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NASA NTRS1991

The implementation and validation of improved landsurface hydrology in an atmospheric general circulation model

Landsurface hydrological parameterizations are implemented in the NASA Goddard Institute for Space Studies (GISS) General Circulation Model (GCM). These parameterizations are: (1) runoff and evapotranspiration functions that include the effects of subgrid scale spatial variability and use physically based equations of hydrologic flux at the soil surface, and (2) a realistic soil moisture diffusion scheme for the movement of water in the soil column. A one dimensional climate model with a complete hydrologic cycle is used to screen the basic sensitivities of the hydrological parameterizations before implementation into the full three dimensional GCM. Results of the final simulation with the GISS GCM and the new landsurface hydrology indicate that the runoff rate, especially in the tropics is significantly improved. As a result, the remaining components of the heat and moisture balance show comparable improvements when compared to observations. The validation of model results is carried from the large global (ocean and landsurface) scale, to the zonal, continental, and finally the finer river basin scales.

Johnson, Kevin D.↗

DOE OSTI2024

WRF-Comfort: simulating microscale variability in outdoor heat stress at the city scale with a mesoscale model

Abstract. Urban overheating and its ongoing exacerbation due to global warming and urban development lead to increased exposure to urban heat and increased thermal discomfort and heat stress. To quantify thermal stress, specific indices have been proposed that depend on air temperature, mean radiant temperature (MRT), wind speed, and relative humidity. While temperature and humidity vary on scales of hundreds of meters, MRT and wind speed are strongly affected by individual buildings and trees and vary on the meter scale. Therefore, most numerical thermal comfort studies apply microscale models to limited spatial domains (commonly representing urban neighborhoods with building blocks) with resolutions on the order of 1 m and a few hours of simulation. This prevents the analysis of the impact of city-scale adaptation and/or mitigation strategies on thermal stress and comfort. To solve this problem, we develop a methodology to estimate thermal stress indicators and their subgrid variability in mesoscale models – here applied to the multilayer urban canopy parameterization BEP-BEM within the Weather Research and Forecasting (WRF) model. The new scheme (consisting of three main steps) can readily assess intra-neighborhood-scale heat stress distributions across whole cities and for timescales of minutes to years. The first key component of the approach is the estimation of MRT in several locations within streets for different street orientations. Second, mean wind speed and its subgrid variability are downscaled as a function of the local urban morphology based on relations derived from a set of microscale LES and RANS simulations across a wide range of realistic and idealized urban morphologies. Lastly, we compute the distributions of two thermal stress indices for each grid square, combining all the subgrid values of MRT, wind speed, air temperature, and absolute humidity. From these distributions, we quantify the high and low tails of the heat stress distribution in each grid square across the city, representing the thermal diversity experienced in street canyons. In this contribution, we present the core methodology as well as simulation results for Madrid (Spain), which illustrate strong differences between heat stress indices and common heat metrics like air or surface temperature both across the city and over the diurnal cycle.

Geology↗

NASA NTRS1993

The implementation and validation of improved land-surface hydrology in an atmospheric general circulation model

New land-surface hydrologic parameterizations are implemented into the NASA Goddard Institute for Space Studies (GISS) General Circulation Model (GCM). These parameterizations are: 1) runoff and evapotranspiration functions that include the effects of subgrid-scale spatial variability and use physically based equations of hydrologic flux at the soil surface and 2) a realistic soil moisture diffusion scheme for the movement of water and root sink in the soil column. A one-dimensional climate model with a complete hydrologic cycle is used to screen the basic sensitivities of the hydrological parameterizations before implementation into the full three-dimensional GCM. Results of the final simulation with the GISS GCM and the new land-surface hydrology indicate that the runoff rate, especially in the tropics, is significantly improved. As a result, the remaining components of the heat and moisture balance show similar improvements when compared to observations. The validation of model results is carried from the large global (ocean and land-surface) scale to the zonal, continental, and finally the regional river basin scales.

Johnson, Kevin D.↗

DOE OSTI2019

The Application of an Evolutionary Programming Process to a Simulation of the ETEX Large-Scale Airborne Dispersion Experiment

Abstract Airborne tracer simulations are typically performed using a dispersion model driven by a high-resolution meteorological model. Besides solving the dynamic equations of momentum, heat, and moisture on the resolved model grid, mesoscale models must account for subgrid-scale fluxes and other unresolved processes. These are estimated through parameterization schemes of eddy diffusion, convection, and surface interactions, and they make use of prescribed parameters set by the user. Such “free” model parameters are often poorly constrained, and a range of plausible values exists for each. Evolutionary programming (EP) is a process to improve the selection of the parameters. A population of simulations is first run with a different set of parameter values for each member, and the member judged most accurate is selected as the “parent” of a new “generation.” After a number of iterations, the simulations should approach a configuration that is best adapted to the atmospheric conditions. We apply the EP process to simulate the first release of the 1994 European Tracer Experiment (ETEX) project, which comprised two experiments in which a tracer was released in western France and sampled by an observing network. The EP process is used to improve a simulation of the RAMS mesoscale weather model, with weather data collected during ETEX being used to “score” the individual members according to how well each simulation matches the observations. The meteorological simulations from before and after application of the EP process are each used to force a dispersion model to create a simulation of the ETEX release, and substantial improvement is observed when these are validated against sampled tracer concentrations.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2019

Towards Unifying the Planetary Boundary Layer and Shallow Convection in CAM5 with the Eddy-Diffusivity/Mass-Flux Approach

The modular structure of the boundary layer and convection parameterizations in atmospheric models have long been affecting the numerical representation of subgrid-scale motions and their mutual interactions. A promising alternative, the eddy-diffusivity/mass-flux approach (EDMF), has the potential for unifying the existing formulations into a consistent scheme and improving some of the long-standing issues. This study documents a step towards developing such a unified approach by implementing a stochastic multi-plume EDMF scheme into the Community Atmosphere Model (Version 5.0). Its performance in single-column mode is evaluated against the control parameterization and large-eddy simulation (LES) for two benchmark cases: marine and continental shallow convection. Overall, the results for the two parameterizations agree well with each other and with LES in terms of mean profiles of moist conserved variables and their vertical fluxes, as well as the updraft properties. However, systematic differences between the two schemes, especially for transient continental convection, are also documented. Using EDMF helps improve some of the parameterized features of shallow convection. In particular, for the highest tested vertical resolution, the EDMF cloud base and top heights and the vertical fluxes of energy and water are remarkably close to LES.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2019

Parameterization of Vertical Profiles of Governing Microphysical Parameters of Shallow Cumulus Cloud Ensembles Using LES with Bin Microphysics

Shallow convection is a subgrid process in cloud-resolving models for which their grid box is larger than the size of small cumulus clouds (Cu). At the same time such Cu substantially affect radiation properties and thermodynamic parameters of the low atmosphere. The main microphysical parameters used for calculation of radiative properties of Cu in cloud-resolving models are liquid water content (LWC), effective droplet radius, and cloud fraction (CF). In this study, these parameters of fields of small, warm Cu are calculated using large-eddy simulations (LESs) performed using the System for Atmospheric Modeling (SAM) with spectral bin microphysics. Despite the complexity of microphysical processes, several fundamental properties of Cu were found. First, despite the high variability of LWC and droplet concentration within clouds and between different clouds, the volume mean and effective radii per specific level vary only slightly. Second, the values of effective radius are close to those forming during adiabatic ascent of air parcels from cloud base. These findings allow for characterization of a cloud field by specific vertical profiles of effective radius and of mean liquid water content, which can be calculated using the theoretical profile of adiabatic liquid water content and the droplet concentration at cloud base. Using the results of these LESs, a simple parameterization of cloud-field-averaged vertical profiles of effective radius and of liquid water content is proposed for different aerosol and thermodynamic conditions. These profiles can be used for calculation of radiation properties of Cu fields in large-scale models. The role of adiabatic processes in the formation of microstructure of Cu is discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Insights of warm-cloud biases in Community Atmospheric Model 5 and 6 from the single-column modeling framework and Aerosol and Cloud Experiments in the Eastern North Atlantic (ACE-ENA) observations

There has been a growing concern that most climate models predict precipitation that is too frequent, likely due to lack of reliable subgrid variability and vertical variations in microphysical processes in low-level warm clouds. In this study, the warm-cloud physics parameterizations in the singe-column configurations of NCAR Community Atmospheric Model version 6 and 5 (SCAM6 and SCAM5, respectively) are evaluated using ground-based and airborne observations from the Department of Energy (DOE) Atmospheric Radiation Measurement (ARM) Aerosol and Cloud Experiments in the Eastern North Atlantic (ACE-ENA) field campaign near the Azores islands during 2017–2018. The 8-month single-column model (SCM) simulations show that both SCAM6 and SCAM5 can generally reproduce marine boundary layer cloud structure, major macrophysical properties, and their transition. The improvement in warm-cloud properties from the Community Atmospheric Model 5 and 6 (CAM5 to CAM6) physics can be found through comparison with the observations. Meanwhile, both physical schemes underestimate cloud liquid water content, cloud droplet size, and rain liquid water content but overestimate surface rainfall. Modeled cloud condensation nuclei (CCN) concentrations are comparable with aircraft-observed ones in the summer but are overestimated by a factor of 2 in winter, largely due to the biases in the long-range transport of anthropogenic aerosols like sulfate. We also test the newly recalibrated autoconversion and accretion parameterizations that account for vertical variations in droplet size. Compared to the observations, more significant improvement is found in SCAM5 than in SCAM6. This result is likely explained by the introduction of subgrid variations in cloud properties in CAM6 cloud microphysics, which further suppresses the scheme's sensitivity to individual warm-rain microphysical parameters. The predicted cloud susceptibilities to CCN perturbations in CAM6 are within a reasonable range, indicating significant progress since CAM5 which produces an aerosol indirect effect that is too strong. The present study emphasizes the importance of understanding biases in cloud physics parameterizations by combining SCM with in situ observations.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

The Application of a Genetic Algorithm to the Optimization of a Mesoscale Model for Emergency Response

Besides solving the equations of momentum, heat, and moisture transport on the model grid, mesoscale weather models must account for subgrid-scale processes that affect the resolved model variables. These are simulated with model parameterizations, which often rely on values preset by the user. Such “free” model parameters, along with others set to initialize the model, are often poorly constrained, requiring that a user select each from a range of plausible values. Finding the values to optimize any forecasting tool can be accomplished with a search algorithm, and one such process—the genetic algorithm (GA)—has become especially popular. As applied to modeling, GAs represent a Darwinian process: an ensemble of simulations is run with a different set of parameter values for each member, and the members subsequently judged to be most accurate are selected as “parents” who pass their parameters onto a new generation. At the U.S. Department of Energy’s Savannah River Site in South Carolina, we are applying a GA to the Regional Atmospheric Modeling System (RAMS) mesoscale weather model, which supplies input to a model to simulate the dispersion of an airborne contaminant as part of the site’s emergency response preparations. An ensemble of forecasts is run each day, weather data are used to “score” the individual members of the ensemble, and the parameters from the best members are used for the next day’s forecasts. As meteorological conditions change, the parameters change as well, maintaining a model configuration that is best adapted to atmospheric conditions. Significance Statement We wanted to develop a forecasting system by which a weather model is run over the Savannah River Site each day and repeatedly adjusted according to how well it performed the previous day. To run the model, a series of values (parameters) must be set to control how the model will calculate winds, temperatures, and other desired variables. Each day the model was run several times using different combinations of these parameters and later compared with observed meteorological conditions. Parameters that produced the most accurate forecasts were preferentially reused to create the forecasts for the next day. The process was tested for the summer of 2020 and exhibited lower errors than forecasts produced by the model using default values of the parameters.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS2011

Evaluation of Convective Transport in the GEOS-5 Chemistry and Climate Model

The NASA Goddard Earth Observing System (GEOS-5) Chemistry and Climate Model (CCM) consists of a global atmospheric general circulation model and the combined stratospheric and tropospheric chemistry package from the NASA Global Modeling Initiative (GMI) chemical transport model. The subgrid process of convective tracer transport is represented through the Relaxed Arakawa-Schubert parameterization in the GEOS-5 CCM. However, substantial uncertainty for tracer transport is associated with this parameterization, as is the case with all global and regional models. We have designed a project to comprehensively evaluate this parameterization from the point of view of tracer transport, and determine the most appropriate improvements that can be made to the GEOS-5 convection algorithm, allowing improvement in our understanding of the role of convective processes in determining atmospheric composition. We first simulate tracer transport in individual observed convective events with a cloud-resolving model (WRF). Initial condition tracer profiles (CO, CO2, O3) are constructed from aircraft data collected in undisturbed air, and the simulations are evaluated using aircraft data taken in the convective anvils. A single-column (SCM) version of the GEOS-5 GCM with online tracers is then run for the same convective events. SCM output is evaluated based on averaged tracer fields from the cloud-resolving model. Sensitivity simulations with adjusted parameters will be run in the SCM to determine improvements in the representation of convective transport. The focus of the work to date is on tropical continental convective events from the African Monsoon Multidisciplinary Analyses (AMMA) field mission in August 2006 that were extensively sampled by multiple research aircraft.

Pickering, Kenneth E.↗

NASA NTRSDate not supplied

Machine Learning Global Simulation of Nonlocal Gravity Wave Propagation

Global climate models typically operate at a grid resolution of hundreds of kilometers and fail to resolve atmospheric mesoscale processes, e.g., clouds, precipitation, and gravity waves (GWs).Model representation of these processes and their sources is essential to the global circulation and planetary energy budget, but subgrid scale contributions from these processes are often only approximately represented in models using parameterizations. These parameterizations are subject to approximations and idealizations, which limit their capability and accuracy. The most drastic of these approximations is the “single-column approximation” which completely neglects the horizontal evolution of these processes, resulting in key biases in current climate models. With a focus on atmospheric GWs, we present the first-ever global simulation of atmospheric GW fluxes using machine learning (ML) models trained on the WINDSET dataset to emulate global GW emulation in the atmosphere, as an alternative to traditional single-column parameterizations. Using an Attention U-Net-based architecture trained on globally resolved GW momentum fluxes, we illustrate the importance and effectiveness of global nonlocality, when simulating GWs using data-driven schemes.

Aman Gupta↗

NASA NTRS1999

Wind Field Measurements With Airborne Doppler Lidar

In collaboration with lidar atmospheric remote sensing groups at NASA Marshall Space Flight Center and National Oceanic and Atmospheric Administration (NOAA) Environmental Technology Laboratory, we have developed and flown the Multi-center Airborne Coherent Atmospheric Wind Sensor (MACAWS) lidar on the NASA DC-8 research aircraft. The scientific motivations for this effort are: to obtain measurements of subgrid scale (i.e. 2-200 km) processes and features which may be used to improve parameterizations in global/regional-scale models; to improve understanding and predictive capabilities on the mesoscale; and to assess the performance of Earth-orbiting Doppler lidar for global tropospheric wind measurements. MACAWS is a scanning Doppler lidar using a pulsed transmitter and coherent detection; the use of the scanner allows 3-D wind fields to be produced from the data. The instrument can also be radiometrically calibrated and used to study aerosol, cloud, and surface scattering characteristics at the lidar wavelength in the thermal infrared. MACAWS was used to study surface winds off the California coast near Point Arena, with an example depicted in the figure below. The northerly flow here is due to the Pacific subtropical high. The coastal topography interacts with the northerly flow in the marine inversion layer, and when the flow passes a cape or point that juts into the winds, structures called "hydraulic expansion fans" are observed. These are marked by strong variation along the vertical and cross-shore directions. The plots below show three horizontal slices at different heights above sea level (ASL). Bottom plots are enlargements of the area marked by dotted boxes above. The terrain contours are in 200-m increments, with the white spots being above 600-m elevation. Additional information is contained in the original.

Menzies, Robert T.↗

DOE OSTI2018

The Impact of Surface Heterogeneities and Land‐Atmosphere Interactions on Shallow Clouds Over ARM SGP Site

Abstract Continental shallow clouds are an important component of the land‐atmosphere coupled climate system because of their role in modulating energy and water budgets. The parameterization of these clouds in climate models presents a significant challenge. We evaluate the potential impact of subgrid‐scale (for climate models) land‐atmosphere interactions on shallow clouds using nested large‐eddy simulations (LESs). We compare LESs that allow for land‐atmosphere interactions to ones that artificially suppress all or part of them by smoothing out surface heterogeneities in surface heat, moisture and radiation fluxes within the domain. The LES domains are coupled to an interactive land surface model and nested inside a mesoscale domain. Three summertime shallow convection cases over the Department of Energy Atmospheric Radiation Measurement Facility's Southern Great Plains site are examined. A consistent increase in cloud water content is observed in all cases when surface heterogeneities and the land‐atmosphere interactions they induce in the LES domain are removed. By comparing experiments where only surface flux heterogeneities induced by cloud shadows are removed to ones where all surface flux heterogeneities are removed, we find that cloud shading‐induced surface heterogeneities can have a larger impact on shallow convection than static land surface heterogeneities in our cases. Furthermore, the impact of cloud shading on cloud water content and cloud size is found to vary significantly with the solar incidence angle. Our results suggest that the impact of cloud shadows needs to be considered when parameterizing land‐atmosphere interactions in the presence of shallow clouds for regional or global climate models.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1990

Modeling of compressible turbulence

The work is directed toward understanding and modeling compressibility effects in turbulent flows. The primary objective is to investigate how compressibility influences the basic turbulence processes such as turbulence production and dissipation, length scale modification, spectral energy transfer, etc. The second objective is to develop parameterization schemes and models to incorporate compressibility into one-point closure models and into the subgrid scale models for LES techniques. The ultimate purpose of this research is to develop compressible turbulence models which are capable of handling the hypersonic regime. Specifically, the emphasis will be on the model capability of predicting: (1) heat and momentum transfer in hypersonic boundary layers; and (2) mixing and growth of high Mach number shear layers, jet and wakes.

Zeman, O.↗

NASA NTRS1999

The Multi-Center Airborne Coherent Atmospheric Wind Sensor: Recent Measurements and Future Applications

The coherent Doppler lidar, when operated from an airborne platform, offers a unique measurement capability for study of atmospheric dynamical and physical properties. This is especially true for scientific objectives requiring measurements in optically-clear air, where other remote sensing technologies such as Doppler radar are at a disadvantage in terms of spatial resolution and coverage. Recent experience suggests airborne coherent Doppler lidar can yield unique wind measurements of--and during operation within--extreme weather phenomena. This paper presents the first airborne coherent Doppler lidar measurements of hurricane wind fields. The lidar atmospheric remote sensing groups of National Aeronautics and Space Administration (NASA) Marshall Space Flight Center, National Oceanic and Atmospheric Administration (NOAA) Environmental Technology Laboratory, and Jet Propulsion Laboratory jointly developed an airborne lidar system, the Multi-center Airborne Coherent Atmospheric Wind Sensor (MACAWS). The centerpiece of MACAWS is the lidar transmitter from the highly successful NOAA Windvan. Other field-tested lidar components have also been used, when feasible, to reduce costs and development time. The methodology for remotely sensing atmospheric wind fields with scanning coherent Doppler lidar was demonstrated in 1981; enhancements were made and the system was reflown in 1984. MACAWS has potentially greater scientific utility, compared to the original airborne scanning lidar system, owing to a factor of approx. 60 greater energy-per-pulse from the NOAA transmitter. MACAWS development was completed and the system was first flown in 1995. Following enhancements to improve performance, the system was re-flown in 1996 and 1998. The scientific motivation for MACAWS is three-fold: obtain fundamental measurements of subgrid scale (i.e., approx. 2-200 km) processes and features which may be used to improve parameterizations in hydrological, climate, and general/regional circulation models; obtain similar datasets to improve understanding and predictive capabilities for similarly-scaled processes and features; and simulate and validate the performance of prospective satellite Doppler lidars for global tropospheric wind measurement.

Rothermel, Jeffry↗

NASA NTRS2002

A New Statistically based Autoconversion rate Parameterization for use in Large-Scale Models

The autoconversion rate is a key process for the formation of precipitation in warm clouds. In climate models, physical processes such as autoconversion rate, which are calculated from grid mean values, are biased, because they do not take subgrid variability into account. Recently, statistical cloud schemes have been introduced in large-scale models to account for partially cloud-covered grid boxes. However, these schemes do not include the in-cloud variability in their parameterizations. In this paper, a new statistically based autoconversion rate considering the in-cloud variability is introduced and tested in three cases using the Canadian Single Column Model (SCM) of the global climate model. The results show that the new autoconversion rate improves the model simulation, especially in terms of liquid water path in all three case studies.

Lin, Bing↗

DOE OSTI2024

Causally‐Informed Deep Learning to Improve Climate Models and Projections

Abstract Climate models are essential to understand and project climate change, yet long‐standing biases and uncertainties in their projections remain. This is largely associated with the representation of subgrid‐scale processes, particularly clouds and convection. Deep learning can learn these subgrid‐scale processes from computationally expensive storm‐resolving models while retaining many features at a fraction of computational cost. Yet, climate simulations with embedded neural network parameterizations are still challenging and highly depend on the deep learning solution. This is likely associated with spurious non‐physical correlations learned by the neural networks due to the complexity of the physical dynamical system. Here, we show that the combination of causality with deep learning helps removing spurious correlations and optimizing the neural network algorithm. To resolve this, we apply a causal discovery method to unveil causal drivers in the set of input predictors of atmospheric subgrid‐scale processes of a superparameterized climate model in which deep convection is explicitly resolved. The resulting causally‐informed neural networks are coupled to the climate model, hence, replacing the superparameterization and radiation scheme. We show that the climate simulations with causally‐informed neural network parameterizations retain many convection‐related properties and accurately generate the climate of the original high‐resolution climate model, while retaining similar generalization capabilities to unseen climates compared to the non‐causal approach. The combination of causal discovery and deep learning is a new and promising approach that leads to stable and more trustworthy climate simulations and paves the way toward more physically‐based causal deep learning approaches also in other scientific disciplines.

Meteorology & Atmospheric Sciences↗

DOE OSTI2024

Evaluation of Autoconversion Representation in E3SMv2 Using an Ensemble of Large-Eddy Simulations of Low-Level Warm Clouds

In numerical atmospheric models that treat cloud and rain droplet populations as separate condensate categories, precipitation initiation in warm clouds is often represented by an autoconversion rate (Au), which is the rate of formation of new rain droplets through the collisions of cloud droplets. Being a function of the cloud droplet size distribution (DSD), the local Au is commonly parameterized as a function of DSD moments: cloud droplet number (n c ) and mass (q c ) concentrations. When applied in a large-scale model, the grid-mean Au must also include a correction, or enhancement factor, to account for the horizontal variability of the cloud properties across the model grid. In this study, we evaluate the Au representation in the Energy Exascale Earth System Model version 2 (E3SMv2) climate model using large-eddy simulations (LES), which explicitly resolve cloud droplet spectra, and therefore the local Au, as well as its spatial variability. The analysis of an ensemble of warm low-level cloud cases shows that the E3SMv2 formulation represents the Au reasonably well compared to the horizontally averaged explicitly computed rate from LES. The agreement, however, comes from a combination of an underestimated E3SM-tuned local Au rate and an overestimated subgrid cloud variability enhancement factor. The latter bias is traced to neglecting the horizontal variability of n c and its co-variability with q c in parameterizing the grid-mean Au.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS2002

Properties of the Residual Stress of the Temporally Filtered Navier-Stokes Equations

The development of a unifying framework among direct numerical simulations, large-eddy simulations, and statistically averaged formulations of the Navier-Stokes equations, is of current interest. Toward that goal, the properties of the residual (subgrid-scale) stress of the temporally filtered Navier-Stokes equations are carefully examined. Causal time-domain filters, parameterized by a temporal filter width 0 less than Delta less than infinity, are considered. For several reasons, the differential forms of such filters are preferred to their corresponding integral forms; among these, storage requirements for differential forms are typically much less than for integral forms and, for some filters, are independent of Delta. The behavior of the residual stress in the limits of both vanishing and in infinite filter widths is examined. It is shown analytically that, in the limit Delta to 0, the residual stress vanishes, in which case the Navier-Stokes equations are recovered from the temporally filtered equations. Alternately, in the limit Delta to infinity, the residual stress is equivalent to the long-time averaged stress, and the Reynolds-averaged Navier-Stokes equations are recovered from the temporally filtered equations. The predicted behavior at the asymptotic limits of filter width is further validated by numerical simulations of the temporally filtered forced, viscous Burger's equation. Finally, finite filter widths are also considered, and a priori analyses of temporal similarity and temporal approximate deconvolution models of the residual stress are conducted.

Pruett, C. D.↗