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DOE OSTI2020

Preferential turbulence enhancement in two-dimensional compressions

When initially isotropic three-dimensional (3D) turbulence is compressed along two dimensions, the compression supplies energy directly to the flow components in the compressed directions, while the flow component in the noncompressed direction experiences the effects of compression only indirectly through the nonlinearity of the hydrodynamic equations. Here we present our study of such 2D compressions using numerical simulations. For initially isotropic turbulence, we find that the nonlinearity can be insufficient to maintain isotropy, with the energy components parallel to the compression coming to dominate the turbulent energy, with a number of consequences. Among these are the possibilities for stronger and more easily sustained growth of turbulent energy than in 3D compressions and for an increasing turbulent Mach number even in a compression without thermal losses.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Turbulence generation by shock interaction with a highly nonuniform medium

An initially planar shock wave propagating into a medium of nonuniform density will be perturbed, leading to the generation of postshock velocity perturbations. Using numerical simulations we study this phenomenon in the case of highly nonuniform density (order-unity normalized variance, $\sigma_\rho/\bar{\rho}\sim1$) and strong shocks (shock Mach numbers $\bar{M}_s\gtrsim10$). This leads to a highly disrupted shock and a turbulent postshock flow. We simulate this interaction for a range of shock drives and initial density configurations meant to mimic those which might be presently achieved in experiments. Theoretical considerations lead to scaling relations, which are found to reasonably predict the postshock turbulence properties. The turbulent velocity dispersion and turbulent Mach number are found to depend on the preshock density dispersion and shock speed in a manner consistent with the linear Richtymer-Meshkov instability prediction. We also show a dependence of the turbulence generation on the scale of density perturbations. The postshock pressure and density, which can be substantially reduced relative to the unperturbed case, are found to be reasonably predicted by a simplified analysis that treats the extended shock transition region as a single normal shock.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Universal Anomalous Diffusion of Quantized Vortices in Ultraquantum Turbulence

In classical viscous fluids, turbulent eddies are known to be responsible for the rapid spreading of embedded particles. However, in inviscid quantum fluids where the turbulence is induced by a chaotic tangle of quantized vortices, dispersion of the particles can be achieved via a nonclassical mechanism, i.e., their binding to the evolving vortices. However, knowledge on how the vortices diffuse and spread in quantum-fluid turbulence is very limited, especially for the so-called ultraquantum turbulence (UQT) generated by a random tangle of vortices. Here we report a systematic numerical study of the apparent diffusion of vortices in UQT in superfluid helium-4 using the full Biot-Savart simulation. We reveal that the vortices in the superfluid exhibit a universal anomalous diffusion (superdiffusion) at small times, which transits to normal diffusion at large times. This behavior is found to be the result of a generic scaling property of the vortex velocity. Our simulation at finite temperatures also nicely reproduces recent experimental observations. Lastly, the knowledge obtained from this study may form the base for understanding turbulent transport and universal vortex dynamics in various quantum fluids.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

An acoustic investigation of the near-surface turbulence on Mars

The Perseverance rover is carrying out an original acoustic experiment on Mars: the SuperCam microphone records the spherical acoustic waves generated by laser sparks at distances from 2 m to more than 8 m. These N-shaped acoustic waves scatter from the multiple local heterogeneities of the turbulent atmosphere. Therefore, large and random fluctuations of sound travel time and intensity develop as the waves cross the medium. The variances of the travel times and the scintillation index (normalized variance of the sound intensity) are studied within the mathematical formalism of the propagation of spherical acoustic waves through thermal turbulence to infer statistical properties of the Mars atmospheric temperature fluctuation field. The comparison with the theory is made by simplifying assumptions that do not include wind fluctuations and diffraction effects. Two Earth years (about one Martian year) of observations acquired during the maximum convective period (10:00–14:00 Mars local time) show a good agreement between the dataset and the formalism: the travel time variance diverges from the linear Chernov solution exactly where the density of occurrence of the first caustic reaches its maximum. Moreover, on average, waves travel faster than the mean speed of sound due to a fast path effect, which is also observed on Earth. To account for the distribution of turbulent eddies, several power spectra are tested and the best match to observation is obtained with a generalized von Karman spectrum with a shallower slope than the Kolmogorov cascade, φ(k)∝(1 + k 2 L 2 ) -4/3 . It is associated with an outer scale of turbulence, L, of 11 cm at 2 m above the surface and a standard deviation of 6 K over 9 s for the temperature. These near-surface atmospheric properties are consistent with a weak to moderate wave scattering regime around noon with little saturation. Overall, this study presents an innovative and promising methodology to probe the near-surface atmospheric turbulence on Mars.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Field Sensitivity Analysis of Turbulence Model Parameters for Flow Over a Wing

Reynolds-averaged-Navier-Stokes (RANS) turbulence models are a critical tool in computational-fluid-dynamics simulations of aerodynamic systems, but simulation results can be highly sensitive to RANS-model parameter choices. Sensitivity analysis can be used to quantify these impacts, and the objective of this study is to demonstrate field sensitivity analysis with respect to ten parameters in the 2003 Menter shear-stress-transport (SST) turbulence model. Here, the analysis is demonstrated for an application relevant to wind energy, namely, flow over a NACA 0015 wing at 12 degree angle of attack and a Reynolds number of 1.5 x 10 6 . We quantify sensitivity using Sobol indices and the mean-squared gradient, which are estimated using polynomial chaos and active subspace models, respectively. Our results indicate that there are substantial spatial variations in parameter sensitivities, with different sets of most-sensitive parameters near the wing, as well as in the downstream wake, consistent with the physical interpretations of the turbulence model inputs. We show that, for this particular turbulence model and flow, simultaneous dimension reduction is possible across all quantities of interest, enabling efficient exploration of model outcomes. Ultimately, this analysis provides new insights into turbulence model parameter sensitivities in incompressible flows, and also demonstrates the implementation of field sensitivity analysis for applications relevant to aerodynamics simulations.

17 WIND ENERGY↗

DOE OSTI2020

Simulating Real Atmospheric Boundary Layers at Gray-Zone Resolutions: How Do Currently Available Turbulence Parameterizations Perform?

Recent computational and modeling advances have led a diverse modeling community to experiment with atmospheric boundary layer (ABL) simulations at subkilometer horizontal scales. Accurately parameterizing turbulence at these scales is a complex problem. The modeling solutions proposed to date are still in the development phase and remain largely unvalidated. This work assesses the performance of methods currently available in the Weather Research and Forecasting (WRF) model to represent ABL turbulence at a gray-zone grid spacing of 333 m. We consider three one-dimensional boundary layer parameterizations (MYNN, YSU and Shin-Hong) and coarse large-eddy simulations (LES). The reference dataset consists of five real-case simulations performed with WRF-LES nested down to 25 m. Results reveal that users should refrain from coarse LES and favor the scale-aware, Shin-Hong parameterization over traditional one-dimensional schemes. Overall, the spread in model performance is large for the cellular convection regime corresponding to the majority of our cases, with coarse LES overestimating turbulent energy across scales and YSU underestimating it and failing to reproduce its horizontal structure. Despite yielding the best results, the Shin-Hong scheme overestimates the effect of grid dependence on turbulent transport, highlighting the outstanding need for improved solutions to seamlessly parameterize turbulence across scales.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

A Search for Correlations between Turbulence and Star Formation in LITTLE THINGS Dwarf Irregular Galaxies

Turbulence has the potential for creating gas density enhancements that initiate cloud and star formation (SF), and it can be generated locally by SF. To study the connection between turbulence and SF, we looked for relationships between SF traced by FUV images, and gas turbulence traced by kinetic energy density (KED) and velocity dispersion (v {sub disp}) in the LITTLE THINGS sample of nearby dIrr galaxies. We performed 2D cross-correlations between FUV and KED images, measured cross-correlations in annuli to produce correlation coefficients as a function of radius, and determined the cumulative distribution function of the cross-correlation value. We also plotted on a pixel-by-pixel basis the locally excess KED, v {sub disp}, and H i mass surface density, Σ{sub HI}, as determined from the respective values with the radial profiles subtracted, versus the excess SF rate density Σ{sub SFR}, for all regions with positive excess Σ{sub SFR}. We found that Σ{sub SFR} and KED are poorly correlated. The excess KED associated with SF implies a ∼0.5% efficiency for supernova energy to pump local H i turbulence on the scale of the resolution here, which is a factor of ∼2 too small for all of the turbulence on a galactic scale. The excess v {sub disp} in SF regions is also small, only ∼0.37 km s{sup −1}. The local excess in Σ{sub HI} corresponding to an excess in Σ{sub SFR} is consistent with a H i consumption time of ∼1.6 Gyr in the inner parts of the galaxies. The similarity between this timescale and the consumption time for CO implies that CO-dark molecular gas has comparable mass to H i in the inner disks.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2020

Dust Growth by Accretion of Molecules in Supersonic Interstellar Turbulence

We show that the growth rate of dust grains in cold molecular clouds is enhanced by the high degree of compressibility of a turbulent, dilute gas. By means of high-resolution (1024 3 ) numerical simulations, we confirm the theory that the spatial mean growth rate is proportional to the gas-density variance. This also results in broadening of the grain-size distribution (GSD) due to turbulence-induced variation of the grain-growth rate. We show, for the first time in a detailed numerical simulation of hydrodynamic turbulence, that the GSD evolves toward a shape that is a reflection of the gas-density distribution, regardless of the initial distribution. That is, in case of isothermal, rotationally forced turbulence, the GSD tends to be a lognormal distribution. We also show that in hypersonic turbulence, decoupling of gas and dust becomes important and that this leads to an even further accelerated grain growth.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Turbulent Regimes in Collisions of 3D Alfvén-wave Packets

Using three-dimensional gyrofluid simulations, we revisit the problem of Alfvén-wave (AW) collisions as building blocks of the Alfvénic turbulent cascade and their interplay with magnetic reconnection at magnetohydrodynamic (MHD) scales. Depending on the large-scale value of the nonlinearity parameter χ 0 (the ratio between the AW linear propagation time and nonlinear turnover time), different regimes are observed. For strong nonlinearities (χ 0 ~ 1), turbulence is consistent with a dynamically aligned, critically balanced cascade—fluctuations exhibit a scale-dependent alignment $\sin {\theta }_{{k}_{\perp }}\propto {k}_{\perp }^{-1/4}$, resulting in a ${k}_{\perp }^{-3/2}$ spectrum and ${k}_{\parallel }\propto {k}_{\perp }^{1/2}$ spectral anisotropy. At weaker nonlinearities (small χ 0 ), a spectral break marking the transition between a large-scale weak regime and a small-scale ${k}_{\perp }^{-11/5}$ tearing-mediated range emerges, implying that dynamic alignment occurs also for weak nonlinearities. At χ 0 < 1 the alignment angle ${\theta }_{{k}_{\perp }}$ shows a stronger scale dependence than in the χ 0 ~ 1 regime, namely $\sin {\theta }_{{k}_{\perp }}\propto {k}_{\perp }^{-1/2}$ at χ 0 ~ 0.5, and $\sin {\theta }_{{k}_{\perp }}\propto {k}_{\perp }^{-1}$ at χ 0 ~ 0.1. Dynamic alignment in the weak regime also modifies the large-scale spectrum, scaling approximately as ${k}_{\perp }^{-3/2}$ for χ 0 ~ 0.5 and as ${k}_{\perp }^{-1}$ for χ 0 ~ 0.1. A phenomenological theory of dynamically aligned turbulence at weak nonlinearities that can explain these spectra and the transition to the tearing-mediated regime is provided; at small χ 0 , the strong scale dependence of the alignment angle combines with the increased lifetime of turbulent eddies to allow tearing to onset and mediate the cascade at scales that can be larger than those predicted for a critically balanced cascade by several orders of magnitude. Such a transition to tearing-mediated turbulence may even supplant the usual weak-to-strong transition.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Turbulence, Waves, and Taylor’s Hypothesis for Heliosheath Observations

Magnetic field fluctuations measured in the heliosheath by the Voyager spacecraft are often characterized as compressible, as indicated by a strong fluctuating component parallel to the mean magnetic field. However, the interpretation of the turbulence data faces the caveat that the standard Taylor’s hypothesis is invalid because the solar wind flow velocity in the heliosheath becomes subsonic and slower than the fast magnetosonic speed, given the contributions from hot pickup ions (PUIs) in the heliosheath. We attempt to overcome this caveat by introducing a 4D frequency-wavenumber spectral modeling of turbulence, which is essentially a decomposition of different wave modes following their respective dispersion relations. Isotropic Alfvén and fast mode turbulence are considered to represent the heliosheath fluctuations. We also include two dispersive fast wave modes derived from a three-fluid theory. We find that (1) magnetic fluctuations in the inner heliosheath are less compressible than previously thought, an isotropic turbulence spectral model with about 25% in compressible fluctuation power is consistent with the observed magnetic compressibility in the heliosheath; (2) the hot PUI component and the relatively cold solar wind ions induce two dispersive fast magnetosonic wave branches in the perpendicular propagation limit, PUI fast wave may account for the spectral bump near the proton gyrofrequency in the observable spectrum; (3) it is possible that the turbulence wavenumber spectrum is not Kolmogorov-like although the observed frequency spectrum has a −5/3 power-law index, depending on the partitioning of power among the various wave modes, and this partitioning may change with wavenumber.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Multipoint Turbulence Analysis with HelioSwarm

Exploration of plasma dynamics in space, including turbulence, is entering a new era of multisatellite constellation measurements that will determine fundamental properties with unprecedented precision. Familiar but imprecise approximations will need to be abandoned and replaced with more-advanced approaches. We present a preparatory study of the evaluation of second- and third-order statistics, using simultaneous measurements at many points. Here, for specificity, the orbital configuration of the NASA Swarm mission is employed in conjunction with 3D magnetohydrodynamics numerical simulations of turbulence. The HelioSwarm nine-spacecraft constellation flies virtually through the turbulence to compare results with the exact numerical statistics. We demonstrate novel increment-based techniques for the computation of (1) the multidimensional spectra and (2) the turbulent energy flux. This latter increment-space estimate of the cascade rate, based on the third-order Yaglom–Politano–Pouquet theory, uses numerous increment-space tetrahedra. Our investigation reveals that HelioSwarm will provide crucial information on the nature of astrophysical turbulence.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Effects of Nonzero-frequency Fluctuations on Turbulence Spectral Observations

In situ observations of turbulence spectra in space plasmas are usually interpreted as wavenumber spectra, assuming that the fluctuation frequency is negligible in the plasma flow frame. We explore the effects of nonzero frequency in the plasma flow frame on turbulence spectral observations. The finite frequency can be caused by either propagating waves or nonlinear broadening of nonpropagating structures. We show that the observed frequency spectrum can be modified by the nonzero frequency of turbulent fluctuations in several ways. Specifically, (i) frequency broadening results in a minor modification to the observed spectrum, primarily acting as a smoothing kernel of the spectrum near the spectral break, while the asymptotic spectral index remains unchanged; (ii) wave propagation can affect the observed spectral index for anisotropic turbulence. The effect is significant at low frequencies and weaker at high frequencies, leading to a "concave" shape of the observed perpendicular spectrum; (iii) the Doppler shift for forward- and backward-propagating Elsasser modes can result in a nonzero cross helicity for critical-balanced turbulence since the effect of the Doppler shift favors outward-propagating waves systematically, resulting in an observed imbalance. These results may have important implications for the interpretation of solar wind flows observed by Parker Solar Probe.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Investigations of correlation and coherence in turbulence from a large-eddy simulation

Abstract. Microscale flow descriptions are often given in terms of mean quantities, turbulent kinetic energy, and/or stresses. Those metrics, while valuable, give limited information about turbulent eddies and coherent turbulent structures. This work investigates the structure of an atmospheric boundary layer using coherence and correlation in space and time with a range of separation distances. We calculate spatial correlations over entire planes of velocity fluctuations, from which we can evaluate the correlation along different directions at different spacings. Similarly, coherence of the three velocity components over separations in the three directions is also investigated. We apply these analyses to a mesoscale–microscale coupled scenario with time-varying conditions and examine nuances in spatial correlations that are often overlooked. Through these analyses and results, this work highlights important differences observed in terms of coherence when comparing large-eddy simulation data to simpler models and suggests ways to improve these simpler models. We note that such differences are important for disciplines like wind energy structural dynamic analysis, in which blade loading and fatigue depend strongly on the structure of the turbulence. We emphasize the additional wealth of data that can be provided by typical atmospheric boundary layer large-eddy simulation when correlation and coherence analysis is included, and we also state the limitations of large-eddy simulation data, which inherently truncate the smaller scales of turbulence.

17 WIND ENERGY↗

DOE OSTI2023

In Situ Wind and Turbulence Measurements in a Field of Full-Size Parabolic Trough Solar Collectors

Concentrated Solar Power (CSP) is a promising method for using Solar power for electricity generation with thermal energy storage. One of the primary drivers of structural design costs of CSP collector structures is wind loading. To date, the design of these structures has relied on data from wind tunnels that do not adequately capture the dynamic effects observed at scale. NREL initiated a field measurement campaign at the operational Nevada Solar One (NSO) powerplant that uses parabolic troughs as solar collectors. The aim of the project is a detailed characterization of prevailing wind and turbulence conditions and resulting operational loads on parabolic troughs, providing insights on structural dynamic response, and generating a first-of-a-kind, comprehensive, high-resolution wind-loading dataset available for validating simulations of wind loading on collector structures. The measurements at NSO consist of Sonic anemometers on masts at different heights to characterize the incoming flow and conditions within and above the trough field, in combination with a Doppler Lidar scanning the horizontal plane above the troughs. The wind measurements at NSO have been continuously operating since October 2021 and provide a year-long dataset characterizing wind and turbulence conditions. The structural load measurements start in November 2022 and will complement the wind measurements. In this poster, we present first results of the wind measurement campaign by highlighting days with different atmospheric flow conditions. We identified three main factors altering the flow over the parabolic troughs: Wind speed, wind direction, and the angle of the parabolic troughs. The highest loads are expected when the wind blows perpendicular to the trough rows. In this case, the first rows experience the highest loads and block the subsequent rows, creating conditions with decreased wind speed and enhanced turbulence within the trough field. Also, turbulent length scales change. These affected conditions produce unique load cases on the structures that will be captured by the load measurements. If the wind blows along the trough rows, wind and turbulence conditions are less influenced by the troughs.

atmospheric turbulence↗

DOE OSTI2023

In Situ Wind and Turbulence Measurements in a Field of Full-Size Parabolic Trough Collectors

concentrated solar power↗

DOE OSTI2021

Data-driven learning of Mori–Zwanzig operators for isotropic turbulence

Developing reduced-order models for turbulent flows, which contain dynamics over a wide range of scales, is an extremely challenging problem. In statistical mechanics, the Mori–Zwanzig (MZ) formalism provides a mathematically exact procedure for constructing reduced-order representations of high-dimensional dynamical systems, where the effects due to the unresolved dynamics are captured in the memory kernel and orthogonal dynamics. Turbulence models based on MZ formalism have been scarce due to the limited knowledge of the MZ operators, which originates from the difficulty in deriving MZ kernels for complex nonlinear dynamical systems. In this work, we apply a recently developed data-driven learning algorithm, which is based on Koopman's description of dynamical systems and Mori's linear projection operator, on a set of fully resolved isotropic turbulence datasets to extract the Mori–Zwanzig operators. With data augmentation using known turbulence symmetries, the extracted Markov term, memory kernel, and orthogonal dynamics are statistically converged and the generalized fluctuation–dissipation relation can be verified. The properties of the memory kernel and orthogonal dynamics, and their dependence on the choices of observables are investigated to address the modeling assumptions that are commonly used in MZ-based models. A series of numerical experiments are then constructed using the extracted kernels to evaluate the memory effects on prediction. The results show that the prediction errors are strongly affected by the choice of observables and can be further reduced by including the past history of the observables in the memory kernel.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Posterior comparison of model dynamics in several hybrid turbulence model forms

Hybrid turbulence models that can accurately reproduce unsteady three-dimensional flow physics across the entire range of grid scales and turbulence dynamics from Reynolds-averaged Navier–Stokes (RANS), through large-eddy simulation (LES), down to direct numerical simulations (DNS) are of increasing interest to the turbulence modeling community. However, despite decades of research and development, the basic tasks of eliminating poor-performing hybrid RANS-LES models and accelerating adoption of superior models through well-designed validation and verification have yet to occur. As a step in this direction, in this work we evaluate thirteen different hybrid RANS-LES models via systematic grid refinement of decaying homogeneous isotropic turbulence. We further derive a novel mathematical framework for assessing the energy partitioning dynamics of each Hybrid RANS-LES model, wherein model-to-model variations in energy partitioning can be interpreted as different feedback mechanisms operating on a low-dimensional nonlinear dynamical system. We found that model forms similar to the flow simulation methodology—also often termed very-large eddy simulation—are dynamically inconsistent with DNS at all resolutions. Additionally, we found a strong dynamical similarity in the feedback mechanisms of all models related to detached eddy simulation and partially averaged Navier–Stokes that is inherent to their general model forms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Mixing across stable density interfaces in forced stratified turbulence

Understanding how turbulence enhances irreversible scalar mixing in density-stratified fluids is a central problem in geophysical fluid dynamics. While isotropic overturning regions are commonly the focus of mixing analyses, we here investigate whether significant mixing may arise in anisotropic statically stable regions of the flow. Focusing on a single forced direct numerical simulation of stratified turbulence, we analyse spatial correlations between the vertical density gradient $\partial \rho /\partial z$ and the dissipation rates of kinetic energy $\epsilon$ and scalar variance $\chi$ , the latter quantifying scalar mixing. The domain is characterized by relatively well-mixed density layers separated by sharp stable interfaces that are correlated with high vertical shear. While static instability is most prevalent within the mixed layers, much of the scalar mixing is localized to the intervening interfaces, a phenomenon not apparent if considering local static instability or $\epsilon$ alone. While the majority of the domain is characterized by the canonical flux coefficient $\varGamma \equiv \chi /\epsilon =0.2$ , often assumed in ocean mixing parametrizations, extreme values of $\chi$ within the statically stable interfaces, associated with elevated $\varGamma$ , strongly skew the bulk statistics. Our findings suggest that current parametrizations of turbulent mixing may be biased by undersampling, such that the most common, but not necessarily the most significant, mixing events are overweighted. Having focused here on a single simulation of stratified turbulence, it is hoped that our results motivate a broader investigation into the role played by stable density interfaces in mixing, across a wider range of parameters and forcing schemes representative of ocean turbulence.

Couchman, Miles M. P. (ORCID:0000000246676829)↗