falls outside of the conditions of KP-FHR. Explicit computational fluid dynamics (CFD) simulations of randomly packed pebble beds have only become feasible recently. This is thanks to the rapid development of computational power and scalable algorithms. In this work, we used the Spectral Element Method (SEM) CFD code NekRS to simulate the randomly packed pebble bed in a cylindrical container. NekRS, which is the GPU variant of Nek5000, but refactored to utilize the computational power of GPUs using the OCCA library to run on hybrid architecture high performance computing systems. It was initially developed with the libParamunal library, but truncated and tuned for large-scale turbulence simulation. As a result, the SEM reaches higher precision with the same degrees of freedom by using a high-order Lagrange polynomial basis distributed on Gauss-Lobatto-Legendre quadrature inside each element, compared to lower-order methods, such the Finite Volume Method and Finite Element Method. The report is divided into five parts. We start with a general discussion of the pebble bed reactor, along with a specific investigation into the KP-FHR. The second part presents the numerical methodology. In the third part, we study a modular pebble bed with 1741 pebbles in a container of 7 pebble-diameter radius. Beyond LES simulations done by NekRS, we also leveraged the thermal radiation model in OpenFOAM to study heat transfer under no-forced-flow scenarios. Then, in the fourth part we simulated a pebble bed similar to the size of the Hermes Test Reactor. The total number of pebbles is in these simulations is 34,374. The container radius is 14 pebble-diameters. Finally, the report concludes in part five, with a discussion of future work.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2023

Growth or Decay – I: universality of the turbulent dynamo saturation

The turbulent small-scale dynamo (SSD) is likely to be responsible for the magnetisation of the interstellar medium (ISM) that we observe in the Universe today. The SSD efficiently converts kinetic energy E kin into magnetic energy E mag , and is often used to explain how an initially weak magnetic field with E mag $\ll$ E kin is amplified, and then maintained at a level E mag ≲ E kin . Usually, this process is studied by initialising a weak seed magnetic field and letting the turbulence grow it to saturation. However, in this Part I of the Growth or Decay series, using three-dimensional, visco-resistive magnetohydrodynamical turbulence simulations up to magnetic Reynolds numbers of 2000, here we show that the same final state in the integral quantities, energy spectra, and characteristic scales of the magnetic field can also be achieved if initially E mag ~ E kin or even if initially E mag $\gg$ E kin . This suggests that the final saturated state of the turbulent dynamo is set by the turbulence and the material properties of the plasma, independent of the initial structure or amplitude of the magnetic field. We discuss the implications this has for the maintenance of magnetic fields in turbulent plasmas and future studies exploring the dynamo saturation.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

A new synthetic correlation electron cyclotron emission diagnostic for validating nonlinear gyrokinetic simulations of electron temperature turbulence

To validate nonlinear gyrokinetic simulations of electron temperature turbulence, the experimental correlation electron cyclotron emission (CECE) measurements are to be compared using a synthetic CECE diagnostic, which generates modeled CECE measurement quantities by implementing realistic measurement parameters (e.g., spatial and wavenumber resolutions, radial location, etc.) to nonlinear gyrokinetic simulations. In this work, we calculate the radial and vertical spatial and wavenumber transfer functions, which are defined by the electron cyclotron emission emissivity radial profile and vertical probing antenna pattern, respectively. These transfer functions are applied to nonlinear gyrokinetic simulations of electron temperature turbulence using the continuum gyrokinetic code. A simultaneous comparison of the experimental electron temperature turbulence power spectrum and root-mean-square (RMS) level, as well as the radial correlation length with the new synthetic CECE diagnostic at a core location ρ ∼ 0.75 in an L-mode DIII-D tokamak plasma, is presented. Here, the preliminary result shows that the synthetic CECE output underestimates the RMS level by ∼42% and overestimates the radial correlation length by ∼40%.

Cyclotron radiation↗
DOE OSTI2023

Mesh and model requirements for capturing deep-stall aerodynamics in low-Mach-number flows

Here, this work presents a comprehensive computational fluid dynamics investigation of the effects of grid resolution and turbulence-model choice for capturing the unsteady three-dimensional aerodynamic performance of NACA 0012 and 0021 airfoils, with specific focus on the deep-stall regime. At high angles of attack (α), wind turbine blades routinely experience vortex-induced vibrations, which can cause significant structural damages. Accurate predictions of post-stall aerodynamics can identify the frequencies at which such vibrations maybe triggered. In this context, the NACA 0012 airfoil simulations are conducted at a chord-based Reynolds number, Re c =2×10 6 , with the k-ω Shear-Stress Transport Reynolds-Averaged Navier-Stokes (RANS) and Improved Delayed Detached Eddy Simulation (IDDES) hybrid RANS-Large Eddy Simulation turbulence models. The effect of mesh resolution both in the wall-normal and spanwise directions is investigated. Only the IDDES model with a minimum spanwise resolution of 24 cells per chord length correctly predicts the aerodynamic forces. Spectral analysis shows the peak primary shedding frequency at α=30°, which signifies the end of the stall region. In the post-stall regime, both lift and drag frequencies drop asymptotically with increasing α. The Strouhal number, based on normalised chord length, remains nearly constant in this region. Based on this study, NACA 0021 airfoil runs are performed with IDDES for Re c =2.7×10 5 and 2.0×10 6 on the finest wall-normal mesh and three spanwise grids. Simulations conducted on the finer spanwise grids demonstrate grid independence and show good agreement with experiments. The effect of varying Rec on the airfoil frequency statistics is investigated. Additionally, comparison studies are presented to investigate the impact of airfoil thickness on the frequency content at Re c =2.0×10 6 . The results from the study provide guidance on the choice of mesh resolution with the IDDES model to accurately capture aerodynamic quantities for complex industrial applications.

17 WIND ENERGY↗
DOE OSTI2021

A multishock model for the density variance of anisotropic, highly magnetized, supersonic turbulence

ABSTRACT Shocks form the basis of our understanding for the density and velocity statistics of supersonic turbulent flows, such as those found in the cool interstellar medium (ISM). The variance of the density field, $\sigma ^2_{\rho /\rho _0}$, is of particular interest for molecular clouds (MCs), the birthplaces of stars in the Universe. The density variance may be used to infer underlying physical processes in an MC, and parametrizes the star formation (SF) rate of a cloud. However, models for $\sigma ^2_{\rho /\rho _0}$ all share a common feature – the variance is assumed to be isotropic. This assumption does not hold when a trans-/sub-Alfvénic mean magnetic field, ${B}_0$, is present in the cloud, which observations suggest is relevant for some MCs. We develop an anisotropic model for $\sigma _{\rho /\rho _0}^2$, using contributions from hydrodynamical and fast magnetosonic shocks that propagate orthogonal to each other. Our model predicts an upper bound for $\sigma _{\rho /\rho _0}^2$ in the high Mach number $(\mathcal {M})$ limit as small-scale density fluctuations become suppressed by the strong ${B}_0$. The model reduces to the isotropic $\sigma _{\rho /\rho _0}^2\!-\!\mathcal {M}$ relation in the hydrodynamical limit. To validate our model, we calculate $\sigma _{\rho /\rho _0}^2$ from 12 high-resolution, three-dimensional, supersonic, sub-Alfvénic magnetohydrodynamical (MHD) turbulence simulations and find good agreement with our theory. We discuss how the two MHD shocks may be the bimodally oriented overdensities observed in some MCs and the implications for SF theory in the presence of a sub-Alfvénic ${B}_0$. By creating an anisotropic, supersonic density fluctuation model, this study paves the way for SF theory in the highly anisotropic regime of interstellar turbulence.

Beattie, James R.↗