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DOE OSTI2023

Controlling Molecular Structure and Spin with Multiconfigurational Quantum Chemistry (Final Technical Report)

For many first-row transition metal complexes, structure-property relationships can be obtained from high-level molecular geometry optimizations and subsequent electronic structure studies. The project funded under this award utilized newly implemented fully internally contracted (FIC) nuclear gradients for extended multi-state (XMS) complete active space second-order multireference perturbation theory (CASPT2) to explore geometry changes in first-row transition metal coordination complexes. At the start of the project, only one full geometry optimization using FIC-CASPT2 analytical gradients had been reported (J. Chem. Theory Comput., 2016, 12 (8), 3781), and many open-questions regarding the performance and achievable accuracy in applying such computations to larger complexes persisted. Key deliverables in the report include the implementation of the numerical Hessian and subsequent vibrational analysis in the BAGEL program package. This includes both full Hessian vibrational analysis (FHVA) and a partial Hessian vibrational analysis (PHVA). The latter of which allows us to reduce the significant cost of computing the vibrational frequencies in a large molecule by focusing on the modes of highest interest. The gradient code also proved useful in the development of an approach to improve the Hubbard-U correction by removing bias in predicting spin-splitting in Fe(II) complexes via plane-wave density functional theory (DFT). Finally, we showed for three families of complexes (spin-crossover (SCO) complexes, metallocorroles complexes, and those with metal-metal bonds) that CASPT2 can result in good molecular geometries and established best practices in undertaking this work. We are now using this approach in collaborative projects with experimental groups, which would not have been possible at the start of this project. A common theme also arose through this work that static and dynamic correlation must be recovered in a balanced way to yield quantitative results. By systematically varying how both effects were included, we were able to make key chemical insights. This work supported the training of two postdoctoral scholars, one graduate student, and one undergraduate student in applying high-level wavefunction based methods to challenging systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Achieving Higher Order Accuracy in Space in Hydrodynamic Simulations of Self-Gravitating Gas

Modern astrophysical simulation codes employ a variety of numerical algorithms capable of achieving higher-order accuracy in both space and time. Albeit they succeed in achieving an effective higher spatial resolution and in suppressing the numerical damping of waves, to our knowledge, all current astrophysical simulations invoking self-gravity are limited to second-order accuracy in space. If we can devise an algorithm to evaluate self-gravity with a higher-order spatial accuracy, we can better the evaluation of the gravitational acceleration and gravitational energy release which dictate the evolution of many astrophysical systems. Herein, we present a numerical algorithm for self-gravitating hydrodynamics capable of achieving fourth order accuracy for a given density distribution on a Cartesian uniform grid. First, we derive the cell-averaged gravitational potential at fourth-order accuracy from the cell-averaged density by solving the Poisson equation. Next, we obtain the cell average of the product of the density and gravitational acceleration, which differs from the cell-averaged density multiplied by the cell-averaged gravitational acceleration. We then show the verification of the algorithm by applying it to critical test problems: (1) maintaining equilibria of self-gravitating slabs, even upon advection, (2) evolving a polytropic sphere with a massive power-law envelope, and (3) conservation of specific entropy during the propagation of a sound wave.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Shadow molecular dynamics and atomic cluster expansions for flexible charge models

A shadow molecular dynamics scheme for flexible charge models is presented, where the shadow Born-Oppenheimer potential is derived from a coarse-grained approximation of range-separated density functional theory. The interatomic potential, including the atomic electronegativities and the charge-independent short-range part of the potential and force terms, are modeled by the linear atomic cluster expansion (ACE), which provides a computationally efficient alternative to many machine learning methods. The shadow molecular dynamics scheme is based on extended Lagrangian (XL) Born-Oppenheimer molecular dynamics (BOMD) [Eur. Phys. J. B 94, 164 (2021)]. XL-BOMD provides a stable dynamics, while avoiding the costly computational overhead associated with solving an all-to-all system of equations, which normally is required to determine the relaxed electronic ground state prior to each force evaluation. To demonstrate the proposed shadow molecular dynamics scheme for flexible charge models using the atomic cluster expansion, we emulate the dynamics generated from self-consistent charge density functional tight-binding (SCC-DFTB) theory using a second-order charge equilibration (QEq) model. The charge-independent potentials and electronegativities of the QEq model are trained for a supercell of uranium oxide (UO2) and a molecular system of liquid water. The combined ACE + XL-QEq dynamics are stable over a wide range of temperatures both for the oxide and the molecular systems, and provide a precise sampling of the Born-Oppenheimer potential energy surfaces. Accurate ground Coulomb energies are produced by the ACE-based electronegativity model during an NVE simulation of UO 2 , predicted to be within 1 meV of those from SCC-DFTB on average during comparable simulations.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2024

On The Jacobian of the ECEF J2 Gravitation Model

An Earth-centered, Earth-fixed (ECEF) inertial navigation system must compute the Jacobian of its employed gravitation model with respect to position while time-propagating the error covariance of the system. One commonly used gravitation model is the ‘J2 model’ which is a second-order truncation of the Earth’s spherical harmonic gravitation model. The J2 model is popular because it can quickly and efficiently be evaluated, and the truncation error is small: The ‘J3 term’ --- the third term in the spherical harmonic expansion --- is approximately 1000 times smaller than the J2 term.

42 ENGINEERING↗

DOE OSTI2025

Hybrid HEFA-HDCJ Process for the Production of Jet Fuel Blendstocks

09 BIOMASS FUELS↗

DOE OSTI2025

Using quantum noise correlation analysis to measure ion temperature

Quantum noise correlation analysis was tested at the proof-of-concept level as a technique to measure ion temperature in a plasma. If eventually successful, this technique could enable a compact, inexpensive, and robust ion temperature diagnostic suitable for a burning plasma environment. Ion temperature is a key parameter determining the fusion performance of a burning plasma, as the fusion cross-section has a strong dependence on ion temperature. This ion temperature diagnostic would require only a small optical view of the plasma through a port to passively record impurity line emission. The instrumentation would be remote from the reactor behind the neutron and bio-shielding. The technique relies solely on quantum correlations of the photons emitted by a plasma impurity to measure ion temperature; there is no grating dispersion of an emission line-width or pulse-height analysis of photon energy. This measurement innovation was tested with instrumentation consisting of two single-photon detectors with high timing resolution, a time-tagging unit, and simple light collection optics. This instrumentation measures the second-order correlation between the light intensity falling on the two detectors. The next steps beyond the proof-of-concept level will be development of diagnostic designs for application of this technique to high-temperature and burning plasmas. Arrays of single-photon avalanche detectors to multiplex measurements of photon correlation will be required to reduce signal integration time to an acceptable duration.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Using Separation-Enhanced Isotope Ratio Mass Spectrometry to Enable Increased Renewable Carbon Content in Transportation Fuels (CRADA 525)

Stable isotope ratio measurements of carbon atoms using isotope ratio mass spectrometry (IRMS) can be an effective tool for quantifying biogenic carbon in co-processed fuels, with results approaching the precision and accuracy of accelerator mass spectrometry (AMS). The lower cost of an IRMS may enable deployment to refineries, improving access and analysis turnaround times (≤2 hours), and, by extension, provide data that can allow process optimization to maximize renewable carbon in desired refinery products. This project explored the integration of chemical separation with IRMS analyses to enable highly detailed tracking of biogenic carbon into fuel product streams separated by boiling point range, chemical class, or specific compound. Forty-nine fuels and fuel components of fossil and biogenic origin, spanning gasoline and diesel boiling point ranges, were received from three refiners and were analyzed for their δ 13 C values via IRMS. Results spanned a 13 C range from ca. 10‰ to 44‰ and reflect materials derived from sustainable sources (e.g., C4 or C3 plants, animal-based pathways, syngas) or from fossil-derived fuels. Common ranges are approximately 18‰ to 9‰ and approximately 30‰ to 20‰ for C4 and C3 plants, respectively, and approximately 34‰ to 24‰ and approximately 70‰ to 33‰ for petroleum-derived fuels and methane, respectively. Fuel-like standards were developed and tested using direct-injection elemental analyzer (EA) IRMS for liquid fuels. This method was compared with the published methods, yielding statistically similar results. Four blend curve sets were produced ranging from 0% to 100% of a fuel containing biogenic carbon, focusing on 0% to 10% biogenic carbon. Linear fits were the most applicable for two of the four blend curve sets; however, two sets were found to exhibit slightly quadratic behavior, which was more pronounced in low biogenic blend samples, necessitating second-order fits. The origin of the slight quadratic behavior remains unclear; however, the discussion points to possible interpretations. CanmetENERGY thoroughly characterized a majority of the samples using one- and two-dimensional gas chromatography (GC and GC×GC, respectively) and other analyses. Selected samples were subjected to solid phase extraction (SPE) for saturate, olefin, aromatic, and polar (SOAP) analysis, and the resulting solvent-diluted fractions containing saturates and aromatics were returned to Pacific Northwest National Laboratory (PNNL), where the solvent was removed via evaporation or physical separation using GC techniques. Characterization and separations provided an understanding of saturate and aromatic content, as well as boiling point ranges for each sample and sample fraction. Samples resulting from SPE were examined using EA-IRMS and gas chromatography combustion IRMS (GC-C-IRMS) analyses. Both approaches suggest that the range in values between end-members can be increased by selecting the paraffinic or aromatic fraction of the end-member or by selecting among individual compounds resulting from GC separation of the paraffinic fractions. Considerable work remains to put these approaches into practice and statistically validate the benefit for using a fraction or individual compound over bulk analysis of a sample. However, initial results suggest that separations provide advantages for samples having blend ratios of less than 10% biogenic blendstocks. 13 C results showed statistically similar biofuel blend results to those obtained at PNNL, although additional work is needed to obtain better reproducibility. Select samples were sent to Los Alamos National Laboratory (LANL) for IRMS measurements and Beta Analytics for AMS measurements. This work suggests that IRMS and AMS yield closely comparable results and in some circumstances, IRMS could serve as a surrogate for AMS. While additional work is needed to better resolve statistical advantages for separations and better show the comparable nature of IRMS and AMS in both the biogenic carbon analysis of bulk chemical classes, initial results from this study suggest that these should be pursued in order to proliferate this approach for quantifying biogenic carbon in transportation fuels to the refinery level, thereby potentially enabling process optimization in co-processing scenarios.

09 BIOMASS FUELS↗

DOE OSTI2025

Hybrid HEFA-HDCJ Process for the Production of Jet Fuel Blendstocks

The hydrotreatment of bio-oil derived from the pyrolysis and biocrude from hydrothermal liquefaction of lignocellulosic materials to produce hydrocarbons faces significant technological challenges, mainly due to the high reactivity and poor thermal stability of bio-oil, resulting in the formation of large quantities of coke. This problem has been addressed by existing PNNL patents with a two-step hydrotreatment technology in which the bio-oil is first stabilized with a noble hydrogenation metal (often Pt or Ru). Then, in the second step, the bio-oil is deoxygenated with a Ni-Mo or Co-Mo sulfide catalyst. The main problem with this approach is that the Pt/Ru catalysts deactivate easily in the presence of S or other impurities, which are commonly present in pyrolysis oils. In this project, we explored technological solutions to mitigate coke formation, avoiding the use of Pt/Ru catalysts. Our strategy is based on three actions: (1) Bio-oil stabilization in the presence of alcohols. In this project, we studied the stabilization with butanol. (2) the use of a cosolvent to solubilize the bio-oil. Because coke formation reactions are second-order reactions a reduction in the concentration of reactive bio-oil molecules. In this case, we used yellow greases as a co-solvent. (3) Separation of bio-oil reactive fractions. In this project, we studied the removal of water-soluble fractions. Our batch co-hydrotreatment studies confirmed that the addition of butanol and methanol and the blend with lipids effectively contributed to mitigating coke formation (reducing coke yield to about 1 wt.% %). The removal of sugars did not have a noticeable effect on the overall coke yield, suggesting that coke precursors are present in all bio-oil fractions. Our analytical work suggests that they may be concentrated in the water-insoluble/CH 2 Cl 2 insoluble fractions of pyrolysis oils. Although the technological strategies tested resulted in significant coke reductions, the levels achieved were not sufficiently low to ensure a reliable operation in continuous, fixed-bed trickle-bed reactors. Long runs of more than 100 hours (maximum: 255 h) of co-processing time on stream were achieved in a continuous 40 mL reactor. When the same test was conducted in a larger 400 mL reactor, pressure drop increases associated with coke formation were observed. This increase in coke formation could be due to larger temperature gradients in the bed. Hydrodeoxygenation tests in moving bed reactors and using more active hydrogenation catalysts (for example Ni) could lead to more reliable operations. Unfortunately, our team did not have access to such experimental setups. The technoeconomic analysis suggests that although alcohol use is an effective means to reduce coke formation, the use of alcohol increases production cost. Thus, its use needs to be minimized. A delicate balance needs to be found between the use of technological solutions that allow the reliable operation of the system (stabilization with Ni catalysts, use of small quantities of solvents, processing in moving bed reactors) with a tolerable level of coke formation for the hydrodeoxygenation reactor used and that result in minimum production costs.

09 BIOMASS FUELS↗

DOE OSTI2023

HLPW-4/GMGW-3: High-Order Discretization Technology Focus Group Workshop Summary

This paper summarizes the High-Order Technical Focus Group (HO-TFG) submissions for the joint 4th AIAA High Lift Prediction (HLPW-4) and 3rd Geometry and Mesh Generation Workshop (GMGW-3). The goal of the workshop was to assess the state-of-the-art in mesh generation and computational fluid dynamics software. The Common Research Model High-Lift (CRM-HL) variant served as the primary focus of the workshop, and a two-dimensional airfoil section from the CRM-HL was used as a verification test case. Here, the HO-TFG was tasked with generating high-order curved meshes for both geometries, and computing high-order solutions using both Reynolds-averaged Navier–Stokes and scale-resolving formulations. While limited by computational resources, the final results demonstrate the potential of higher-order methods to increase solution accuracy with a lower degree-of-freedom count relative to second-order discretizations.

42 ENGINEERING↗

DOE OSTI2024

Laser-Doppler Anemometry Measurements of Turbulent Swirling Wakes

This study considers the development and evolution of the swirling turbulent wake and their link to the turbulence present in the wake. A wake generator produces swirling wakes with a minimum of artifacts that would complicate the flow. Four swirling wakes have been studied with swirl numbers ranging from 0.19 to 0.37, and the results are compared to those of a nonswirling wake. Two-component laser-Doppler anemometry has been used to measure mean and turbulence quantities in the wake, and the uncertainty of these quantities has been determined. Careful alignment of the laser-Doppler anemometry system and large numbers of independent samples were used to obtain second-order turbulence statistics with low uncertainty. The results indicate that swirl strength impacts wake behavior, and changes in the behavior are linked to modifications in the turbulence. Faster wake width growth and centerline velocity deficit decay have been observed for wakes with higher swirl strength. The results indicate that a minimum swirl level is required to significantly impact wake behavior, and, at some level of swirl, the enhanced wake evolution observed saturates. For the conditions tested, the swirl number that enhances wake diffusion before saturation has been determined to lie between 0.21 and 0.37.

Engineering↗

DOE OSTI2024

High-Order Wall-Modeled Large-Eddy Simulation of High-Lift Configuration

This paper presents the assessment of several recent enhancements for a high-order wall-modeled large-eddy simulation (WMLES) approach and demonstrates order independence with a fixed data exchange location in the wall model. The two enhancements include the use of isotropic tetrahedral elements to improve accuracy and an explicit subgrid-scale model, the Vreman model, to improve accuracy and robustness. The [Formula: see text] study focused on the high-lift Common Research Model (HL-CRM) at the angle of attack of 19.57 deg, a benchmark problem from the 4th AIAA High-Lift Prediction Workshop. Solution polynomial orders of [Formula: see text], and 5 were used in the study. The study demonstrated [Formula: see text] independence in integrated forces, pitch moment, velocity profile in the wall-normal direction, and surface flow topology. It also showed that a [Formula: see text] order of at least 3 ([Formula: see text]) was needed to correctly predict the external inviscid flow and the surface flow topology. Thereafter, [Formula: see text] simulations over several other angles of attack demonstrated that the high-order WMLES approach can correctly predict the maximum lift and flow separation regions for HL-CRM with about 40 million degrees of freedom (DOF) compared to at least 250 million DOF required by second-order methods.

Engineering↗

DOE OSTI2025

Block-Structured Operator Inference for Coupled Multiphysics Model Reduction

This work presents a block-structured formulation of Operator Inference as a way to learn structured reduced-order models for multiphysics systems. The approach specifies the governing equation structure for each physics component and the structure of the coupling terms. Once the multiphysics structure is specified, the reduced-order model is learned from snapshot data following the nonintrusive Operator Inference methodology. In addition to preserving physical system structure, which in turn permits preservation of system properties such as stability and second-order structure, the block-structured approach has the advantages of reducing the overall dimensionality of the learning problem and admitting tailored regularization for each physics component. The numerical advantages of the block-structured formulation over a monolithic Operator Inference formulation are demonstrated for aeroelastic analysis, which couples aerodynamic and structural models. For the benchmark test case of the AGARD 445.6 wing, block-structured Operator Inference provides an average 20% online prediction speedup over monolithic Operator Inference across subsonic and supersonic flow conditions in both the stable and fluttering parameter regimes while preserving the accuracy achieved with monolithic Operator Inference.

42 ENGINEERING↗

DOE OSTI2025

Dark Energy Survey Year 6 Results: Point-Spread Function Modeling

We present the point-spread function (PSF) modeling for weak lensing shear measurement using the full six years of the Dark Energy Survey (DES Y6) data. We review the PSF estimation procedure using the PIFF (PSFs In the Full FOV) software package and describe the key improvements made to PIFF and modeling diagnostics since the DES year three (Y3) analysis: (i) use of external Gaia and infrared photometry catalogs to ensure higher purity of the stellar sample used for model fitting, (ii) addition of color-dependent PSF modeling, the first for any weak lensing analysis, and (iii) inclusion of model diagnostics inspecting fourth-order moments, which can bias weak lensing measurements to a similar degree as second-order modeling errors. Through a comprehensive set of diagnostic tests, we demonstrate the improved accuracy of the Y6 models evident in significantly smaller systematic errors than those of the Y3 analysis, in which all g band data were excluded due to insufficiently accurate PSF models. For the Y6 weak lensing analysis, we include g band photometry data in addition to the riz bands, providing a fourth band for photometric redshift estimation. Looking forward to the next generation of wide-field surveys, we describe several ongoing improvements to PIFF, which will be the default PSF modeling software for weak lensing analyses for the Vera C. Rubin Observatory’s Legacy Survey of Space and Time.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2026

Mechanistic Modeling of TEG Dehydrator Emissions in Oil and Gas Industry

This work presents a mechanistic modeling approach for simulating methane emissions from triethylene glycol (TEG) dehydrators used in oil & gas (O&G) operations. The model was developed as a modular component of the Mechanistic Air Emissions Simulator (MAES) tool, incorporating species-specific absorption and emission dynamics through two-level, second-order polynomial regression (PR) models trained on ProMax simulation data: (1) species-level regression models that track the transfer rates of individual gas species within the dehydrator unit streams, and (2) outlet flow stream regression models that predict the fraction of inlet gas distributed among the outlet streams of the dehydrator unit. These behaviors were characterized over a range of glycol circulation ratios, wet gas pressures, and temperatures. The model was validated using root mean square error (RMSE) analysis. The species-level PR achieved low root mean square error (RMSE) values (<0.03) for light hydrocarbon species across all dehydrator components, ranging from 0.0009 for methane to 0.029 for normal pentane. Similarly, the outlet-level PR yielded RMSE values below 0.002 for the dry gas fraction, 0.001 for the flash tank fraction, and 0.002 for the still vent fraction, demonstrating strong agreement between predicted and reference ProMax values. When deployed at field facilities, the model significantly improved MAES-simulated dehydrator emissions, revealing that gas-assisted glycol pump emissions are the dominant contributors to both dehydrator-level and site-level methane emissions under uncontrolled conditions. Further analysis of the 154 dehydrator units reported by operators under the AMI 2024 project showed that 54 units (31%) used gas-driven glycol pumps, of which 6 units (11%) operated with uncontrolled flash tanks, and 22 units (40.7%) were identified as potentially oversized. Of the six dehydrator units with uncontrolled gas-assisted pumps, pump emissions accounted for 90.25% of total dehydrator emissions and 63.10% of total site-level emissions. These findings highlight substantial opportunities for emissions mitigation through equipment upgrades.

MAES↗

DOE OSTI2024

A Quantum Mechanical MP2 Study of the Electronic Effect of Nonplanarity on the Carbon Pyramidalization of Fullerene C 60

Among C 60 ’s diverse functionalities, its potential application in CO 2 sequestration has gained increasing interest. However, the processes involved are sensitive to the molecule’s electronic structure, aspects of which remain debated and require greater precision. To address this, we performed structural optimization of fullerene C 60 using the QM MP2/6–31G* method. The nonplanarity of the optimized icosahedron is characterized by two types of dihedral angles: 138° and 143°. The 120 dihedrals of 138° occur between two hexagons intersecting at C–C bonds of 1.42 Å, while the 60 dihedrals of 143° are observed between hexagons and pentagons at C–C bonds of 1.47 Å. NBO analysis reveals less pyramidal sp 1.78 hybridization for carbons at the 1.42 Å bonds and more pyramidal sp 2.13 hybridization for the 1.47 Å bonds. Electrostatic potential charges range from -0.04 a.u. to 0.04 a.u. on the carbon atoms. Second-order perturbation analysis indicates that delocalization interactions in the C–C bonds of 1.42 Å (143.70 kcal/mol) and 1.47 Å (34.98 kcal/mol) are 22% and 38% higher, respectively, than those in benzene. MP2/Def2SVP calculations yield a correlation energy of 13.49 kcal/mol per electron for C 60 , slightly higher than the 11.68 kcal/mol for benzene. However, the results from HOMO-LUMO calculations should be interpreted with caution. This study may assist in the rational design of fullerene C 60 derivatives for CO 2 reduction systems.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Strong Coupling of Hydrodynamics and Reactions in Nuclear Statistical Equilibrium for Modeling Convection in Massive Stars

We build on the simplified spectral deferred corrections (SDC) coupling of hydrodynamics and reactions to handle the case of nuclear statistical equilibrium (NSE) and electron/positron captures/decays in the cores of massive stars. Our approach blends a traditional reaction network on the grid with a tabulated NSE state from a very large, ${\mathcal O }(100)$ nuclei network. We demonstrate how to achieve second-order accuracy in the simplified-SDC framework when coupling NSE to hydrodynamics, with the ability to evolve the star on the hydrodynamics time step. We discuss the application of this method to convection in massive stars leading up to core collapse. We also show how to initialize the initial convective state from a 1D model in a self-consistent fashion. All of these developments are done in the publicly available Castro simulation code and the entire simulation methodology is fully GPU-accelerated.

Explosive nucleosynthesis↗

DOE OSTI2025

An Agnostic Approach to Building Empirical Type Ia Supernova Light Curves: Evidence for Intrinsic Chromatic Flux Variation Using Nearby Supernova Factory Data

We present a new empirical Type Ia supernova (SN Ia) model with three chromatic flux variation templates: one phase dependent and two phase independent. No underlying dust extinction model or patterns of intrinsic variability are assumed. Implemented with Stan and trained using spectrally binned Nearby Supernova Factory spectrophotometry, we examine this model's 2D, phase-independent flux variation space using two motivated basis representations. In both, the first phase-independent template captures variation that appears dust-like, while the second captures a combination of effectively intrinsic variability and second-order dust-like effects. We find that ≈13% of the modeled phase-independent flux variance is not dust-like. Previous empirical SN Ia models either assume an effective dust extinction recipe in their architecture, or only allow for a single mode of phase-independent variation. The presented results demonstrate such an approach may be insufficient, because it could "leak" noticeable intrinsic variation into phase-independent templates.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Evolution of Magnetohydrodynamic Turbulence in the Expanding Solar Wind: Residual Energy and Intermittency

We conduct 3D magnetohydrodynamic simulations of decaying turbulence in the context of the solar wind. To account for the spherical expansion of the solar wind, we implement the expanding box model. The initial turbulence comprises uncorrelated counterpropagating Alfvén waves and exhibits an isotropic power spectrum. Our findings reveal the consistent generation of negative residual energy whenever nonlinear interactions are present, independent of the normalized cross helicity σc and compressibility. The spherical expansion facilitates this process. The resulting residual energy is primarily distributed in the perpendicular direction, with S 2 (b) − S 2 (u) ∝ l ⊥ or equivalently –E r ∝ k$^{–2}_{⟂}$. Here S 2 (b) and S 2 (u) are second-order structure functions of magnetic field and velocity respectively. In most runs, S 2 (b) develops a scaling relation S 2 (b) ∝ $l$$^{1/2}_{⊥}$ (E b ∝ k$^{–3/2}_{⟂}$). In contrast, S 2 (u) is consistently shallower than S 2 (b), which aligns with in situ observations of the solar wind. We observe that the higher-order statistics of the turbulence, which act as a proxy for intermittency, depend on the initial σc and are strongly affected by the expansion effect. Generally, the intermittency is more pronounced when the expansion effect is present. Finally, we find that in our simulations, although the negative residual energy and intermittency grow simultaneously as the turbulence evolves, the causal relation between them seems to be weak, possibly because they are generated on different scales.

Interplanetary turbulence↗