Search NASA⌕ Search

SEARCH · Search NASA

Results for “Spatial Simulation”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 55 records · Page 3

The Analysis of the Patterns of Radiation-Induced DNA Damage Foci by a Stochastic Monte Carlo Model of DNA Double Strand Breaks Induction by Heavy Ions and Image Segmentation Software

To create a generalized mechanistic model of DNA damage in human cells that will generate analytical and image data corresponding to experimentally observed DNA damage foci and will help to improve the experimental foci yields by simulating spatial foci patterns and resolving problems with quantitative image analysis. Material and Methods: The analysis of patterns of RIFs (radiation-induced foci) produced by low- and high-LET (linear energy transfer) radiation was conducted by using a Monte Carlo model that combines the heavy ion track structure with characteristics of the human genome on the level of chromosomes. The foci patterns were also simulated in the maximum projection plane for flat nuclei. Some data analysis was done with the help of image segmentation software that identifies individual classes of RIFs and colocolized RIFs, which is of importance to some experimental assays that assign DNA damage a dual phosphorescent signal. Results: The model predicts the spatial and genomic distributions of DNA DSBs (double strand breaks) and associated RIFs in a human cell nucleus for a particular dose of either low- or high-LET radiation. We used the model to do analyses for different irradiation scenarios. In the beam-parallel-to-the-disk-of-a-flattened-nucleus scenario we found that the foci appeared to be merged due to their high density, while, in the perpendicular-beam scenario, the foci appeared as one bright spot per hit. The statistics and spatial distribution of regions of densely arranged foci, termed DNA foci chains, were predicted numerically using this model. Another analysis was done to evaluate the number of ion hits per nucleus, which were visible from streaks of closely located foci. In another analysis, our image segmentaiton software determined foci yields directly from images with single-class or colocolized foci. Conclusions: We showed that DSB clustering needs to be taken into account to determine the true DNA damage foci yield, which helps to determine the DSB yield. Using the model analysis, a researcher can refine the DSB yield per nucleus per particle. We showed that purely geometric artifacts, present in the experimental images, can be analytically resolved with the model, and that the quantization of track hits and DSB yields can be provided to the experimentalists who use enumeration of radiation-induced foci in immunofluorescence experiments using proteins that detect DNA damage. An automated image segmentaiton software can prove useful in a faster and more precise object counting for colocolized foci images.

Ponomarev, Artem↗

Simulations of bypass transition for spatially evolving disturbances

The spatial evolution of disturbances in plane Poiseuille flow and zero pressure gradient boundary layer flow is considered. For disturbances governed by the linearized equations, potential for significant transient growth of the amplitude is demonstrated. The maximum amplification occurs for disturbances with zero or near zero frequencies. Spatial numerical simulations of the transition scenario involving a pair of oblique waves has been conducted for both flows. A fully spectral solver using a simple but efficient fringe region technique allowed the flows to be computed with high resolution into the fully turbulent domain. A modal decomposition of the simulation results indicates that non-linear excitation of the transient growth is responsible for the rapid emergence of low-frequency structures. Physically, this corresponds to streaky flow structures, as seen from the results of a numerical amplitude expansion. Thus, this spatial transition scenario has been found to be similar to the corresponding temporal one. In the boundary layer simulations the streaks are seen to break down from what appears to be a secondary instability.

Lundbladh, A.↗

Numerical simulation of swept-wing flows

Efforts of the last six months to computationally model the transition process characteristics of flow over swept wings are described. Specifically, the crossflow instability and crossflow/Tollmien-Schlichting wave interactions are analyzed through the numerical solution of the full 3D Navier-Stokes equations including unsteadiness, curvature, and sweep. This approach is chosen because of the complexity of the problem and because it appears that linear stability theory is insufficient to explain the discrepancies between different experiments and between theory and experiment. The leading edge region of a swept wing is considered in a 3D spatial simulation with random disturbances as the initial conditions.

Reed, Helen L.↗

Navier-Stokes simulation of the crossflow instability in swept-wing flows

The computational modeling of the transition process characteristic of flows over swept wings are described. Specifically, the crossflow instability and crossflow/T-S wave interactions are analyzed through the numerical solution of the full three-dimensional Navier-Stokes equations including unsteadiness, curvature, and sweep. This approach is chosen because of the complexity of the problem and because it appears that linear stability theory is insufficient to explain the discrepancies between different experiments and between theory and experiments. The leading edge region of a swept wing is considered in a three-dimensional spatial simulation with random disturbances as the initial conditions. The work has been closely coordinated with the experimental program of Professor William Saric, examining the same problem. Comparisons with NASA flight test data and the experiments at Arizona State University were a necessary and an important integral part of this work.

Reed, Helen L.↗

The Signature of Ozone Depletion in Recent Antarctic Precipitation Change: A Study with the Community Earth System Model

Although precipitation is a primary control on Antarctic ice sheet (AIS) mass balance, long-term historical AIS precipitation trends and their underlying external climate drivers remain inconclusive. In this study, we use a novel pair of climate model ensembles to identify a simulated spatial signature of ozone depletion-forced AIS precipitation change. Distinct areas of little change or precipitation decrease, arising from interaction between ozone depletion-forced atmospheric circulation changes and ice sheet topography, are outweighed by large-scale precipitation increases. This signature bears notable similarities to a new ice core-based reconstruction of AIS accumulation change and yields a significant increase in annual integrated precipitation (38 ± 10 Gt/year over the 1986–2005 period or 51 ± 11 Gt/year over the 1991–2005 period). Remarkably, this simulated ozone depletion-forced precipitation change is of a similar absolute magnitude to recent observed AIS mass loss trends and as a consequence, it may play a role in dampening recent AIS sea level rise contributions.

Lenaerts, Jan T. M.↗

Quantitative Nonlinear Optical Polarimetry with High Spatial Resolution

Nonlinear optical microscopy such as in the optical second-harmonic generation (SHG) modality has become a popular tool today for probing materials in the physical and biological sciences. While imaging and spectroscopy are widely used in the microscopy mode, nonlinear polarimetry, which can shed light on materials’ symmetry and microstructure, is relatively underdeveloped. This is partly because quantitative analytical modeling of the optical SHG response for anisotropic crystals and films largely assumes low-numerical aperture (NA) focusing of light, where the plane-wave approximation is sufficient. Tight focusing provides unique benefits in revealing out-of-plane polarization responses, which cannot be detected by near-plane-wave illumination at normal incidence. Here, we outline a method for quantitatively analyzing SHG polarimetry measurements obtained under high-NA focusing within a microscope geometry. Experiments and simulations of a variety of standard samples, from single crystals to thin films, are in good agreement, including measured and simulated spatial SHG maps of ferroelectric domains. A solution to the inverse problem is demonstrated, where the spatial distribution of an SHG tensor with unknown tensor coefficient magnitudes is determined by experimentally measured polarimetry. The ability to extract the out-of-plane component of the nonlinear polarization in normal incidence is demonstrated, which can be valuable for high-resolution polarimetry of 2D materials, thin films, heterostructures, and uniaxial crystals with a strong out-of-plane response.

36 MATERIALS SCIENCE↗

Numerical Simulation of a High Mach Number Jet Flow

The recent efforts to develop accurate numerical schemes for transition and turbulent flows are motivated, among other factors, by the need for accurate prediction of flow noise. The success of developing high speed civil transport plane (HSCT) is contingent upon our understanding and suppression of the jet exhaust noise. The radiated sound can be directly obtained by solving the full (time-dependent) compressible Navier-Stokes equations. However, this requires computational storage that is beyond currently available machines. This difficulty can be overcome by limiting the solution domain to the near field where the jet is nonlinear and then use acoustic analogy (e.g., Lighthill) to relate the far-field noise to the near-field sources. The later requires obtaining the time-dependent flow field. The other difficulty in aeroacoustics computations is that at high Reynolds numbers the turbulent flow has a large range of scales. Direct numerical simulations (DNS) cannot obtain all the scales of motion at high Reynolds number of technological interest. However, it is believed that the large scale structure is more efficient than the small-scale structure in radiating noise. Thus, one can model the small scales and calculate the acoustically active scales. The large scale structure in the noise-producing initial region of the jet can be viewed as a wavelike nature, the net radiated sound is the net cancellation after integration over space. As such, aeroacoustics computations are highly sensitive to errors in computing the sound sources. It is therefore essential to use a high-order numerical scheme to predict the flow field. The present paper presents the first step in a ongoing effort to predict jet noise. The emphasis here is in accurate prediction of the unsteady flow field. We solve the full time-dependent Navier-Stokes equations by a high order finite difference method. Time accurate spatial simulations of both plane and axisymmetric jet are presented. Jet Mach numbers of 1.5 and 2.1 are considered. Reynolds number in the simulations was about a million. Our numerical model is based on the 2-4 scheme by Gottlieb & Turkel. Bayliss et al. applied the 2-4 scheme in boundary layer computations. This scheme was also used by Ragab and Sheen to study the nonlinear development of supersonic instability waves in a mixing layer. In this study, we present two dimensional direct simulation results for both plane and axisymmetric jets. These results are compared with linear theory predictions. These computations were made for near nozzle exit region and velocity in spanwise/azimuthal direction was assumed to be zero.

Hayder, M. Ehtesham↗

Observationally constrained analysis on the distribution of fine- and coarse-mode nitrate in global models

Nitrate plays an important role in the Earth system and air quality. A key challenge in simulating the life cycle of nitrate aerosol in global models is to accurately represent mass size distribution of nitrate aerosol. In this study, we evaluate the performance of the Energy Exascale Earth System Model version 2 (E3SMv2) and the Community Earth System Model version 2 (CESM2), along with Aerosol Comparisons between Observations and Models (AeroCom) phase III models, in simulating spatial distribution of fine-mode nitrate, the mass size distribution of fine- and coarse-mode nitrate, and the gas–aerosol partitioning between nitric acid gas and nitrate, using long-term ground-based observations and measurements from multiple aircraft campaigns. We find that most models underestimate the annual mean PM 2.5 (particulate matter with diameter less than 2.5 µm) nitrate surface concentration averaged over all sites. The observed nitrate PM 2.5 / PM 10 and PM 1 / PM 4 ratios are influenced by the relative contribution of fine sulfate or organic particles and coarse dust or sea salt particles. Overall, the ground-based observations give an annual mean surface nitrate PM 2.5 / PM 10 ratio of 0.7. Most models underestimate the annual mean PM 2.5 / PM 10 ratio in all regions. There are large spreads in the modeled nitrate PM 1 / PM 4 ratios, which span the full range from 0 to 1. Most models underestimate the surface molar ratio of nitrate to total inorganic nitrate averaged across all sites. Our study indicates the importance of gas–aerosol partition parameterization and the simulation of dust and sea salt in correctly simulating the mass size distribution of nitrate.

Nitrate↗

A lumped particle direct simulation Monte-Carlo method combined with the collisional-radiative model for simulations of non-equilibrium laser-induced plasma plumes

Collisional plasma plumes induced by laser irradiation of material targets exhibit large variations in local density as well as ionization and excitation states, making purely hydrodynamic or kinetic simulations inaccurate or infeasible. To address this challenge and capture non-equilibrium effects in laser-induced plasma plumes at arbitrary degrees of ionization, we develop a hybrid computational approach that combines the kinetic direct simulation Monte Carlo (DSMC) method with a collisional-radiative model (CRM). This ℓDSMC-CRM approach utilizes a lumped particle method to represent minor fractions of excited ions in particle-based simulations and a special coarse-graining technique for atomic spectra and photoionization rates, ensuring numerical convergence at reduced computational cost. The hybrid approach is applied to simulate spatially homogeneous relaxation as well as one- and two-dimensional expansions of plasma plumes induced by irradiation of a copper target by a nanosecond laser pulse in a vacuum or background gas. The comparison with an equilibrium model, where local Saha-Boltzmann equilibrium is enforced, shows that the non-equilibrium effects play a dominant role. The equilibrium model can fail to predict the flow structure and strongly underestimate the degree of absorption of laser radiation by the plume. The ℓDSMC-CRM approach is validated against experimental data demonstrating reasonable agreement with the experimental electron density and temperature, while the equilibrium model is found to dramatically underestimate electron density and temperature. The flexibility of the ℓDSMC-CRM approach allows for its seamless integration into existing DSMC frameworks, making it a valuable tool for high-fidelity plasma modeling in laser-material interactions, laser-based manufacturing, and beyond.

97 MATHEMATICS AND COMPUTING↗

Global Simulations of Phase State and Equilibration Time Scales of Secondary Organic Aerosols with GEOS-Chem

The phase state of secondary organic aerosols (SOA) can range from liquid through amorphous semisolid to glassy solid, which is important to consider as it influences various multiphase processes including SOA formation and partitioning, multiphase chemistry, and cloud activation. In this study, we simulate the glass transition temperature and viscosity of SOA over the globe using the global chemical transport model, GEOS-Chem. The simulated spatial distributions show that SOA at the surface exist as liquid over equatorial regions and oceans, semisolid in the midlatitude continental regions, and glassy solid over lands with low relative humidity. The predicted SOA viscosities are mostly consistent with the available measurements. In the free troposphere, SOA particles are mostly predicted to be semisolid at 850 hPa and glassy solid at 500 hPa, except over tropical regions including Amazonia, where SOA are predicted to be low viscous. Phase state also exhibits seasonal variation with a higher frequency of semisolid and solid particles in winter compared to warmer seasons. We calculate equilibration time scales of SOA partitioning (τ eq ) and effective mass accommodation coefficient (α eff ), indicating that τ eq is shorter than the chemical time step of GEOS-Chem of 20 min and αeff is close to unity for most locations at the surface level, supporting the application of equilibrium SOA partitioning. However, τ eq is prolonged and α eff is lowered over drylands and most regions in the upper troposphere, suggesting that kinetically limited growth would need to be considered for these regions in future large-scale model studies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Stable Simulation of the Community Atmosphere Model Using Machine‐Learning Physical Parameterization Trained With Experience Replay

In recent years, machine learning (ML) models have been used to improve physical parameterizations of general circulation models (GCMs). A significant challenge of integrating ML models into GCMs is the online instability when they are coupled for long‐term simulation. We present a new strategy that demonstrates robust online stability when the physical parameterization package of an atmospheric GCM is replaced by a deep ML model. The method uses experience replay with a multistep training scheme of the ML model in which the model's own output at the previous time step is used in the training. Predicted physics tendencies in the replay buffer with the most recent errors in the training iterations are reused, making the ML model learn from its own errors. The training method reduces the gap between the offline and online environments of the ML model. The method is used to train the ML model as the physical parameterization of the Community Atmosphere Model (CAM5) with training data from the Multi‐scale Modeling Framework high resolution simulations. Three 6‐year online simulations of the CAM5 are carried out by using the ML physics package. The simulated spatial distributions of precipitation, surface temperature and zonally averaged atmospheric fields demonstrate overall better accuracy than that of the standard CAM5 and benchmark model even without the use of additional physical constraints or tuning. This work is the first to demonstrate a solution to address the online instability problem in climate modeling with ML physics by using experience replay.

54 ENVIRONMENTAL SCIENCES↗

Poleward Migration of the Latitude of Maximum Tropical Cyclone Intensity—Forced or Natural?

Abstract Past studies have shown a significant observed poleward trend in the latitude at which tropical cyclones reach their lifetime maximum intensity (LMI), especially in the northwest Pacific basin. Given the brevity of the historical record, it remains difficult to separate the forced trend from internal variability of the climate system. A recently developed tropical cyclone downscaling model is used to downscale the Community Earth System Model, version 2 (CESM2), preindustrial control simulation. It is found that the observed trend in the latitude at which tropical cyclones reach their LMI in the northwest Pacific is very unlikely to be caused by internal variability. The same downscaling model is then used to downscale CESM2 simulations under historical forcing. The resulting trend distribution shows a significant poleward migration of tropical cyclone LMI even after regressing out both natural variability and the part of the forced warming pattern that projects onto natural variability. The results indicate that the observed poleward migration of the latitude at which tropical cyclones reach their LMI in the northwest Pacific basin is likely to be, at least in part, forced. However, the magnitude of the projected poleward trend in climate models can be significantly modulated by the simulated spatial pattern of ocean warming. This highlights how discrepancies between models and observations, with regard to projected changes to the equatorial zonal sea surface temperature gradient under anthropogenic forcing, can lead to large uncertainties in projected changes to the LMI latitude of tropical cyclones. Significance Statement Observations in the northwest Pacific basin show that the latitude at which tropical cyclones are at their most intense has been trending northward in the recent half century. These changes are important since tropical cyclones could bring hazardous weather to coastal areas that are poorly equipped to handle them. Here, we show that natural variations in Earth’s climate are very unlikely to explain the observed poleward trend in the latitude that tropical cyclone reach their maximum intensity. We find that it is much more likely that the observed trend is forced by human-related emissions, though the spatial pattern of warming in response to greenhouse emissions can have significant impacts on the magnitude of the trend.

Lin, Jonathan↗

Stability of three-dimensional boundary layers

The computational modeling of the transition process characteristic of flows over swept wings is discussed. Specifically, the crossflow instability and crossflow/Tollmien-Schlichting wave interactions are analyzed through the numerical solution of the full three-dimensional Navier-Stokes equations including unsteadiness, curvature, and sweep. This approach is chosen because of the complexity of the problem and because it appears that regular stability theory is insufficient to explain the discrepancies between experiments and between theory and experiment. The leading edge region of a swept wing will be considered in a three-dimensional spatial simulation with random disturbances as the initial conditions.

Reed, Helen L.↗

The NASA MSFC Earth Global Reference Atmospheric Model-2007 Version

Reference or standard atmospheric models have long been used for design and mission planning of various aerospace systems. The NASA/Marshall Space Flight Center (MSFC) Global Reference Atmospheric Model (GRAM) was developed in response to the need for a design reference atmosphere that provides complete global geographical variability, and complete altitude coverage (surface to orbital altitudes) as well as complete seasonal and monthly variability of the thermodynamic variables and wind components. A unique feature of GRAM is that, addition to providing the geographical, height, and monthly variation of the mean atmospheric state, it includes the ability to simulate spatial and temporal perturbations in these atmospheric parameters (e.g. fluctuations due to turbulence and other atmospheric perturbation phenomena). A summary comparing GRAM features to characteristics and features of other reference or standard atmospheric models, can be found Guide to Reference and Standard Atmosphere Models. The original GRAM has undergone a series of improvements over the years with recent additions and changes. The software program is called Earth-GRAM2007 to distinguish it from similar programs for other bodies (e.g. Mars, Venus, Neptune, and Titan). However, in order to make this Technical Memorandum (TM) more readable, the software will be referred to simply as GRAM07 or GRAM unless additional clarity is needed. Section 1 provides an overview of the basic features of GRAM07 including the newly added features. Section 2 provides a more detailed description of GRAM07 and how the model output generated. Section 3 presents sample results. Appendices A and B describe the Global Upper Air Climatic Atlas (GUACA) data and the Global Gridded Air Statistics (GGUAS) database. Appendix C provides instructions for compiling and running GRAM07. Appendix D gives a description of the required NAMELIST format input. Appendix E gives sample output. Appendix F provides a list of available parameters to enable the user to generate special output. Appendix G gives an example and guidance on incorporating GRAM07 as a subroutine in other programs such as trajectory codes or orbital propagation routines.

Leslie, F.W.↗

The NASA Marshall Space Flight Center Earth Global Reference Atmospheric Model-2010 Version

Reference or standard atmospheric models have long been used for design and mission planning of various aerospace systems. The NASA Marshall Space Flight Center Global Reference Atmospheric Model was developed in response to the need for a design reference atmosphere that provides complete global geographical variability and complete altitude coverage (surface to orbital altitudes), as well as complete seasonal and monthly variability of the thermodynamic variables and wind components. In addition to providing the geographical, height, and monthly variation of the mean atmospheric state, it includes the ability to simulate spatial and temporal perturbations.

Leslie, F. W.↗

An Assessment of Southern Ocean Water Masses and Sea Ice During 1988-2007 in a Suite of Interannual CORE-II Simulations

We characterise the representation of the Southern Ocean water mass structure and sea ice within a suite of 15 global ocean-ice models run with the Coordinated Ocean-ice Reference Experiment Phase II (CORE-II) protocol. The main focus is the representation of the present (1988-2007) mode and intermediate waters, thus framing an analysis of winter and summer mixed layer depths; temperature, salinity, and potential vorticity structure; and temporal variability of sea ice distributions. We also consider the interannual variability over the same 20 year period. Comparisons are made between models as well as to observation-based analyses where available. The CORE-II models exhibit several biases relative to Southern Ocean observations, including an underestimation of the model mean mixed layer depths of mode and intermediate water masses in March (associated with greater ocean surface heat gain), and an overestimation in September (associated with greater high latitude ocean heat loss and a more northward winter sea-ice extent). In addition, the models have cold and fresh/warm and salty water column biases centred near 50 deg S. Over the 1988-2007 period, the CORE-II models consistently simulate spatially variable trends in sea-ice concentration, surface freshwater fluxes, mixed layer depths, and 200-700 m ocean heat content. In particular, sea-ice coverage around most of the Antarctic continental shelf is reduced, leading to a cooling and freshening of the near surface waters. The shoaling of the mixed layer is associated with increased surface buoyancy gain, except in the Pacific where sea ice is also influential. The models are in disagreement, despite the common CORE-II atmospheric state, in their spatial pattern of the 20-year trends in the mixed layer depth and sea-ice.

Sea ice↗

Ecosystem age-class dynamics and distribution in the LPJ-wsl v2.0 global ecosystem model

Forest ecosystem processes follow classic responses with age, peaking production around canopy closure and declining thereafter. Although age dynamics might be more dominant in certain regions over others, demographic effects on net primary production (NPP) and heterotrophic respiration (Rh) are bound to exist. Yet, explicit representation of ecosystem demography is notably absent in many global ecosystem models. This is concerning because the global community relies on these models to regularly update our collective understanding of the global carbon cycle. This paper aims to present the technical developments of a computationally efficient approach for representing age-class dynamics within a global ecosystem model, the Lund–Potsdam–Jena – Wald, Schnee, Landschaft version 2.0 (LPJ-wsl v2.0) dynamic global vegetation model and to determine if explicit representation of demography influenced ecosystem stocks and fluxes at global scales or at the level of a grid cell. The modeled age classes are initially created by simulated fire and prescribed wood harvesting or abandonment of managed land, otherwise aging naturally until an additional disturbance is simulated or prescribed. In this paper, we show that the age module can capture classic demographic patterns in stem density and tree height compared to inventory data, and that simulated patterns of ecosystem function follow classic responses with age. We also present two scientific applications of the model to assess the modeled age-class distribution over time and to determine the demographic effect on ecosystem fluxes relative to climate. Simulations show that, between 1860 and 2016, zonal age distribution on Earth was driven predominately by fire, causing a 45- to 60-year difference in ages between older boreal (50–90° N) and younger tropical (23° S–23° N) ecosystems. Between simulation years 1860 and 2016, land-use change and land management were responsible for a decrease in zonal age by −6 years in boreal and by −21 years in both temperate (23–50° N) and tropical latitudes, with the anthropogenic effect on zonal age distribution increasing over time. A statistical model helped to reduce LPJ-wsl v2.0 complexity by predicting per-grid-cell annual NPP and Rh fluxes by three terms: precipitation, temperature, and age class; at global scales, R2 was between 0.95 and 0.98. As determined by the statistical model, the demographic effect on ecosystem function was often less than 0.10 kg C/sq. myr but as high as 0.60 kg C/sq. myr where the effect was greatest. In the eastern forests of North America, the simulated demographic effect was of similar magnitude, or greater than, the effects of climate; simulated demographic effects were similarly important in large regions of every vegetated continent. Simulated spatial datasets are provided for global ecosystem ages and the estimated coefficients for effects of precipitation, temperature and demography on ecosystem function. The discussion focuses on our finding of an increasing role of demography in the global carbon cycle, the effect of demography on relaxation times (resilience) following a disturbance event and its implications at global scales, and a finding of a 40 Pg C increase in biomass turnover when including age dynamics at global scales. Whereas time is the only mechanism that increases ecosystem age, any additional disturbance not explicitly modeled will decrease age. The LPJ-wsl v2.0 age module represents another step forward towards understanding the role of demography in global ecosystems.

LPJ-wsl↗

Spatial Direct Numerical Simulation of Boundary-Layer Transition Mechanisms: Validation of PSE Theory

A study of instabilities in incompressible boundary-layer flow on a flat plate is conducted by spatial direct numerical simulation (DNS) of the Navier-Stokes equations. Here, the DNS results are used to critically evaluate the results obtained using parabolized stability equations (PSE) theory and to study mechanisms associated with breakdown from laminar to turbulent flow. Three test cases are considered: two-dimensional Tollmien-Schlichting wave propagation, subharmonic instability breakdown, and oblique-wave break-down. The instability modes predicted by PSE theory are in good quantitative agreement with the DNS results, except a small discrepancy is evident in the mean-flow distortion component of the 2-D test problem. This discrepancy is attributed to far-field boundary- condition differences. Both DNS and PSE theory results show several modal discrepancies when compared with the experiments of subharmonic breakdown. Computations that allow for a small adverse pressure gradient in the basic flow and a variation of the disturbance frequency result in better agreement with the experiments.

Joslin, R. D.↗