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At least 955 records · Page 53

Turbulence kinetic energy budget and conditional sampling of momentum, scalar, and intermittency fluxes in thermally stratified wind farms

A description of the turbulence kinetic energy budget is investigated to understand the dynamics and turbulence energy transfer between the atmospheric boundary layer and large wind farms. The turbulence kinetic energy budget terms are a dominant factor in explaining the energy supply process in wind farms. Large eddy simulations are used to generate the thermally stratified wind turbine array boundary layer, where stable and unstable conditions are considered. The wakes represent a sink of mean kinetic energy, and turbulence transport redistributes energy in the wake region. The energy balance between the budget terms is dependent on the physical location in the wind farm. During the unstable scenario, turbulence is driven by the production, transport, and buoyancy terms. Further, the contribution of the turbulence kinetic energy budget terms is reduced with increasing atmospheric stability, especially above the shear layer, where the mechanical production is the dominant term. Pressure diffusion redistributes the turbulent energy from the streamwise direction into the other components of the normal Reynolds stresses. This distinctive feature of the changing thermal stratification is presented through the quadrant analysis. The momentum ejection and sweep frequencies are both comparable and dominant. The scalar flux shows an increase in the contribution of the negative correlation in the quadrants. The quadrant analysis is extended to account for intermittency based on the pointwise Holder exponents. As a result, positive correlations are dominant in the wake and in higher layers of the domain for both considered cases.

17 WIND ENERGY↗

a priori uncertainty quantification of reacting turbulence closure models using Bayesian neural networks

While many physics-based closure model forms have been posited for the sub-filter scale (SFS) in large eddy simulation (LES), vast amounts of data available from direct numerical simulations (DNS) create opportunities to leverage data-driven modeling techniques. Albeit flexible, data-driven models still depend on the dataset and the functional form of the model chosen. Increased adoption of such models requires reliable uncertainty estimates both in the data-informed and out-of-distribution regimes. Here, in this work, we employ Bayesian neural networks (BNNs) to capture both epistemic and aleatoric uncertainties in a reacting flow model. In particular, we model the filtered progress variable scalar dissipation rate which plays a key role in the dynamics of turbulent premixed flames. We demonstrate that BNN models can provide unique insights about the structure of uncertainty of the data-driven closure models. We also propose a method for the incorporation of out-of-distribution information in a BNN, which can be used for out-of-distribution query detection. The efficacy of the model is demonstrated by a priori evaluation on a dataset consisting of a variety of flame conditions and fuels.

97 MATHEMATICS AND COMPUTING↗

Machine learning assisted modeling of mixing timescale for LES/PDF of high-Karlovitz turbulent premixed combustion

Accurate modeling of mixing in the transported probability density function (PDF) method remains a great challenge, especially for turbulent premixed combustion under extreme conditions such as high Karlovitz number Ka. Recently, a power-law based mixing timescale model was developed for the large-eddy simulations (LES)/PDF modeling of high-Ka number turbulent premixed flames. It is found in this work that the power-law mixing timescale model is highly sensitive to the model parameters. It is thus critically needed to develop accurate calibration of these model parameters. The empirical specification of the model parameters developed in Zhang et. al. is found to be inadequate for accurate modeling of the mixing timescale. Here, machine learning is introduced as an attractive alternative in this work for the specification of the model parameters. A high-Ka number DNS jet flame is used as the training and validation of the machine learning models. The choices of the input parameters are discussed and compared for the machine learning models. The effect of differential molecular diffusion on mixing is examined by including the effect of the Lewis number in the training of the machine learning models. The performance of different machine learning algorithms is compared for the specification of the mixing model parameters. Overall, excellent performance of the machine learning models is observed for assisting the mixing modeling. The feasibility, interpretability, applicability, generality, and portability of using machine learning are discussed in general to provide a perspective on applying data-driven machine learning for turbulent combustion modeling studies.

42 ENGINEERING↗

New Capabilities and Improvements to the High-Order Glenn Flux Reconstruction Code

The Glenn Flux Reconstruction (GFR) code is a computational fluid dynamics (CFD) code under development at NASA Glenn Research Center. GFR is based on the high-order flux reconstruction (FR) method and provides a large-eddy simulation (LES) capability that is both accurate and efficient for complex aeropropulsion flows. Three significant new capabilities have been added to the code that improve its performance and functionality. First, a variety of explicit Runge-Kutta methods, including some with adaptive time stepping, were added to GFR with two methods offering a 33% improvement in time-to-solution. Second, GFR can now utilize fully unstructured, mixed-element meshes to more easily facilitate the grid generation process for complex geometries. Finally, a rotating reference frame capability has been added to GFR for solving rotating turbomachinery problems. A selection of results demonstrating these new capabilities are presented in this work. The Taylor-Green vortex problem is used to verify the new unstructured capability by showing similar accuracy and resolution for all element types. LES of the Turbulent Heat Flux Phase III (THX3) experiment with comparison to another high-order LES code and a popular Reynolds-averaged Navier-Stokes (RANS) code demonstrates the accuracy of the code for complex aeropropulsion flows. Finally, LES of a spacecraft cabin ventilation fan shows the ability of GFR to efficiently establish a fan performance map and identify operating points for further analysis at high orders of accuracy.

High-Order Methods↗

Evaluation of Wall-Modeled Les for Flow Over A Multi-Element Airfoil

We perform wall-modeled large-eddy simulations (WMLES) of turbulent flow over a 30P30N multielement airfoil at various angles of attack to assess its ability to accurately predict lift using an unstructured node-based finite-volume methodology. The flow conditions are based on the experiments reported in Klausmeyer & Lin [NASA /TM-112858]. The oncoming flow Mach number is 0.2, and the stowed chord-based Reynolds number (𝑅𝑒𝑐) is 9 million. The angle of attack (𝛼) is varied between 8◦ and 23◦ with the expected stall angle of around 21◦. The simulated geometry is periodic in the span, thus any three-dimensional effects present in the experiment are ignored. We first analyze the predictions with baseline isotropic and anisotropic grids containing over 16 grid points per boundary-layer thickness. The near-wall streamwise/nominal spacing ratio is 0.4 at the leading/trailing edges of the slat, main element and flap, and 1 elsewhere, and the first wall-normal/nominal spacing ratio is 0.375 over most of the airfoil for the anisotropic grid, while these are unity for the isotropic grid. It is found that the predicted lift and wall pressures, near-wall velocity profiles, and the location of onset of resolved turbulence are sensitive to the near-wall grid anisotropy. Further sensitivities were explored at lower angles of attack by independently varying the streamwise and wall-normal grid anisotropies. The effects of both off-wall and near-wall grid refinement were also quantified. For the grid resolutions used here, our results suggest that the first wall-normal spacing, which coincides with the WMLES exchange location, has a dominant effect on the predictions for this flow configuration.

Computational Fluid Dynamics↗

A Finite Element Method for Compressible and Turbulent Multiphase Flow Instabilities with Heat Transfer

We present a new finite element framework for modeling compressible, turbulent multiphase flows with heat transfer. For two-fluid systems with a free surface, the Volume of Fluid (VOF) method is implemented without the need for interface reconstruction, while turbulence is resolved using a dynamic Vreman large eddy simulation (LES) model. Unlike most two-phase VOF studies, which neglect heat transfer, the present approach incorporates energy transport equations within the VOF formulation to account for heat exchange, an effect particularly important in turbulent flows. Conjugate heat transfer is often challenging in finite volume methods, which require explicit specification of heat fluxes at the solid–fluid interface, limiting accuracy and predictive capability. By contrast, the finite element formulation does not require heat flux inputs, allowing more accurate and robust simulation of heat transfer between solids and fluids. The method is demonstrated through three representative cases. First, a two-fluid instability with a single-mode perturbation is simulated and validated against analytical growth rates. Second, conjugate heat transfer is examined in a high-temperature flow over a cold metal cylinder, with validation performed both quantitatively—via pressure coefficient comparisons with experimental data—and qualitatively using vector field topology. Finally, compressible spray injection and breakup are modeled, demonstrating the ability of the framework to capture interfacial dynamics and atomization under turbulent, high-speed conditions. In the compressible spray injection and breakup case, the results indicate that the finite element formulation achieved higher predictive accuracy and robustness than the finite-volume method. With the same mesh resolution, the FEM reduced the root mean square error (RMSE) and mean absolute percentage error (MAPE) from 6.96 mm and 26.0% (for the FVM) to 4.85 mm and 12.7%, respectively, demonstrating improved accuracy and robustness in capturing interfacial dynamics and heat transfer. The study also introduced vector field topology to visualize and interpret coherent flow structures and instabilities, offering insights beyond conventional scalar-field analyses.

97 MATHEMATICS AND COMPUTING↗

Effect of soot concentration on radiative transport in a 2 m JP-8 pool fire

Hubbard et al. (2024) investigated conjugate heat transfer in a 7.9 m JP-8 pool fire, utilizing both heavily sooting and non-sooting fuel models. Their findings indicated that all models produced pool radiative heat fluxes within the measurement uncertainty for large-scale outdoor experiments. This study aims to further investigate the influence of soot concentration on radiative transport. To this end, Large Eddy Simulations (LES) of a 2 m diameter JP-8 pool fire were conducted, employing four turbulent combustion chemistry models: the Eddy Dissipation Concept (EDC) and three variants of flamelet model. Additionally, three variations of the one-equation subgrid scale turbulence kinetic energy model, and multiple mesh resolutions were utilized. The primary validation metrics were pool radiative heat flux and plume radiative fraction, with simulation data compared to experimental results published by Blanchat et al. (2010). The EDC model produced high soot concentrations near the pool surface, resulting in a significant shielding effect. In contrast, the flamelet combustion model has different kinetic limiters for soot production, leading to soot formation higher in the flame, where it can be more readily oxidized. Flamelet models incorporating both acetylene and benzene contributions to soot growth demonstrated better agreement with experimental data. To assess the sensitivity of pool radiative heat flux to soot mass concentration, we used a one-dimensional approximation over a wide range of soot concentrations and compared it to three-dimensional solutions obtained using Discrete Ordinates. Furthermore, this analysis illustrates the impacts of soot shielding and Turbulence Radiation Interactions (TRI), with TRI emission enhancement factors predicted to be in the range of 3–5 near the edges of the plume.

Computational fluid dynamics↗

Preconditioning of overcast-to-broken cloud transitions by riming in marine cold air outbreaks

Marine cold air outbreaks (CAOs) commonly form overcast cloud decks that transition into broken cloud fields downwind, dramatically altering the local radiation budget. In this study, we investigate the impact of frozen hydrometeors on these transitions. We focus on a CAO case in the NW Atlantic, the location of the multi-year flight campaign ACTIVATE (Aerosol Cloud meTeorology Interactions oVer the western ATlantic Experiment). We use MERRA-2 (Modern-Era Retrospective analysis for Research and Applications, version 2) reanalysis fields to drive large eddy simulations with mixed-phase two-moment microphysics in a Lagrangian framework. We find that transitions are triggered by substantial rain (rainwater paths >25 g m−2), and only simulations that allow for aerosol depletion result in sustained breakups, as observed. Using a range of diagnostic ice nucleating particle concentrations, Ninp, we find that increasing ice progressively accelerates transitions, thus abbreviating the overcast state. Ice particles affect the cloud-topped boundary layer evolution, primarily through riming-related processes prior to substantial rain, leading to (1) a reduction in cloud liquid water, (2) early consumption of cloud condensation nuclei, and (3) early and light precipitation cooling and moistening below cloud. We refer to these three effects collectively as “preconditioning by riming”. Greater boundary layer aerosol concentrations available as cloud condensation nuclei (CCN) delay the onset of substantial rain. However, cloud breakup and low CCN concentration final stages are found to be inevitable in this case, due, primarily, to liquid water path buildup. An ice-modulated cloud transition speed suggests the possibility of a negative cloud–climate feedback. To address prevailing uncertainties in the model representation of mixed-phase processes, the magnitude of ice formation and riming impacts and, thereby, the strength of an associated negative cloud–climate feedback process, requires further observational evaluation by targeting riming hot spots with in situ imaging probes that allow for both the characterization of ice particles and abundance of supercooled droplets.

Marine cold air outbreaks↗

Analysis of direct and indirect noise in a next-generation aviation gas turbine combustor

A large-eddy simulation (LES) of a next-generation combustor is performed to examine effects of this combustor concepts on direct and indirect combustion noise characteristics. Direct noise is computed considering the unsteady heat release predictions while entropy fluctuations in the downstream part of the combustor are used to estimate indirect noise through the transfer function of the outlet nozzle. A low-order acoustic reconstruction technique, which utilizes the Green’s function of the configuration, is developed to compute the acoustics inside the combustor. Comparisons to experimental results are reported, showing the reasonable accuracy of the LES and combustion noise computations. The direct noise spectrum peaks at frequencies around 3 kHz because of the fast timescales associated with the chemical reactions inside the combustor. In addition, the indirect noise is dominant at low frequencies, i.e., less than 400 Hz, because of the characteristics of the entropy spectrum at the outlet nozzle. Further, compared to a conventional rich-quench-lean (RQL) combustor configuration, significant differences in the acoustics are observed, and are explained by two specific technological novelties. Firstly, the direct noise spectrum peaks at significantly higher frequencies due to the combustor’s compactness. Secondly, the entropy inhomogeneties downstream of the combustion region are an order of magnitude smaller in amplitude due to the lack of dilution with cold air. This leads to a significant reduction in the indirect noise amplitude at low frequencies, where it is the dominant source of noise. These results suggest opportunities for advanced combustion technologies to achieve substantial reductions in combustion-related noise.

42 ENGINEERING↗

On the interaction of a wind turbine wake with a conventionally neutral atmospheric boundary layer

In this work, we investigate the dynamics of wind turbine tip-vortex breakdown in a conventionally neutral atmospheric boundary layer (ABL). To this end, high-resolution data are collected from large-eddy simulations of a wind turbine operating within a neutral ABL and studied by means of proper orthogonal decomposition (POD) and Fourier analysis. The high resolution of the generated data in both space and time allows us to gain insight into the tip-vortex breakdown mechanisms by (i) capturing the energy modes of the coherent structures, (ii) studying their contribution to the tip-vortex breakdown through their power spectra functions and mean kinetic energy (MKE) flux, and (iii) analysing the growth rate of each contributing perturbation frequency along tip vortices. Our analysis shows that under a fully turbulent scenario, the growth rate of perturbations along the tip vortices is largest for low wave numbers, i.e. long-wave perturbations. Additionally, the MKE flux reaches its highest value at two diameters downstream of the rotor plane, a behaviour that can be attributed to the coexistence of multiple interacting POD modes, with the streamwise vortex roller mode being the primary contributor to the total MKE flux budget, contributing approximately . Finally, comparisons with a laminar, uniform flow scenario subject to a single-frequency perturbation highlight the differences between the two ambient flow conditions. In the non-turbulent, uniform flow scenario, the growth rate attains its maximum value at a wave number corresponding to the out-of-phase mutual-inductance mechanism, whereas the MKE flux exhibits local minima and maxima along the wake and at different downstream locations depending on the perturbation frequency. Our analyses suggest that the breakdown of the wind turbine tip vortices under a fully turbulent neutral ABL inflow is due to complex interactions across a range of excitation frequencies, in which the mutual-inductance instability may not be the dominant one.

17 WIND ENERGY↗

A priori analysis on deep learning of subgrid-scale parameterizations for Kraichnan turbulence

In the present study, we investigate different data-driven parameterizations for large eddy simulation of two-dimensional turbulence in the a priori settings. These models utilize resolved flow field variables on the coarser grid to estimate the subgrid-scale stresses. We use data-driven closure models based on localized learning that employs a multilayer feedforward artificial neural network with point-to-point mapping and neighboring stencil data mapping, and convolutional neural network fed by data snapshots of the whole domain. The performance of these data-driven closure models is measured through a probability density function and is compared with the dynamic Smagorinksy model (DSM). The quantitative performance is evaluated using the cross-correlation coefficient between the true and predicted stresses. We analyze different frameworks in terms of the amount of training data, selection of input and output features, their characteristics in modeling with accuracy, and training and deployment computational time. We also demonstrate computational gain that can be achieved using the intelligent eddy viscosity model that learns eddy viscosity computed by the DSM instead of subgrid-scale stresses. Here, we detail the hyperparameters optimization of these models using the grid search algorithm.

42 ENGINEERING↗

Scalar Flux Profiles in the Unstable Atmospheric Surface Layer Under the Influence of Large Eddies: Implications for Eddy Covariance Flux Measurements and the Non‐Closure Problem

How convective boundary-layer (CBL) processes modify fluxes of sensible (SH) and latent (LH) heat and CO 2 (F c ) in the atmospheric surface layer (ASL) remains a recalcitrant problem. Here, large eddy simulations for the CBL show that while SH in the ASL decreases linearly with height regardless of soil moisture conditions, LH and F c decrease linearly with height over wet soils but increase with height over dry soils. This varying flux divergence/convergence is regulated by changes in asymmetric flux transport between top-down and bottom-up processes. Such flux divergence and convergence indicate that turbulent fluxes measured in the ASL underestimate and overestimate the “true” surface interfacial fluxes, respectively. While the non-closure of the surface energy balance persists across all soil moisture states, it improves over drier soils due to overestimated LH. The non-closure does not imply that F c is always underestimated; F c can be overestimated over dry soils despite the non-closure issue.

Geology↗

Predictive LES Modeling and Validation of High-Pressure Turbulent Flames and Flashback in Hydrogen-enriched Gas Turbines

The overall objective of this project is to make advances in large-eddy simulation modeling of swirl-flame flashback at elevated pressure, where the reactants can be premixed or stratified, and composed of methane enriched with hydrogen. The modeling effort was conducted with a companion experimental validation effort that focused on high-speed measurements of flashback in a model swirl-flame combustor. The modeling effort focused on the development of manifold-based combustion model for flashback simulations. The main complexity in this configuration comes from the flames’ propagation through a stratified fuel-air mixture along with heat loss near the walls. For this purpose, a non-adiabatic flamelet model was developed and tested using canonical flow configurations. Further, extensive validation in premixed configurations is used to establish the model’s accuracy in capturing heat loss and flame propagation. Finally, the model was tested using the UT flame flashback experiment, and was shown to accurately capture the flame flashback process. The end products from this work are a) a full validated flameout-based approach for modeling flame flashback; b) a complete implementation of the model in the open source OpenFOAM framework, which has been made available to both industry and academia; c) an extensive suite of validation studies performed using the OpenFOAM solver. In addition, new techniques for flame modeling, subfilter modeling of scalars, and simulation of low Mach number flows were developed and tested. In the experimental validation effort, flashback was studied in a premixed and stratified swirl flame by using high-speed imaging diagnostics. Fuels tested included CH 4 enriched with H 2 , with H 2 enrichment up to 84% by volume. These flashback experiments are conducted at pressures ranging from 1 to 5 atm. A swirler-based fuel-injection system was used to create the fuel-air stratification in the radial direction. For the high-pressure measurements, an optically accessible elevated pressure chamber was used. The spatial distribution of the equivalence ratio under non-reacting conditions was characterized using planar laser-induced fluorescence with acetone as the fuel tracer. It was observed that fuel-air pockets were distributed across the mixing tube width, although in an average sense, the fuel-air mixture was radially stratified. The global behavior of upstream flame propagation was investigated for different levels of hydrogen-enrichment. For stratified hydrogen-rich flashback, the propagation path of the flame changed from the inner wall to outer wall, which was induced by the faster chemistry of stoichiometric mixtures that are frequently present near the outer wall. This behavior of hydrogen-rich flashback persists even at elevated pressures up to 5 atm, although the propagation of the flame occurs as a wide flame tongue as opposed to the acute-tipped flame structures present in the atmospheric cases. The end product of the experimental effort is greatly improved knowledge of flashback physics and a unique database that can be used for model validation.

08 HYDROGEN↗

Is There a Scalar Atmospheric Surface Layer Within a Convective Boundary Layer? Implications for Flux Measurements

Top‐down entrainment shapes the vertical gradients of sensible heat, latent heat, and CO 2 fluxes, influencing the interpretation of eddy covariance (EC) measurements in the unstable atmospheric surface layer (ASL). Using large eddy simulations for convective boundary layer flows, we demonstrate that decreased temperature gradients across the entrainment zone increase entrainment fluxes by enhancing the entrainment velocity, amplifying the asymmetry between top‐down and bottom‐up flux contributions. These changes alter scalar flux profiles, causing flux divergence or convergence and leading to the breakdown of the constant flux layer assumption (CFLA) in the ASL. As a result, EC‐measured fluxes either underestimate or overestimate “true” surface fluxes during divergence or convergence phases, contributing to energy balance non‐closure. The varying degrees of the CFLA breakdown are a fundamental cause for the non‐closure issue. These findings highlight the underappreciated role of entrainment in interpreting EC fluxes, addressing non‐closure, and understanding site‐to‐site variability in flux measurements.

eddy covariance fluxes of scalars↗

Steady RANS methodology for calculating pressure drop in an in-line molten salt compact crossflow heat exchanger

We report the development of molten salt cooled reactors (MSR) and fluoride-salt cooled high temperature reactors (FHR) requires the use of advanced design tools for the primary heat exchanger design. Due to geometric and flow characteristics, compact (pitch to diameter ratios equal to or less than 1.25) heat exchangers with a crossflow flow arrangement can become desirable for these reactors. Unfortunately, the available experimental data is limited for compact tube bundles or banks in crossflow. Computational Fluid Dynamics can be used to alleviate the lack of experimental data in these tube banks. Previous computational efforts have been primarily focused on large S/D ratios (larger than 1.4) using unsteady Reynolds averaged Navier-Stokes and Large Eddy Simulation frameworks. These approaches are useful, but have large computational requirements that make comprehensive design studies impractical. A CFD study was conducted with steady RANS in an effort to provide a starting point for future design work. The study was performed for an in-line tube bank geometry with FLiBe (LiF-BeF2), a frequently selected molten salt, as the working fluid. Based on the estimated pressure drops, the pressure and velocity distributions in the domain, an appropriate meshing strategy was determined and presented. Periodic boundaries in the spanwise direction transverse flow were determined to be an appropriate boundary condition for reduced computational domains. The domain size was investigated and a minimum of 2-flow channels for a domain is recommended to ensure the behavior is accounted for. Finally, the standard low Re κ-ε (Lien) turbulence model was determined to be the most appropriate for steady RANS of this case at the time of writing.

42 ENGINEERING↗

Simulating Atmospheric Boundary Layer Turbulence with Nek5000/RS

We present large-eddy-simulation (LES) modeling approaches for the simulation of atmospheric boundary layer turbulence that are of direct relevance to wind energy production. In this report, we study a GABLS benchmark problem using high-order spectral element code Nek5000/RS, which is supported under the DOE’s Exascale Computing Project (ECP) Center for Efficient Exascale Discretizations (CEED) project, targeting application simulations on various acceleration-device based exascale computing platforms [1, 2]. We demonstrate our newly developed subgrid-scale (SGS) models based on high-pass filter (HPF), mean-field eddy viscosity (MFEV), and Smagorinsky (SMG) with no-slip and traction boundary conditions, provided with low-order statistics, convergence and turbulent structure analysis. The model fidelity and scaling performance of Nek5000/RS on DOE’s leadership computing platforms in comparison to those of AMR-Wind, a block-structured second-order finite-volume code with adaptive-mesh-refinement capabilities, are discussed in [3].

17 WIND ENERGY↗

Increased power gains from wake steering control using preview wind direction information

Abstract. Yaw controllers typically rely on measurements taken at the wind turbine, resulting in a slow reaction to wind direction changes and subsequent power losses due to misalignments. Delayed yaw action is especially problematic in wake steering operation because it can result in power losses when the yaw misalignment angle deviates from the intended one due to a changing wind direction. This study explores the use of preview wind direction information for wake steering control in a two-turbine setup with a wind speed in the partial load range. For these conditions and a simple yaw controller, results from an engineering model identify an optimum preview time of 90 s. These results are validated by forcing wind direction changes in a large-eddy simulation model. For a set of six simulations with large wind direction changes, the average power gain from wake steering increases from only 0.44 % to 1.32 %. For a second set of six simulations with smaller wind direction changes, the average power gain from wake steering increases from 1.24 % to 1.85 %. Low-frequency fluctuations are shown to have a larger impact on the performance of wake steering and the effectiveness of preview control, in particular, than high-frequency fluctuations. From these results, it is concluded that the benefit of preview wind direction control for wake steering is substantial, making it a topic worth pursuing in future work.

17 WIND ENERGY↗

Two Dimensional Wake Vortex Simulations in the Atmosphere: Preliminary Sensitivity Studies

A numerical large-eddy simulation model is currently being used to quantify aircraft wake vortex behavior with meteorological observables. The model, having a meteorological framework, permits the interaction of wake vortices with environments characterized by crosswind shear, stratification, and humidity. The addition of grid-scale turbulence as an initial condition appeared to have little consequence. Results show that conventional nondimensionalizations work very well for vortex pairs embedded in stably stratified flows. However, this result is based on simple environments with constant Brunt-Vaisala frequency. Results presented here also show that crosswind profiles exert important and complex interactions on the trajectories of wake vortices. Nonlinear crosswind profiles tended to arrest the descent of wake vortex pairs. The member of the vortex pair with vorticity of same sign as the vertical change in the ambient along-track vorticity may be deflected upwards.

Proctor, F. H.↗