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DOE OSTI2020

Learning how structures form in drift-wave turbulence

Drift-wave turbulence produces anomalous transport via cross-correlations between fluctuations. This transport has profound implications for confinement, structure formation, and virtually all aspects of the non-linear turbulent dynamics. Herein, we use a data-driven method based on deep learning in order to study turbulent transport in the 2D Hasegawa–Wakatani system and infer a reduced mean-field model from numerical solution. In addition to the usual turbulent diffusion, we find an effect which couples the particle flux to the local gradient of vorticity, which tends to modulate the density profile. The direct coupling to the shear is relatively weak. In addition, the deep learning method finds a model for spontaneous zonal flow generation by negative viscosity, stabilized by non-linear and hyperviscous terms. We compare these results to analytic calculations using quasilinear theory and wave kinetics, finding qualitative agreement, though the calculations miss certain higher-order effects. A simplified, 1-D model for the evolution of the profile, flow, and intensity based on the deep learning results is solved numerically and compared to previous models for staircasing based on bistability. We see that the physics uncovered by the deep learning method provided simple explanations for the formation of zonal structures in the density, flow, and turbulence fields. We highlight the important role of symmetry in the deep learning method and speculate on the portability of the method to other applications.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Measuring the Effects of Wake Steering With Nacelle-Mounted Scanning Lidar

In large wind plants, wakes from upwind turbines affect downwind turbines by reducing wind speeds and increasing turbulence. Wake steering may mitigate this effect by deflecting the wakes of upwind turbines away from downwind units. Here, we characterize the impact of wakes from yawed turbines at a commercial-scale wind plant under varying atmospheric and turbine operating conditions. Six months of nacelle-based lidar measurements were collected as part of a field campaign in 2019-2020 in the northern US Great Plains to test the effectiveness of wake steering. We separate these lidar scans by atmospheric stability and turbine operating condition to summarize how yawed wind turbine wakes vary with these input parameters in the atmospheric boundary layer. We summarize the impact of wake steering on various wake characteristics including velocity deficit, wake width, and wake center as retrieved from these lidar data. Yawed wakes have significantly different centerline characteristics compared to unyawed wakes, with large regions of meander in the mid wake region. Yawed wakes are also deflected farther than unyawed wakes in less turbulent conditions with velocity deficits persisting further downstream in stable atmospheric conditions. Overall, yawed wind turbine wakes are larger and wider in lower wind speed environments, and yawed wakes are deflected farther in less turbulent conditions, suggesting that wake steering is most effective in stable atmospheric stratification.

17 WIND ENERGY↗

DOE OSTI2020

Conservative discontinuous Galerkin scheme of a gyro-averaged Dougherty collision operator

Here, a conservative discontinuous Galerkin scheme for a non-linear Dougherty collision operator in full-f long-wavelength gyrokinetics is presented. Analytically this model operator has the advective-diffusive form of Fokker-Planck operators, it has a non-decreasing entropy functional, and conserves particles, momentum and energy. Discretely these conservative properties are maintained exactly as well, independent of numerical resolution. In this work the phase space discretization is performed using a novel version of the discontinuous Galerkin scheme, carefully constructed using concepts of weak equality and recovery. Discrete time advancement is carried out with an explicit time-stepping algorithm, whose stability limits we explore. The formulation and implementation within the long-wavelength gyrokinetic solver of Gkeyll are validated with relaxation tests, collisional Landau-damping benchmarks and the study of 5D gyrokinetic turbulence on helical, open field lines.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Turbulence model reduction by deep learning

A defining problem of turbulence theory is to produce a predictive model for turbulent fluxes. These have profound implications for virtually all aspects of the turbulence dynamics. In magnetic confinement devices, drift-wave turbulence produces anomalous fluxes via cross-correlations between fluctuations. In this work, we introduce an alternative, data-driven method for parametrizing these fluxes. The method uses deep supervised learning to infer a reduced mean-field model from a set of numerical simulations. We apply the method to a simple drift-wave turbulence system and find a significant new effect which couples the particle flux to the local gradient of vorticity. Notably, here, this effect is much stronger than the oft-invoked shear suppression effect. We also recover the result via a simple calculation. The vorticity gradient effect tends to modulate the density profile. In addition, our method recovers a model for spontaneous zonal flow generation by negative viscosity, stabilized by nonlinear and hyperviscous terms. We highlight the important role of symmetry to implementation of the new method.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Two-Phase Turbulence Statistics from High Fidelity Dispersed Droplet Flow Simulations in a Pressurized Water Reactor (PWR) Sub-Channel with Mixing Vanes

In the dispersed flow film boiling regime (DFFB), which exists under post-LOCA (loss-of-coolant accident) conditions in pressurized water reactors (PWRs), there is a complex interplay between droplet dynamics and turbulence in the surrounding steam. Experiments have accredited particular significance to droplet collision with the spacer-grids and mixing vane structures and their consequent positive feedback to the heat transfer recorded in the immediate downstream vicinity. Enabled by high-performance computing (HPC) systems and a massively parallel finite element-based flow solver—PHASTA (Parallel Hierarchic Adaptive Stabilized Transient Analysis)—this work presents high fidelity interface capturing, two-phase, adiabatic simulations in a PWR sub-channel with spacer grids and mixing vanes. Selected flow conditions for the simulations are informed by the experimental data found in the literature, including the steam Reynolds number and collision Weber number (Wec={40,80}), and are characteristic of the DFFB regime. Data were collected from the simulations at an unprecedented resolution, which provides detailed insights into the continuous phase turbulence statistics, highlighting the effects of the presence of droplets and the comparative effect of different Weber numbers on turbulence in the surrounding steam. Further, axial evolution of droplet dynamics was analyzed through cross-sectionally averaged quantities, including droplet volume, surface area and Sauter mean diameter (SMD). The downstream SMD values agree well with the existing empirical correlations for the selected range of Wec. The high-resolution data repository from the simulations herein is expected to be of significance to guide model development for system-level thermal hydraulic codes.

Saini, Nadish↗

DOE OSTI2022

Subcell limiting strategies for discontinuous Galerkin spectral element methods

Here, we present a general family of subcell limiting strategies to construct robust high-order accurate nodal discontinuous Galerkin (DG) schemes. The main strategy is to construct compatible low order finite volume (FV) type discretizations that allow for convex blending with the high-order variant with the goal of guaranteeing additional properties, such as bounds on physical quantities and/or guaranteed entropy dissipation. For an implementation of this main strategy, four main ingredients are identified that may be combined in a flexible manner: (i) a nodal high-order DG method on Legendre–Gauss–Lobatto nodes, (ii) a compatible robust subcell FV scheme, (iii) a convex combination strategy for the two schemes, which can be element-wise or subcell-wise, and (iv) a strategy to compute the convex blending factors, which can be either based on heuristic troubled-cell indicators, or using ideas from flux-corrected transport methods. By carefully designing the metric terms of the subcell FV method, the resulting methods can be used on unstructured curvilinear meshes, are locally conservative, can handle strong shocks efficiently while directly guaranteeing physical bounds on quantities such as density, pressure or entropy. We further show that it is possible to choose the four ingredients to recover existing methods such as a provably entropy dissipative subcell shock-capturing approach or a sparse invariant domain preserving approach. We test the versatility of the presented strategies and mix and match the four ingredients to solve challenging simulation setups, such as the KPP problem (a hyperbolic conservation law with non-convex flux function), turbulent and hypersonic Euler simulations, and MHD problems featuring shocks and turbulence.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

A Comparison of Adverse Meteorology Inputs for Emergency Management and Safety Basis Dispersion Modeling Applications at SRS

The MELCOR Accident Consequence Calculation System (MACCS), used for safety basis accident analyses at SRS, implements adjustment factors to consider the increased vertical turbulence associated with local surface roughness and the increased lateral turbulence associated with time-based plume meander. The two models used for SRS emergency planning radiological consequence assessment, i.e., Hotspot and Puff/Plume, currently do not have an option to input or apply diffusion adjustments for meander or surface roughness. Adverse meteorology conditions at SRS have been determined as E stability class and 1.3 meters per second wind speed for ground level releases. This is the input used for emergency planning models. Contrastingly safety basis analyses use a different input, representing adverse meteorology values as F stability class and wind speeds of 1.3 meters per second (for a ground level release). This results in an apparent discrepancy between the two approaches. In this report we document the differing modeling assumptions, discuss the logic behind each modeling approach used to represent local roughness and plume meander conditions, and numerically compare dispersion coefficients and concentration estimates obtained from each set of model inputs.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

New insights on wind turbine wakes from large‐eddy simulation: Wake contraction, dual nature, and temperature effects

Abstract Large‐eddy simulation (LES) has been adopted to study wind turbine wakes because it can capture fine‐scale details of turbulent wind flows and interactions with wind turbines. Here, we use the LES version of the Weather Research and Forecasting (WRF) model with an actuator disk model to gain insights on several wake effects that have been traditionally difficult to measure. The first finding is that the wake has a “dual nature,” meaning that the wind speed deficit behaves differently from the added turbulent kinetic energy (TKE) and the two are not co‐located in space. For example, the wind speed deficit peaks at hub height and reaches the ground within 8D (D is the rotor diameter), but added TKE peaks near the rotor tip and generally remains aloft. Second, temperature changes near the ground are driven by the added TKE in the rotor area and by atmospheric stability. The combination of these two factors determines the sign and intensity of the vertical heat flux divergence below the rotor, with convergence and warming associated with stable conditions and weak divergence and modest cooling with unstable conditions. Third, wakes do not expand indefinitely, as suggested by similarity theory applied to the wind speed deficit, but eventually stop expanding and actually contract, at different rates depending on atmospheric stability. The implication of these findings is that, in order to study wakes, it is not sufficient to focus on wind speed deficit alone, because TKE is also important and yet behaves differently from the wind speed deficit.

17 WIND ENERGY↗

DOE OSTI2021

Study of Stratus-Lowering Marine-Fog Events Observed During C-FOG

Two stratus lowering marine fog events observed on 28 September and 04 October 2018 during the Coastal Fog (C-Fog) field campaign that took place offshore of Eastern Canada during 1 September to 6 October 2018 are described. In-situ, profiling and remote sensing observations were made at selected land sites in eastern Newfoundland (NL) and Nova Scotia (NS) as well as aboard the research vessel (R/V) Hugh R. Sharp that cruised in adjoining coastal waters. Synoptic scale analysis showed that both fog episodes were an outcome of the interaction between synoptic-scale surface level low-pressure systems and a contiguous high-pressure system. At the same time, back trajectories revealed that the bulk of the fog layer is formed due to differential advection. Here, the diameter of the fog droplets at the surface gradually decreased from the centre of the fog layer to its leading/trailing edges. The bimodal fog droplet diameter distribution with peaks at 5-10 µm and 20-25 µm provided clues on droplet collision and coalescence processes. The observed difference between microphysical variables and droplet distribution between the two fog events and within same fog layer may have been governed by atmospheric boundary layer conditions (e.g., humidity conditions and turbulence) prevailed in the fog layer. Overall, it is concluded that the life cycle of observed stratus-lowering coastal-fog episodes is dependent on synoptic conditions as well as atmospheric boundary layer characteristics such as stability, cloud top cooling and entrainment.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

On the role of ion temperature gradient turbulence in driving ion thermal transport in neutral beam injection-heated L-mode plasmas in a superconducting tokamak

In this paper, we report a detailed experimental study of the role of ion-temperature-gradient driven turbulence in driving ion thermal transport in neutral beam injection (NBI)-heated L-mode plasmas in Experimental Advanced Superconducting Tokamak (EAST) (Wan et al 2000 Nucl. Fusion 40 1057) coupled with linear and nonlinear gyrokinetic simulations. Significant ion-scale turbulence k ⟂ < cm −1 (k ⟂ < 1.5, where k ⟂ where is the perpendicular wavenumber and ρ s is the ion gyroradius calculated using local electron temperature T e ), measured with a microwave reflectometer, is observed in the plasma core at for r/a ≈ 0.265 and 0.5 (where r is half the diameter of the closed flux surface at a given radial position, and a is half the diameter of the last closed flux surface). Local linear stability analysis with experimental equilibrium quantities at these two radial locations using the GS2 gyrokinetic code shows that the most unstable ion-scale micro-instability is the ion temperature gradient (ITG) mode. Since the computed maximum ion-scale linear growth rates are larger than the local Waltz-Miller E × B shearing rate (Waltz and Miller 1999 Phys. Plasmas 6 4265), the E × B shear is unable to suppress ion-scale turbulence, consistent with the experimental observation of ion-scale turbulence. Experimental ion and electron thermal transports, calculated with power balance analysis, are both anomalous with ion thermal transport being the dominant channel. Nonlinear gyrokinetic simulations using the electrostatic global particle-in-cell gyrokinetic tokamak simulation (GTS) code (Weixing Wang et al 2010 Phys. Plasmas 17 072511) show good quantitative agreement between predicted ion thermal transport and that from the power balance analysis. These results demonstrate for the first time the important role of ITG turbulence in driving thermal transport in NBI-heated L-mode plasmas in EAST, showing the effectiveness of GTS code in simulating electrostatic turbulence in EAST and the need of suppressing ITG turbulence to improve energy confinement in EAST.

Sun, P. J. [Chinese Academy of Sciences (CAS), Hef↗

DOE OSTI2022

Machine Learning for Improving Surface-Layer-Flux Estimates

Abstract Flows in the atmospheric boundary layer are turbulent, characterized by a large Reynolds number, the existence of a roughness sublayer and the absence of a well-defined viscous layer. Exchanges with the surface are therefore dominated by turbulent fluxes. In numerical models for atmospheric flows, turbulent fluxes must be specified at the surface; however, surface fluxes are not known a priori and therefore must be parametrized. Atmospheric flow models, including global circulation, limited area models, and large-eddy simulation, employ Monin–Obukhov similarity theory (MOST) to parametrize surface fluxes. The MOST approach is a semi-empirical formulation that accounts for atmospheric stability effects through universal stability functions. The stability functions are determined based on limited observations using simple regression as a function of the non-dimensional stability parameter representing a ratio of distance from the surface and the Obukhov length scale (Obukhov in Trudy Inst Theor Geofiz AN SSSR 1:95–115, 1946), $$z/L$$ z / L . However, simple regression cannot capture the relationship between governing parameters and surface-layer structure under the wide range of conditions to which MOST is commonly applied. We therefore develop, train, and test two machine-learning models, an artificial neural network (ANN) and random forest (RF), to estimate surface fluxes of momentum, sensible heat, and moisture based on surface and near-surface observations. To train and test these machine-learning algorithms, we use several years of observations from the Cabauw mast in the Netherlands and from the National Oceanic and Atmospheric Administration’s Field Research Division tower in Idaho. The RF and ANN models outperform MOST. Even when we train the RF and ANN on one set of data and apply them to the second set, they provide more accurate estimates of all of the fluxes compared to MOST. Estimates of sensible heat and moisture fluxes are significantly improved, and model interpretability techniques highlight the logical physical relationships we expect in surface-layer processes.

Meteorology & Atmospheric Sciences↗

DOE OSTI2020

How Should Machine Learning Be Successfully Used for Wind Speed Vertical Extrapolation?

An accurate characterization of the wind resource available at hub-height is required for an efficient and bankable wind farm project. However, direct measurement of wind speed at the constantly increasing height of the hub of commercial wind turbines is oftentimes challenging and expensive, so that it is common practice to vertically extrapolate the wind resource from lower and more easily accessible levels. Conventional techniques for wind speed vertical extrapolation include the use of a power law and a logarithmic profile. While simple, the limits in accuracy of these methods have been shown in various studies. Recently, machine learning has been proposed as a new method to vertically extrapolate winds. All the published studies on the topic assess the performance of machine learning techniques in vertically extrapolating the wind resource at the same location where the algorithm has been trained. However, in real-world applications, the wind resource is measured at the instrument location, but it then needs to be extrapolated at hub height at the location of the wind turbines within the find farm. To be able to fully recommend the use of machine learning techniques over the simple power law and logarithmic law, the spatial variability of the performance improvements of the machine learning approaches needs to be assessed. Here, we propose a round-robin validation of a machine learning-based method for wind speed extrapolation. We use 20 months of observations at four locations spanning a 100 km wide region at the Southern Great Plains (SGP) atmospheric observatory, in north-central Oklahoma. At each location, we train a random forest to predict 30-min average wind speed at 143 m AGL. We use as input features lidar wind speed at 65 m AGL, time of day, sonic anemometer wind speed at 4 m AGL, turbulent kinetic energy, and Obukhov length. First, we perform a same-site comparison of the performance of the proposed random forest against the conventional techniques for wind speed extrapolation (namely power law and logarithmic profile, with widely accepted stability corrections). We find that the random forest outperforms the power law in vertically extrapolating wind speed in all the considered stability regimes, with a 33% reduction in MAE for stable conditions, and a 31% reduction in unstable conditions. Similar results are found when comparing predictions of extrapolated winds from the logarithmic profile and the random forest with the observed values. Next, we propose a round-robin validation, to use the random forest trained at each site to extrapolate wind speed at the remaining three sites. We find that the performance of the random forest approach degrades when the algorithm is tested at a site different than the training one. However, even under those circumstances, the machine learning-based approach still outperforms the conventional techniques for wind speed extrapolation, with, on average, a reduction in mean absolute error between 15 and 20% over the conventional methods, with the largest benefits obtained under stable conditions.

Monte Carlo↗

DOE OSTI2026

Investigation of onshore wind farm wake recovery with in situ aircraft measurements during AWAKEN

The share of wind power for electricity supply is increasing worldwide. This highly variable resource requires the improved prediction of power output for network stability. The interaction between wind farm wakes and the atmospheric boundary layer (ABL) introduces uncertainties in power production that warrant detailed investigation. The flow downwind of wind farms is characterized by a reduction in wind speed and an increase in turbulence, which both vary with atmospheric conditions. During the American WAKE experimeNt (AWAKEN), the Technische Universität Braunschweig conducted measurement flights with a research aircraft upwind and downwind of onshore wind farms in the southern Great Plains in Oklahoma in the USA. This study utilizes data from 20 flights conducted at approximately hub height in September 2023 to investigate the wind field variability downwind of the wind farms and vertical profiles to observe atmospheric stratification. The flights were aligned perpendicular to the main wind direction downwind of the King Plains and Armadillo Flats wind farms. Additionally, lidar data from both upwind and downwind ground-based measurement sites and sonic anemometer data were used for comprehensive analysis. Results indicate that under stable ABL conditions, the wake persists at greater downwind distances with a higher velocity deficit in the wake relative to the undisturbed flow compared to unstable stratification. In homogeneous terrain under stable conditions, wake recovery to 95 % occurs between a distance of 4.5 and 9 km downwind of the wind farm. In the semi-complex terrain characterized by shallow hills, slopes, and valleys, the wake exhibits a higher velocity deficit compared to homogeneous terrain, while in some cases the wake was amplified by the terrain resulting in higher velocity deficit 10 km downwind of the wind farm compared to the measurements closer to the wind farm. The turbulent kinetic energy (TKE) and “TKE difference” was found to be a valuable measure in understanding wakes in a semi-complex terrain, showing a clear wake recovery and formation depending on the stratification of the ABL.

17 WIND ENERGY↗

DOE OSTI2020

Scaling Behavior of a Turbulent Kinetic Energy Closure Scheme for the Stably Stratified Atmosphere: A Steady-State Analysis

Abstract We present a turbulent kinetic energy (TKE) closure scheme for the stably stratified atmosphere in which the mixing lengths for momentum and heat are not parameterized in the same manner. The key difference is that, while the mixing length for heat tends toward the stability independent mixing length for momentum in neutrally stratified conditions, it tends toward one based on the Brunt–Väisälä time scale and square root of the TKE in the limit of large stability. This enables a unique steady-state solution for TKE to be obtained, which we demonstrate would otherwise be impossible if the mixing lengths were the same. Despite the model’s relative simplicity, it is shown to perform reasonably well with observational data from the 1999 Cooperative Atmosphere–Surface Exchange Study (CASES-99) using commonly employed model constants. Analyzing the scaling behavior of the nondimensional velocity and potential temperature gradients, or of the stability (correction) functions, reveals that for large stability the present model scales in the same manner as the first-order operational scheme of Viterbo et al. Alternatively, it appears as a blend of two cases of the TKE closure scheme of Baas et al. Critically, because a unique steady-state TKE can be obtained, the present model avoids the nonphysical behavior identified in one of the cases of Baas et al.

Meteorology & Atmospheric Sciences↗

DOE OSTI2023

A numerical investigation of coal particle modeling for the inlet section of a pressurized oxy-combustion burner

Concerns over climate change have led to numerous efforts to develop low-carbon technologies, and pressurized oxy-combustion (POC) is a promising candidate to reduce carbon emissions in the power industry. Designing an effective burner for such technologies is vital for the development of these and other coal combustion technologies. Because of the high pressure, the volume fraction of coal particles at the fuel inlet of the pressurized oxy-combustor burner is close to or even higher than the maximum limit for commercial CFD codes (e.g., ANSYS FLUENT). At these high particle volume fractions, the interactions among particles, fluid flow and wall need to be re-evaluated. The present computational work is a first step in a systematic analysis of the influence of various parameters, like method of particle release, release location, and particle size, in a pilot-scale POC combustor, developed at Washington University in St. Louis (WUSTL). In the POC process, pulverized coal is burned under elevated pressure in an O2-CO2 environment. Specifically, a 15-bar, 100 kWth, POC combustor is modeled employing Ansys FLUENT commercial sodtware using the Reynolds-Averaged Navier-Stokes (RANS) approach. It is revealed that for this pilot-scale, pressurized burner, velocity profiles in the near-wall region exhibit some anomalies. In order to investigate the influence of particle loading in the near-wall region, particle release location was investigated. The numerical simulations incorporate the coupling between the turbulent flow and the particles. A sensitivity investigation of particle release location found that by tuning the release location, the velocity profile can be consistent with the pure gas flow velocity profile. More importantly, the particle releasing location also affects flame stability. Particle size was also found to have a significant impact on particle trajectory, flame stability and temperature. Finally, Large Eddy Simulations (LES) were performed and compared with the results from two-dimensional RANS.

Li, Lei↗

DOE OSTI2022

Hybrid large-eddy simulation with adaptive downstream anisotropic eddy viscosity model

Turbulence pervades most flows of engineering interest, and its prediction remains a challenge on both accuracy and cost. One promising predictive approach that reduces cost combines large-eddy simulation (LES) with simulation based on Reynolds averaged Navier–Stokes equations (RANS). This study presents a method to overcome stability and accuracy issues associated with these hybrid LES-RANS methods. The method developed involves extracting the Reynolds stresses from the upstream LES solution and then using that information to convert the downstream RANS model from a scalar eddy-viscosity model to an anisotropic nonlinear eddy-viscosity model. The method developed differs from the downstream tensorial eddy-viscosity model by being independent of the coordinate system. The method developed was evaluated by computing film cooling of a flat plate with the coolant injected through one row of circular holes. Results obtained show instabilities at the LES-to-RANS interface to be eliminated. Also, the method developed yielded solutions that compare reasonably well with those from LES, even though a significant portion of the flow is computed by the adapted anisotropic RANS model instead of LES, which significantly reduced the number of grid points and computational time needed. Since modification of the downstream RANS model is based on information extracted from the upstream LES solution, the method developed is adaptive to the problem being studied.

42 ENGINEERING↗

DOE OSTI2022

A two-fluid single-column model of turbulent shallow convection. Part II: Single-column model formulation and numerics

The two-fluid single-column model of Thuburn et al. (Quart. J. R. Meteorol. Soc., 2019, 145, 1535–1550) is extended to include moisture and horizontal wind shear. Turbulent kinetic energy is introduced as a prognostic variable, dependence on a diagnosed boundary-layer height is removed, and subfilter fluxes are approximated using a two-fluid version of a Mellor–Yamada scheme. Three mechanisms for entrainment and detrainment processes are introduced, which represent entrainment of unstable air at the surface, forced detrainment of air at the top of the boundary/cloud layers, and turbulent mixing that relaxes the convective fluid to a reference profile. A semi-implicit Eulerian discretization replaces the semi-implicit semi-Lagrangian implementation of Thuburn et al. (Quart. J. R. Meteorol. Soc., 2019, 145, 1535–1550) to improve numerical stability and conservation. The equations for the implicit time step are solved using a quasi-Newton method, which is shown to perform well in numerical tests for conservation and convergence. The two-fluid single-column model presented in this article will be applied to simulations of shallow cumulus convection in Part III.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Stable and unstable supersonic stagnation of an axisymmetric rotating magnetized plasma

The Naval Research Laboratory ‘Mag Noh problem’, described in this paper, is a self-similar magnetized implosion flow, which contains a fast magnetohydrodynamic (MHD) outward propagating shock of constant velocity. We generalize the classic Noh ( OSTI Tech. Rep. 577058, 1983) problem to include azimuthal and axial magnetic fields as well as rotation. Our family of ideal MHD solutions is five parametric, each solution having its own self-similarity index, gas gamma, magnetization, the ratio of axial to the azimuthal field and rotation. While the classic Noh problem must have a supersonic implosion velocity to create a shock, our solutions have an interesting three-parametric special case with zero initial velocity in which magnetic tension, instead of implosion flow, creates the shock at $t=0+$ . Our self-similar solutions are indeed realized when we solve the initial value MHD problem with the finite volume MHD code Athena. We numerically investigated the stability of these solutions and found both stable and unstable regions in parameter space. Stable solutions can be used to test the accuracy of numerical codes. Unstable solutions have also been widely used to test how codes reproduce linear growth, transition to turbulence and the practically important effects of mixing. Now we offer a family of unstable solutions featuring all three elements relevant to magnetically driven implosions: convergent flow, magnetic field and a shock wave.

Mechanics↗