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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Impact of the magnetic horizon on the interpretation of the Pierre Auger Observatory spectrum and composition data

The flux of ultra-high energy cosmic rays reaching Earth above the ankle energy (5 EeV) can be described as a mixture of nuclei injected by extragalactic sources with very hard spectra and a low rigidity cutoff.Extragalactic magnetic fields existing between the Earth and the closest sources can affect the observed CR spectrum by reducing the flux of low-rigidity particles reaching Earth. We perform a combined fit of the spectrum and distributions of depth of shower maximum measured with the Pierre Auger Observatory including the effect of this magnetic horizon in the propagation of UHECRs in the intergalactic space.We find that, within a specific range of the various experimental and phenomenological systematics, the magnetic horizon effect can be relevant for turbulent magnetic field strengths in the local neighbourhood in which the closest sources lieof order B$_{rms}$ ≃ (50–100) nG (20 Mpc/d$_{s}$)( 100 kpc/L$_{coh}$)$^{1/2}$, with d$_{s}$ the typical intersource separation and L$_{coh}$ the magnetic field coherence length. When this is the case,the inferred slope of the source spectrum becomes softer and can be closer to the expectations of diffusive shock acceleration, i.e., ∝ E$^{-2}$.An additional cosmic-ray population with higher source density and softer spectra, presumably also extragalactic and dominating the cosmic-ray flux at EeV energies, is also required to reproduce the overall spectrum and composition results for all energies down to 0.6 EeV.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

A new process-based and scale-aware desert dust emission scheme for global climate models – Part I: Description and evaluation against inverse modeling emissions

Desert dust accounts for most of the atmosphere's aerosol burden by mass and produces numerous important impacts on the Earth system. However, current global climate models (GCMs) and land-surface models (LSMs) struggle to accurately represent key dust emission processes, in part because of inadequate representations of soil particle sizes that affect the dust emission threshold, surface roughness elements that absorb wind momentum, and boundary-layer characteristics that control wind fluctuations. Furthermore, because dust emission is driven by small-scale (~ 1 km or smaller) processes, simulating the global cycle of desert dust in GCMs with coarse horizontal resolutions (~ 100 km) presents a fundamental challenge. This representation problem is exacerbated by dust emission fluxes scaling nonlinearly with wind speed above a threshold wind speed that is sensitive to land-surface characteristics. Here, we address these fundamental problems underlying the simulation of dust emissions in GCMs and LSMs by developing improved descriptions of (1) the effect of soil texture on the dust emission threshold, (2) the effects of nonerodible roughness elements (both rocks and green vegetation) on the surface wind stress, and (3) the effects of boundary-layer turbulence on driving intermittent dust emissions. We then use the resulting revised dust emission parameterization to simulate global dust emissions in a standalone model forced by reanalysis meteorology and land-surface fields. We further propose (4) a simple methodology to rescale lower-resolution dust emission simulations to match the spatial variability of higher-resolution emission simulations in GCMs. The resulting dust emission simulation shows substantially improved agreement against regional dust emissions observationally constrained by inverse modeling. We thus find that our revised dust emission parameterization can substantially improve dust emission simulations in GCMs and LSMs.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

High-Fidelity Simulation Aerodynamics Dataset of NACA 0012 and 0021 Airfoils

The repository contains time series data of pressure, viscous and moment forces for the NACA 0012 and 0021 airfoils at angles of attack (AOA), 5, 17, 30, 45, 60 and 90 degrees. The data was generated during the high-fidelity simulations of the airfoils using the open-source CFD code, Nalu-Wind (https://github.com/Exawind/nalu-wind). The research objective was to study the effects of mesh resolution and turbulence model on the three-dimensional deep stall aerodynamics of the airfoils, which has been published in the Journal of Turbulence (https://doi.org/10.1080/14685248.2023.2225141). Several meshes of the O-grid type were generated using the modified Pointwise Glyph script of Carrigan (https://github.com/pointwise/AirfoilMesh) by varying the wall normal and spanwise resolutions. Note that, the geometry was extruded by four chord lengths in the spanwise direction. In the paper, we showed that Improved Delayed Detached Eddy Simulation (IDDES) hybrid RANS/LES turbulence model with a minimum of 24 cells per chord length in the spanwise direction is necessary to correctly predict the loads in the deep stall regime. Under the NACA 0012 airfoil directory, the data for several combinations of wall-normal and spanwise resolutions are presented in each of the AOA subdirectories. The corresponding experimental data for the lift and drag polars can be found in the "exp_data" subdirectory. The directory for the NACA 0021 airfoil consists of CFD force data and airfoil polars for Reynolds numbers 2.7e5 and 2.0e6.

17 WIND ENERGY↗
DOE OSTI2021

Suppression of ITG turbulence due to spectral shift during biasing induced H-mode on HBT-EP

Investigations of biasing induced H-mode discharges on HBT-EP show that the edge turbulence is consistent with the ion temperature gradient) mode and have allowed for the controlled observation of the effect of applied flow shear on the turbulence. Measurements of the radial wavenumber spectrum of floating potentials at the edge show that the turbulence intensity decreases with increasing shift in the spectrum average ⟨ k r ⟩ when increasing amounts of bias probe voltage (and increasing amounts of flow shear) is applied. This is in agreement with the spectral shift model [Staebler et al., Phys. Rev. Lett. 110, 055003 2013] for turbulence suppression via sheared flow. A shift in the wavenumber spectrum occurs at applied electrode voltages and currents below the threshold needed for an L–H transition, and a dithering transition is obtained when biasing near the threshold. Suppression of blob-filament turbulence in the scrape-off layer (SOL) precedes the L–H transition, with the SOL turbulence remaining low throughout the dithering phase, despite the modulation of turbulence levels in the nearby edge. This demonstrates that the SOL turbulence “decouples” from the edge turbulence. The spectral shift in the measured radial wavenumber is corroborated by the direct measurement of eddy tilt angle using a novel time delay analysis technique first developed for Doppler reflectometry [Pinzon et al., Plasma Phys. Controlled Fusion 61, 105009 (2019)] but adapted here for floating potential measurements.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

High-fidelity Experiments of Turbulent Buoyant Jets from Simultaneous Particle Image Velocimetry and Laser Induced Fluorescence

Accurate models of turbulent buoyant flows are essential for the design of nuclear reactors thermal hydraulics and passive safety systems. However, available models fail to fully capture the physics of turbulent mixing when buoyancy becomes predominant with respect to momentum. Therefore, high-fidelity experiments of well-controlled fundamental flows are needed to develop and validate more accurate models. We performed experiments of positive and negative turbulent buoyant jets, both in uniform and stratified environments, with the aim of understanding the thermal hydraulics of turbulent mixing with variable density and providing high-fidelity data for the development and validation of turbulence models. Non-intrusive, simultaneous Particle Image Velocimetry and Laser Induced Fluorescence measurements were carried out to acquire instantaneous velocity and concentration fields on a vertical section parallel to the axis of a jet in the self-similar region. The Refractive Index Matching method was applied to measure high-resolution buoyant jets with up to 8.6% density difference. These data are free of the typical errors that characterize optical measurements of buoyancy driven flows (e.g., natural and mixed convection) where the refractive index of the fluid is inhomogeneous throughout the measurement domain. Turbulent statistics and entrainment of buoyant jets in uniform and stratified environments are presented. These data are compared with non-buoyant jets in uniform environment, as a reference to investigate the effects of buoyancy and stratification on turbulent mixing. The results will be used for the assessment of current turbulence models and as basis for the development of a new one that captures turbulent mixing.

42 ENGINEERING↗
DOE OSTI2024

High-Fidelity Velocity and Concentration Measurements of Turbulent Buoyant Jets

Accurate models of turbulent buoyant flows are essential for the design of the cooling circuit of nuclear reactors and passive safety systems. However, available models fail to fully capture the physics of turbulent mixing when buoyancy becomes predominant with respect to momentum. Therefore, high-fidelity experiments of well-controlled fundamental flows are needed to develop and validate more accurate models. We analyze experiments of positive and negative turbulent buoyant jets, both in uniform and stratified environments, with the aim of understanding the thermal hydraulics of turbulent mixing with variable density and providing high-fidelity data for the development and validation of turbulence models. Non-intrusive, simultaneous particle image velocimetry and laser-induced fluorescence measurements were carried out to acquire instantaneous velocity and concentration fields on a vertical section parallel to the axis of a jet in the self-similar region. The refractive index matching method was applied to measure high-resolution buoyant jets with up to 8.6% density difference. These data are free of the typical errors that characterize optical measurements of buoyancy-driven flows (e.g. natural and mixed convection) where the refractive index of the fluid is inhomogeneous throughout the measurement domain. Turbulent statistics and entrainment of buoyant jets in uniform and stratified environments are presented. These data are compared with non-buoyant jets in a uniform environment, as a reference to investigate the effects of buoyancy and stratification on turbulent mixing. The results will be used for the assessment of current turbulence models and as a basis for the development of a new model that captures turbulent mixing.

laser induced fluorescence↗
DOE OSTI2020

Sweeping Jet Film Cooling at High Blowing Ratio on a Turbine Vane

Abstract Experimental and numerical investigations were performed to study the effects of high blowing ratios and high freestream turbulence on sweeping jet film cooling. Experiments were conducted on a nozzle guide vane suction surface in a low-speed linear cascade at a range of blowing ratios of 0.5–3.5 and freestream turbulence of 0.6% and 14.3%. Infrared thermography was used to estimate the adiabatic cooling effectiveness. Thermal field and boundary layer measurements were conducted at a cross-plane at x/D = 12 downstream of the hole exit. Results were compared with a baseline 777-shaped hole and showed that the sweeping jet hole has improved cooling effectiveness at high blowing ratios (M > 1). The thermal field data revealed that the coolant separates from the surface at high blowing ratios for the 777-shaped hole while the coolant remains attached for the sweeping jet hole. Boundary layer measurements further confirmed that due to the sweeping motion of the jet, the effective jet momentum of the sweeping jet hole remains much lower than that of a 777-shaped hole. Thus, the coolant remains closer to the wall even at high blowing ratios. Large Eddy simulations (LES) were performed for both the sweeping jet and 777-shaped hole to evaluate the interaction between the coolant jet and the freestream in the near hole regions. Results showed that 777-shaped hole has a strong jetting at high blowing ratio that originates inside the hole breakout edges thus causing the jet to blow-off from the surface. In contrast, the sweeping jet does not show this behavior due to its internal geometry and flapping motion of the jet.

Engineering↗
DOE OSTI2023

Physics-Driven Convolutional Autoencoder Approach for CFD Data Compressions: Preprint

With the growing size and complexity of turbulent flow models, data compression approaches are of the utmost importance to analyze, visualize, or restart the simulations. Recently, in-situ autoencoder-based compression approaches have been proposed and shown to be effective at producing reduced representations of turbulent flow data. However, these approaches focus solely on training the model using point-wise sample reconstruction losses that do not take advantage of the physical properties of turbulent flows. In this paper, we show that training autoencoders with additional physics-informed regularizations, e.g., enforcing incompressibility and preserving enstrophy, improves the compression model in three ways: (i) the compressed data better conform to known physics for homogeneous isotropic turbulence without negatively impacting point-wise reconstruction quality, (ii) inspection of the gradients of the trained model uncovers changes to the learned compression mapping that can facilitate the use of explainability techniques, and (iii) as a performance byproduct, training losses are shown to converge up to 12x faster than the baseline model.

auto-encoders↗
DOE OSTI2021

A new method for measuring the 3D turbulent velocity dispersion of molecular clouds

ABSTRACT The structure and star formation activity of a molecular cloud are fundamentally linked to its internal turbulence. However, accurately measuring the turbulent velocity dispersion is challenging due to projection effects and observational limitations, such as telescope resolution, particularly for clouds that include non-turbulent motions, such as large-scale rotation. Here, we develop a new method to recover the 3D turbulent velocity dispersion (σv,3D) from position–position–velocity (PPV) data. We simulate a rotating, turbulent, collapsing molecular cloud, and compare its intrinsic σv,3D with three different measures of the velocity dispersion accessible in PPV space: (1) the spatial mean of the 2nd-moment map, σi, (2) the standard deviation of the gradient/rotation-corrected 1st-moment map, σ(c − grad), and (3) a combination of (1) and (2), called the ‘gradient-corrected parent velocity dispersion’, $\sigma _{\mathrm{(p}-\mathrm{grad)}}=(\sigma _{\mathrm{i}}^2+\sigma _{(\mathrm{c}-\mathrm{grad)}}^2)^{1/2}$. We show that the gradient correction is crucial in order to recover purely turbulent motions of the cloud, independent of the orientation of the cloud with respect to the line of sight. We find that with a suitable correction factor and appropriate filters applied to the moment maps, all three statistics can be used to recover σv,3D, with method 3 being the most robust and reliable. We determine the correction factor as a function of the telescope beam size for different levels of cloud rotation, and find that for a beam full width at half-maximum f and cloud radius R, the 3D turbulent velocity dispersion can best be recovered from the gradient-corrected parent velocity dispersion via $\sigma _{v,\mathrm{3D}}= \left[(-0.29\pm 0.26)\, f/R + 1.93 \pm 0.15\right] \sigma _{\mathrm{(p}-\mathrm{grad)}}$ for f/R < 1, independent of the level of cloud rotation or LOS orientation.

Stewart, Madeleine↗
DOE OSTI2020

Development of a Comprehensive Two-Phase Flow Database for the Validation of NEK-2P

Three-dimensional (3-D) two-phase Computational Fluid Dynamics (CFD) codes are emerging as a powerful and potentially practical tool for applications in which detailed local flow information is needed. However, two-phase flow models and associated closure relations are not well established for CFD applications, which is partly due to the lack of high-quality validation data. The main objective of this work is to develop a comprehensive database of two-phase flows that can be used to validate two-phase CFD codes such as NEK-2P. In this project, four advanced local measurement systems, including Particle Image Velocimetry and Planar Laser-Induced Fluorescence (PIV-PLIF), high-speed imaging, x-ray densitometry, and multi-sensor conductivity probe are employed to measure the local two-phase flow parameters of both gas and liquid phases. By combining these techniques, the local void fraction, bubble velocity, interfacial area concentration, bubble frequency, liquid velocity, turbulence intensity, etc., in various two-phase flow regimes can be obtained. These local measurement techniques are first used in a 25.4 mm circular pipe test section. Seven air-water two-phase flow conditions spanning the bubbly, slug, churn-turbulent, and annular flow regimes are measured in this facility. The obtained database contains the radial profiles of both gas- and liquid-phase parameters at three axial locations along the test section. The second facility used in this work contains a 30 mm × 10 mm rectangular test section, in which three two-phase flow and two single-phase flow conditions are measured. Two-dimensional distributions of local two-phase flow parameters in the cross-sectional plane are measured in this facility at three axial locations as well. A facility featuring a 3×3 electrically heated rod bundle is also designed and being constructed in this project. This facility is specially designed for optical measurements and is expected to provide high-quality boiling data in the future. Preliminary analyses have been performed for the data taken in the 25.4 mm circular pipe. Both center-peaked and wall-peaked void fraction profiles have been observed in the data depending on the two-phase flow conditions and/or developing lengths. The 1-D drift-flux model was evaluated with the newly obtained datasets, in which both gas- and liquid-phases data were directly measured. The distribution parameter model has been optimized based on a new void-profile classification method proposed in this study. The optimized drift-flux model shows a significant improvement in predicting both gas velocity and void fraction. The measured liquid-phase turbulence was used to benchmark Sato’s turbulence model considering the bubble-induced shear stress for the three tested bubbly flows. The benchmark results showed good agreement between the PIV measurements and model predictions. In the bubbly flows tested that have low void fractions less than 3%, the effect of the bubble-induced turbulence was found not significant. However, the bubble-induced shear stress becomes important with the increase of the void fraction. The Conjugate Heat Transfer (CHT) model was developed and implemented in NEK-2P. This model allows the coupled simulation of the solid domain and two-phase fluid domain, allowing the specification of realistic boundary conditions. The CHT implementation was verified first with non-boiling simulations. The predicted temperatures in the fluid domain were shown to be identical in simulations with or without the CHT model. The CHT model was then validated through simulations of three Becker benchmark CHF tests performed under both Dryout (DO) and Departure from Nucleate Boiling (DNB) conditions. Reasonably good agreement was obtained between calculated wall temperatures and corresponding experimental data.

42 ENGINEERING↗
DOE OSTI2020

Liquid-phase turbulence measurements in air-water two-phase flows using particle image velocimetry

Liquid-phase turbulence plays a vital role in determining various gas-liquid two-phase flow parameters, such as void fraction distribution, bubble morphology, bubble-bubble interactions, and interfacial area concentration. In this study, a two-phase flow database including both the gas- and liquid-phases measurements was developed focusing on three bubbly flow conditions in an air-water two-phase flow loop with a vertical one-inch diameter circular pipe test section. A particle image velocimetry (PIV) system integrating an optical phase separation method, i.e., the planar laser-induced fluorescence (PLIF) technique using fluorescent particles and optical filtration, was applied to measure the liquid-phase turbulence information, including the time-averaged velocity, Reynolds stress, and turbulent kinetic energy for the liquid phase. The PIV measurements were taken at three ports along the test section at 14.5, 51.5, and 88.5 pipe inner diameters downstream of a bubble injector. In addition, a double-sensor conductivity probe was used to measure radial distributions of the local time-averaged void fraction and gas velocity. The measured liquid-phase turbulence was used to benchmark Sato's turbulence model considering the bubble-induced shear stress for the three tested bubbly flows. The benchmark results showed good agreement between the PIV measurements and model predictions. Lastly, in the two bubbly flows tested that have low void fractions being less than 3%, the effect of the bubble-induced turbulence was found not significant. However, the bubble-induced shear stress becomes important with the increase of the void fraction.

42 ENGINEERING↗
DOE OSTI2020

A new mechanism for filament disconnection at the X-point: poloidal shear in radial E × B velocity

Plasma filaments generated by turbulence in the scrape-off layer are sometimes observed in experiments and simulations to disconnect from the target plate in the vicinity of the X-point, resulting in a ‘quiescent zone’ with reduced fluctuations, possibly affecting the fluctuating part of the divertor heat loads. This phenomena is usually explained by the flux tubes squeezing, induced by flux expansion, down to scales where collisions dominate. In this work, we consider an additional mechanism spontaneously arising at the X-point: the poloidal shear in radial E × B velocity. Through a simple model, tested against 3D global turbulence simulations, herein we quantify the effectiveness of this disconnection mechanism and identify ways to control it.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Deuterium and tritium anomalous transport in the generalized Hasegawa–Wakatani resistive drift wave turbulence model with finite ion Larmor radius

Anomalous transport of mixed deuterium–tritium plasma in the edge of magnetic fusion reactors is investigated using numerical solutions of resistive drift wave turbulence model equations, including finite Larmor radius effects, that are derived within the generalized Hasegawa–Wakatani framework. The anomalous cross field diffusivities of deuterium and tritium are compared in turbulence regimes with different values of the electron adiabaticity parameter controlling the existence of zonal flow. The dependence of the tritium-to-deuterium diffusivity ratio on the deuterium and tritium densities and the logarithmic density gradients is analyzed, and a scaling relation is obtained.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Parasitic Modulation of Microwave Signals by a Hypersonic Plasma Layer

During hypersonic flight, compressional and viscous heating of the air can form a plasma layer which encases the aircraft. If the boundary layer becomes turbulent, then the electron density fluctuations can effect a parasitic modulation in microwave signals transmitted through the plasma. We developed an approach for studying the interaction of microwave signals with a turbulent, hypersonic plasma layer. The approach affords a great deal of flexibility in both the plasma layer model and the antenna configuration. We then analyzed a situation in which microwaves, transmitted from a rectangular aperture antenna, propagate through a turbulent plasma layer to a distant receiver. We characterized the first-and second-order statistics of the computed parasitic modulation and quantified the depolarization of the signal. The amplitude fluctuations are lognormally distributed at low frequencies and Rice-distributed at high frequencies. Fluctuations in the copolarized phase and amplitude of the far-field signal are strongly anticorrelated. Here, we used a multioutput Gaussian process (MOGP) to model these quantities. The efficacy of the MOGP model is demonstrated by recovering the time evolution of the copolarized phase given the copolarized amplitude and occasional measurements of the phase.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Numerical study to predict the effect of surface roughness on the thermal and hydraulic performance of additively manufactured heat exchangers

Heat exchangers are used in many industries to transfer thermal energy between two or more objects with an associated thermal and hydraulic performance indicated by thermal effectiveness and pressure drop respectively. Many investigations have aimed to enhance the thermal effectiveness of heat exchangers by introducing turbulent flow inducers that increase the heat transfer rate at the expense of increasing pressure drop. Flow inducers like surface roughness can be controlled with advanced manufacturing methods like additive manufacturing for heat exchanger production. Selecting and manufacturing an optimal surface roughness for heat exchangers requires a more comprehensive approach that accounts for the surface roughness effect on the thermal and hydraulic performance of a sample. Since fabricating samples with additive manufacturing to a desired surface roughness can be an extensive experimental process, this study will fundamentally investigate the effect of surface roughness on the thermal and velocity boundary layers for various surface roughness profiles with physics-based computational modeling. To accurately model the surface roughness effect on thermohydraulic performance, correlations like roughness ratio, friction factor, and Nusselt number are investigated. This study expects to indicate correlations for different flow regimes which can successfully predict the effect of surface roughness on thermohydraulic performance. Results generated from modeling surface roughness effect with unique correlations are then compared to experimental data obtained from literature for validation. The results of this study will provide insight to understand the thermal fluid physics associated with surface roughness and design guidelines for heat exchangers produced with additive manufacturing.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Impact of particle size and particle-flow-wall coupling on pressurized oxy-combustion in the down-fired burner

Concerns over climate change have led to numerous efforts in developing low-carbon energy technologies. Pressurized oxy-combustion (POC) is a promising candidate to reduce carbon emissions in power generation. Designing an effective burner plays a vital role in developing new coal combustion technologies. Because of the high pressure, the volume fraction of coal particles at the fuel inlet of the burner of a pressurized oxy-combustor is close or even higher than the maximum limit that commercial CFD codes (e.g., ANSYS FLUENT) can handle. At this high particle volume fraction, the interactions among particles, fluid flow, and wall need to be re-evaluated. The present computational work is the first step of a systematic analysis of the particle influence, like releasing method, releasing locating, and particle size, in a pilot-scale POC combustor, developed at Washington University in St. Louis (WUSTL). In a POC process, pulverized coal is burned under elevated pressure and O2-CO2 environment. Specifically, a 15-bar, 100 kWth, POC combustor is modeled employing ANSYS FLUENT, using Reynolds-averaged Navier-Stokes (RANS) modeling. It is revealed that for this pilot-scale, pressurized burner, velocity profiles of the near-wall region in this POC facility exhibit some discrepancy against the near-wall turbulent flow velocity profile. In order to investigate the particle influence in the near-wall region, particle releasing location will be investigated. Numerical simulation results exhibit the coupling effect of turbulence flow and particles in this case. The particle size also demonstrates a great effect on particle trajectory, then further has an impact on flame stability and temperature.

Li, Lei↗
DOE OSTI2024

Phase-space entropy cascade and irreversibility of stochastic heating in nearly collisionless plasma turbulence

We consider a nearly collisionless plasma consisting of a species of “test particles” in one spatial and one velocity dimension, stirred by an externally imposed stochastic electric field—a kinetic analog of the Kraichnan model of passive advection. The mean effect on the particle distribution function is turbulent diffusion in velocity space—known as stochastic heating. Accompanying this heating is the generation of fine-scale structure in the distribution function, which we characterize with the collisionless (Casimir) invariant C 2 ∝ ∫ ∫ d x d v 〈 f 2 〉 —a quantity that here plays the role of (negative) entropy of the distribution function. We find that C 2 is transferred from large scales to small scales in both position and velocity space via a phase-space cascade enabled by both particle streaming and nonlinear interactions between particles and the stochastic electric field. We compute the steady-state fluxes and spectrum of C 2 in Fourier space, with k and s denoting spatial and velocity wave numbers, respectively. In our model, the nonlinearity in the evolution equation for the spectrum turns into a fractional Laplacian operator in k space, leading to anomalous diffusion. Whereas even the linear phase mixing alone would lead to a constant flux of C 2 to high s (towards the collisional dissipation range) at every k , the nonlinearity accelerates this cascade by intertwining velocity and position space so that the flux of C 2 is to both high k and high s simultaneously. Integrating over velocity (spatial) wave numbers, the k -space ( s -space) flux of C 2 is constant down to a dissipation length (velocity) scale that tends to zero as the collision frequency does, even though the rate of collisional dissipation remains finite. The resulting spectrum in the inertial range is a self-similar function in the ( k , s ) plane, with power-law asymptotics at large k and s . Our model is fully analytically solvable, but the asymptotic scalings of the spectrum can also be found via a simple phenomenological theory whose key assumption is that the cascade is governed by a “critical balance” in phase space between the linear and nonlinear timescales. We argue that stochastic heating is made irreversible by this entropy cascade and that, while collisional dissipation accessed via phase mixing occurs only at small spatial scales rather than at every scale as it would in a linear system, the cascade makes phase mixing even more effective overall in the nonlinear regime than in the linear one. Published by the American Physical Society 2024

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗