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NASA NTRS1998

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.↗

NASA NTRS2021

Nighttime Convection in Water-ice Clouds at High Northern Latitudes on Mars

We investigate water-ice clouds and their influence on the temperature structure of the Mar-tian atmosphere at high northern latitudes in early summer. New results are obtained throughcoordinated analysis of two types of data from Mars Global Surveyor: atmospheric profiles re-trieved from radio occultation (RO) measurements and wide-angle images from the Mars OrbiterCamera (MOC). Some RO profiles contain a layer of neutral static stability, which indicates thepresence of convective mixing at a local time (about 5 h) when it does not usually occur. Thesenocturnal mixed layers (NMLs) were observed frequently in early summer of Mars year 27 atlatitudes of 53–72◦N and longitudes of 210–330◦E. The base of a typical NML is 3 km abovethe surface, about the same height as the nighttime cloud layer detected by the Phoenix LIDARin early summer of Mars year 29 at 234◦E, 68◦N. The depth of the NMLs ranges from less than1 km to more than 5 km. Comparisons with nearly simultaneous MOC images demonstrate thatNMLs are closely associated with water-ice clouds. There is a dense cluster of NMLs within theannular cloud that appears every year in early summer between Alba Mons and the north polarresidual ice cap. The lighting conditions at this location and season allowed MOC to observe theannular cloud on most orbits, at 118-min intervals. Its appearance varies dramatically with localtime, becoming more symmetrical and better organized at night and dissipating to a crescentshape during the day. According to high-resolution numerical simulations (Spiga et al., 2017),including a large-eddy simulation at the Phoenix landing site, NMLs form when radiative cool-ing by water-ice aerosols causes convective instability; the mixed layer is forced from above bynegative buoyancy. Our results strongly support this conclusion. In addition, MOC images frommidsummer contain eastward-moving frontal clouds. Temperature profiles within these cloudsshow signs of near-surface advection of warm air, which reduces the static stability of the loweratmosphere and contributes, along with cloud radiation, to the formation of an NML.

David Hinson↗

NASA NTRSDate not supplied

Flow Physics at a Large Rotor Tip Gap in a Multi-Stage Axial Compressor

The flow physics in a large rotor tip gap in a 1.5-stage axial compressor is investigated in the current study. The flow structure in the rotor tip region is complex with several dominant vortical structures of opposite rotation, resulting in inhomogeneous and highly anisotropic turbulence. Earlier measurements show that eddy viscosity is negative over large parts of the tip region and eddy viscosity varies among stress/strain components. The present study aims to understand how the complex nature of rotor tip leakage flow affects compressor performance when the tip gap size is greater than 4–5% of the rotor span, which is typical of advanced small core engines. Unsteady Reynolds-averaged Navier-Stokes (URANS) and Large Eddy Simulation (LES) techniques are applied to study flow physics in a large rotor tip gap (5.5% of rotor span) in a 1.5-stage axial compressor. Calculated flow fields from the two different approaches are compared with available measurements and examined in detail. LES calculates the pressure rise in the present compressor fairly well, while URANS with a standard two-equation turbulence closure underpredicts the pressure rise by 15-20% of the measured values. The current study shows that URANS with the current turbulence closure produces much higher all-positive eddy viscosity in the tip-gap region compared to measurements and LES. The distribution of eddy viscosity in the URANS simulation is also wrong. Consequently, the flow in the tip region is highly damped with significantly larger blockage generation, which results in the tip leakage vortex (TLV) staying closer to the blade suction side compared to the measurement. When the TLV stays closer to the blade, both flow turning and the pressure rise across the compressor are reduced compared to the measurements. It appears that this effect is amplified by a large rotor tip gap.

tip gap↗

DOE OSTI2026

High-Resolution Mesoscale Simulations of Historical U.S. Gulf Coast Hurricanes

This dataset provides coupled mesoscale and microscale (large-eddy simulation; LES) atmospheric simulations of five historical U.S. Gulf Coast hurricanes. Meso-microscale coupled simulations of Hurricanes Harvey (2017), Nate (2017), Michael (2018), Laura (2020), and Delta (2020) were performed with the Weather Research and Forecasting (WRF) model v4.1.5. The mesoscale component captures the multi-day evolution of each storm's track, intensity, and large-scale structure across the Gulf of Mexico, while the LES component explicitly resolves the dominant turbulent eddies in the hurricane boundary layer at a horizontal grid spacing of 33.33 m. Together, these simulations characterize tropical cyclone wind fields across atmospheric scales ranging from ~100 km down to ~100 m, spanning storm intensities from Category 2 through Category 4 on the Saffir–Simpson scale. This dataset contains the mesoscale simulations, separated by each storm.

17 WIND ENERGY↗

DOE OSTI2025

Toward integrating high-fidelity CFD approaches in the thermal-hydraulic analysis of turbulent dry cask systems

Nuclear power plants have been supplying resilient and reliable electricity for decades, contributing to energy independence of the U.S.. However, nuclear waste management remains one of the most significant challenges in the industry. The safety of dry cask storage systems relies heavily on their thermal-hydraulic performance. Computational Fluid Dynamics (CFD) simulations are often used to demonstrate this performance and ensure that the system design meets safety standards. This study presents reduced numerical models for various types of dry cask systems. These numerical models can produce efficient and fast results based on the employed modeling strategies. Additionally, the study uses a novel approach to high-fidelity simulations to evaluate modeling assumptions in dry cask modeling. Large Eddy Simulations (LES) are used for this purpose, particularly in regions where fluid velocity is relatively high and the turbulence characteristics become important. Furthermore, the results of these high-fidelity simulations will enhance the interpretation of outcomes produced from a lower-fidelity CFD model.

CFD↗

DOE OSTI2025

Investigating the relationship between simulation parameters and flow variables in simulating atmospheric gravity waves for wind energy applications

Wind farms, particularly offshore clusters, are becoming larger than ever before. Besides influencing the surface wind flow and the inflow for downstream wind farms, large wind farms can trigger atmospheric gravity waves in the inversion layer and the free atmosphere aloft. Wind-farm-induced gravity waves can cause adverse pressure gradients upstream of the wind farm, which contribute to the global blockage effect, and can induce favorable pressure gradients above and downstream of the wind farm that enhance wake recovery. Numerical modeling is a powerful means of studying these wind-farm-induced atmospheric gravity waves, but it comes with the challenge of handling spurious reflections of these waves from domain boundaries. Typically, approaches which employ radiation boundary conditions and forcing zones are used to avoid these reflections. However, the simulation setup of these approaches relies heavily on ad hoc processes. For instance, the widely used Rayleigh damping method requires ad hoc tuning to produce a setup that may only produce satisfactory results for a particular case. To provide more systematic guidance on setting up realistic simulations of atmospheric gravity waves, we conduct a large-eddy simulation (LES) study of flow over a 2D hill and through a wind farm canopy that explores the optimum domain size and damping layer setup depending on the fundamental parameters which determine the flow characteristics. In this work, we only consider linearly stratified conditions (i.e., no inversion layer), thereby focusing on internal gravity waves in the free atmosphere and their reflections from the domain boundaries. This type of flow is governed by a single Froude number, which dictates most of the internal wave properties, such as wavelength, amplitude, and direction. This, in turn, will dictate the optimum domain size and Rayleigh damping layer setup. We find the effective horizontal and vertical wavelengths (the representative wavelengths of the entire wave spectrum) to be the appropriate length scales to size the domain and damping layer thickness, and the optimal Rayleigh damping coefficient scales with the Brunt–Väisälä frequency. Considering Froude numbers seen in wind farm applications, we propose recommendations to limit the reflections to less than 10 % of the total upward-propagating wave energy. Typically, damping is done at the top boundary, but given the non-periodic lateral boundary conditions of practical wind farm simulation domains, we find that damping the inflow–outflow boundaries is of equal importance to damping the top boundary. The Brunt–Väisälä frequency-normalized damping coefficient should be between 1 and 10. The damping layer thickness should be at least one effective vertical wavelength; damping layers exceeding 1.5 times the vertical wavelength are found to be unnecessary. The domain length and height should accommodate at least one effective horizontal and vertical wavelength, respectively. Moreover, Rayleigh damping does not damp the waves completely, and the non-damped energy might accumulate over the simulation time.

17 WIND ENERGY↗

DOE OSTI2025

Summary Report Of The FY25 Computational Fluid Dynamics Verification And Validation Exercises In The Advanced Reactor Technologies - Gas-cooled Reactor Program

Verification and Validation (V&V) of numerical tools is critical for ensuring reasonable predictions during design, safety analysis, and licensing. Recent work in the Advanced Reactor Technologies - Gas-cooled Reactor (ART-GCR) program has focused on V&V of common Computational Fluid Dynamics (CFD) tools that are used within the Untied States. This report presents an update on these CFD V&V activities. These Generation IV Forum (GIF) Very High Temperature Reactor (VHTR) Computational Methods, Validation, and Benchmarking (CMVB) is an international organization dedicated to the verification and validation of High Temperature Gas-Cooled Reactor (HTGR) simulation tools. Participation in the CMVB provides additional value to the V&V activities, as it allows for access to a wider range of data, and provides valuable benchmarking exercises. Three HTGR phenomena are targeted: Reactor Cavity Cooling System (RCCS) performance, core bypass flow, and lower plenum mixing. Simulations of the University of Wisconsin-Madison (UW-Madison) RCCS facilities are performed with Reynolds Averaged Navier-Stokes (RANS) in StarCCM+. Results are compared for both forced and natural convection conditions, with both exhibiting good agreement with experimental measurements. The Idaho National Laboratory (INL) matched index of refraction (MIR) and Korean Atomic Energy Research Institute (KAERI) bypass flow expeirments are used to validation CFD predictions of bypass flow. Simulations are performed with RANS in StarCCM+ and with Large Eddy Simulation (LES) in NekRS. Finally, preliminary simulations of the Institute of Nuclear and New Energy Technology (INET) lower plenum mixing facilities are presented. Initial work has developed models with LES, RANS, and porous media models. These preliminary models are presented and compared to each other to gauge differences in predictions with each of the three methods.

and Benchmarking (CMVB)↗

NASA NTRS2015

Detached Eddy Simulation for the F-16XL Aircraft Configuration

Numerical simulations for the flow around the F-16XL configuration as a contribution to the Cranked Arrow Wing Aerodynamic Project International 2 (CAWAPI-2) have been performed. The NASA Langley Tetrahedral Unstructured Software System (TetrUSS) with its USM3D solver was used to perform the unsteady flow field simulations for the subsonic high angle-of-attack case corresponding to flight condition (FC) 25. Two approaches were utilized to capture the unsteady vortex flow over the wing of the F-16XL. The first approach was to use Unsteady Reynolds-Averaged Navier-Stokes (URANS) coupled with standard turbulence closure models. The second approach was to use Detached Eddy Simulation (DES), which creates a hybrid model that attempts to combine the most favorable elements of URANS models and Large Eddy Simulation (LES). Computed surface static pressure profiles are presented and compared with flight data. Time-averaged and instantaneous results obtained on coarse, medium and fine grids are compared with the flight data. The intent of this study is to demonstrate that the DES module within the USM3D solver can be used to provide valuable data in predicting vortex-flow physics on a complex configuration.

Elmiligui, Alaa↗

NASA NTRS2004

Single-column Model Intercomparison for a Stably Stratified Atmospheric Boundary Layer

The parameterization of the stably stratified atmospheric boundary layer is a difficult issue, which has a large impact on the medium-range weather forecasts and on climate integrations. A non-strongly stratified arctic case is simulated by nineteen single-column turbulence schemes. The statistics from the Large-eddy simulation (LES) intercomparison made for the same case by eight different models are used as a guiding reference. The single-column parameterizations include research schemes and operational schemes from major forecast and climate research centres. First order schemes, a large number of turbulence kinetic energy closures, and other proposals have submitted results. There is a large spread in the results; in general, the operational schemes mix more efficiently than the research ones, and the TKE and other higher order closures give results closer to the LES statistics. The sensitivities of the schemes to the parameters of their turbulence closures are partially explored.

Cuxart, J.↗

NASA NTRS2000

Wake Vortex Transport and Decay in Ground Effect: Vortex Linking with the Ground

Numerical simulations are carried out with a three-dimensional Large-Eddy Simulation (LES) model to explore the sensitivity of vortex decay and transport in ground effect (IGE). The vortex decay rates are found to be strongly enhanced following maximum descent into ground effect. The nondimensional decay rate is found to be insensitive to the initial values of circulation, height, and vortex separation. The information gained from these simulations is used to construct a simple decay relationship. This relationship compares well with observed data from an IGE case study. Similarly, a relationship for lateral drift due to ground effect is constructed from the LES data. In the second part of this paper, vortex linking with the ground is investigated. Our numerical simulations of wake vortices for IGE show that a vortex may link with its image beneath the ground, if the intensity of the ambient turbulence is moderate to high. This linking with the ground (which is observed in real cases)gives the appearance of a vortex tube that bends to become vertically oriented and which terminates at the ground. From the simulations conducted, the linking time for vortices in the free atmosphere; i.e., a function of ambient turbulence intensity.

Proctor, Fred H.↗

NASA NTRS2003

Simulation of Combustion Systems with Realistic g-jitter

In this project a transient, fully three-dimensional computer simulation code was developed to simulate the effects of realistic g-jitter on a number of combustion systems. The simulation code is capable of simulating flame spread on a solid and nonpremixed or premixed gaseous combustion in nonturbulent flow with simple combustion models. Simple combustion models were used to preserve computational efficiency since this is meant to be an engineering code. Also, the use of sophisticated turbulence models was not pursued (a simple Smagorinsky type model can be implemented if deemed appropriate) because if flow velocities are large enough for turbulence to develop in a reduced gravity combustion scenario it is unlikely that g-jitter disturbances (in NASA's reduced gravity facilities) will play an important role in the flame dynamics. Acceleration disturbances of realistic orientation, magnitude, and time dependence can be easily included in the simulation. The simulation algorithm was based on techniques used in an existing large eddy simulation code which has successfully simulated fire dynamics in complex domains. A series of simulations with measured and predicted acceleration disturbances on the International Space Station (ISS) are presented. The results of this series of simulations suggested a passive isolation system and appropriate scheduling of crew activity would provide a sufficiently "quiet" acceleration environment for spherical diffusion flames.

Mell, William E.↗

NASA NTRSDate not supplied

Simulating Transonic Buffet Aerodynamics for the Boeing Transonic Truss-Braced Wing Aircraft

The flow past the Boeing Transonic Truss-Braced Wing (TTBW) aircraft is simulated with a Hybrid Reynolds-Averaged Navier Stokes Large-Eddy Simulations (HRLES) turbulence modeling approach to study transonic buffet onset and evaluate the predictive capability of the numerical approach. All simulations used structured overset curvilinear grids for the free-air configuration, with all simulations performed using the Launch, Ascent, and Vehicle Aerodynamics (LAVA) computational framework. Aerodynamic loads and surface pressure obtained from the HRLES solutions are compared to results from unsteady RANS (URANS) and experiments conducted at NASA Ames 11-by 11-Foot Transonic Wind Tunnel. Overall good agreement is obtained in the predicted loads and surface pressure. Unsteady pressure data from HRLES and URANS simulations is utilized to compute power spectral density (PSD) to predict transonic buffet onset and compared to the Kulite data obtained from the experiment. Comparisons of the PSD spectrum also show reasonable agreement with the wind tunnel data, with HRLES and URANS predicting buffet onset at a slightly earlier angle-of-attack than the experiment.

AATT↗

DOE OSTI2024

Identification of Climatological Representative Days in the Mid-Atlantic for High-Fidelity Offshore Wind Energy Modeling

The goal of reaching 30 GW of offshore wind energy by 2030 becomes more realistic with the continued approval of offshore wind energy areas by the Biden Administration. In the Mid-Atlantic, where wind energy projects are in the most advanced stages of development, there is increased research focus on the eventual interaction of these wind farms. These interactions, in the form of wakes and cluster wakes, or wakes from multiple wind farms, could have detrimental effects on power production and forecastability for downwind wind farms (Pryor et al. 2022, Golbazi et al. 2022, Rosencrans et al. 2023). To help alleviate these issues, numerical simulations in the form of numerical weather prediction (NWP) and large eddy simulations (LES) can provide insight into when cluster wake situations may occur, but running such simulations can be expensive and difficult to run for multiple years. In this study, we leverage and build upon existing techniques in the literature (Fischereit et al. 2022) to identify climatologically representative days for wind energy areas in the Mid-Atlantic where conditions would promote cluster wake situations. We select meteorological variables (wind speed, wind direction, atmospheric stability, boundary-layer height, TKE) critical to understanding wind energy production and wake propagation. We then consider two different NWP datasets of varying spatial and temporal resolution: ERA5 provides data at hourly intervals from 1940 to present at 0.25 deg (31 km) spatial resolution (Hersbach et al. 2020), and the NOW-23 dataset provides data at 5-minute resolution for 21 years at 2-km spatial resolution (Bodini et al. 2020). Our first step is to compare these two datasets for an overlapping 21-year time period. Initial results show that the required number of days to represent the long-term climate increases with each additional variable considered. In their study of the German Bight, Fischereit et al. (2022) found that they could represent the long-term wind and wave climate in a "near-perfect" way with -180 days, by reaching a Perkins Skill Score (PSS) of 0.9; our investigation of the mid-Atlantic wind resource region with ERA5 and NOW-23 data suggests that we will need -100 days to reach a PSS of 0.9. As we expand our parameter space to include multiple variables, the number of required days will likely grow. These results will ultimately be used to select case studies to best represent cluster wake conditions that apply to this region for the lifetime of likely wind farms in this mid-Atlantic region.

clusterwakes↗

NASA NTRS2022

Simulation and Scaling of the Turbulent Vertical Heat Transport and Deep-Cycle Turbulence Across the Equatorial Pacific Cold Tongue

Microstructure observations in the Pacific cold tongue reveal that strong turbulence often penetrates into the thermocline producing hundreds of W/m2 of downward heat transport during nighttime and early morning. However, virtually all observations of this deep-cycle turbulence (DCT) are from 0◦N,140◦W. Here, a hierarchy of ocean process simulations including submesoscale-permitting regional models and turbulence-permitting large eddy simulations (LES) embedded in a regional model provide insight into DCT at and beyond 0◦N,140◦W. A regional hindcast quantifies the spatio-temporal variability of subsurface turbulent heat fluxes throughout the cold tongue from 1999-2016. Climatologically, the mean heat flux is strongest (∼100W/m2) within2◦ of the equator. The heat flux is slightly (∼10 W/m2) stronger in the northern than southern hemisphere throughout the cold tongue. The seasonal cycle of the heat flux, which is not everywhere aligned with the surface flux, ranges from 150 W/m2 near the equator to 30 W/m2 and 10 W/m2 at 4◦N and S respectively. Aseasonal variability of turbulent heat fluxes is logarithmically distributed and temporally uncorrelated with surface heat fluxes. The aseasonal variability of turbulence is highlighted in 34-day LES of Boreal autumn at 0◦N and 3◦N,140◦W. Intense DCT occurs frequently above the undercurrent at 0◦N and intermittently at 3◦N. Daily-mean heat fluxes scale with the bulk vertical shear and the wind stress, which together explain ∼90% of the daily variance across both LES. Observational validation of the scaling at 0◦N,140◦W is encouraging, but observations beyond 0◦N,140◦W can facilitate needed refinement of mixing parameterization in ocean models.

Simulation↗

DOE OSTI2026

Simulations of a hypersonic turbulent boundary layer over wavy surfaces

Here, we conduct large-eddy simulations of a Mach 5.84 cold wall turbulent boundary layer over one-dimensional wavy walls with varying amplitudes and wavelengths. Across all wall topologies, a series of alternating shock and expansion waves is shown to influence the entire boundary layer, and generate repeating wave patterns in the turbulent stresses, dispersive stresses, and turbulent kinetic energy budget. The series of alternating shocks and expansions imposes repeating adverse and favourable pressure gradients across the wavy wall, and at sufficient wall amplitude, triggers flow separation in the trough of the wave. Flow separation is demonstrated to influence the behaviour of wall pressure fluctuations over the wavy wall. In attached flows, the prominent frequencies are consistent with integral-scale boundary layer turbulence, whereas in separated flows, a two-decade frequency range is present, akin to two-dimensional shock–boundary layer interactions. Counter-rotating streamwise-oriented structures are observed on the windward side of the wave, which diminish over the wave crest. A conditional analysis demonstrates that these structures are present in the upstream boundary layer, and are amplified with increasing wall amplitude. An examination of the Görtler number and probability density function (PDF) of the fluctuating lateral wall shear stress demonstrates the strong correlation between a large Görtler number and growth of the PDF tail density, suggesting that the amplification of the counter-rotating streamwise-oriented structures are linked to centrifugal instabilities in regions of streamline concavity.

boundary layers↗

NASA NTRS2015

Noise Characteristics of a Four-Jet Impingement Device Inside a Broadband Engine Noise Simulator

The noise generation mechanisms for four directly impinging supersonic jets are investigated employing implicit large eddy simulations with a higher-order accurate weighted essentially non-oscillatory shock-capturing scheme. Impinging jet devices are often used as an experimental apparatus to emulate a broadband noise source. Although such devices have been used in many experiments, a detailed investigation of the noise generation mechanisms has not been conducted before. Thus, the underlying physical mechanisms that are responsible for the generation of sound waves are not well understood. The flow field is highly complex and contains a wide range of temporal and spatial scales relevant for noise generation. Proper orthogonal decomposition of the flow field is utilized to characterize the unsteady nature of the flow field involving unsteady shock oscillations, large coherent turbulent flow structures, and the sporadic appearance of vortex tubes in the center of the impingement region. The causality method based on Lighthill's acoustic analogy is applied to link fluctuations of flow quantities inside the source region to the acoustic pressure in the far field. It will be demonstrated that the entropy fluctuation term in the Lighthill's stress tensor plays a vital role in the noise generation process. Consequently, the understanding of the noise generation mechanisms is employed to develop a reduced-order linear acoustic model of the four-jet impingement device. Finally, three linear acoustic FJID models are used as broadband noise sources inside an engine nacelle and the acoustic scattering results are validated against far-field acoustic experimental data.

Broadband↗

NASA NTRS1990

Subgrid-scale backscatter in transitional and turbulent flows

Most subgrid-scale (SGS) models for large-eddy simulations are absolutely dissipative (that is, they remove energy from the large scales at each point in the physical space). The actual SGS stresses, however, may transfer energy to the large scales (backscatter) at a given location. Direct numerical simulations of turbulent channel flow and compressible isotropic turbulence are used to study the backscatter phenomena. In all flows considered roughly 50 percent of the grid points were experiencing backscatter when a Fourier cutoff filter was used. The backscatter fraction was less with a Gaussian filter, and intermediate with a box filter in physical space. Moreover, the backscatter and forward scatter contributions to the SGS dissipation were comparable, and each was often much larger than the total SGS dissipation. The SGS dissipation (normalized by total dissipation) increased with filter width almost independently of filter type and Reynolds number. The amount of backscatter showed an increasing trend with Reynolds numbers. In the near-wall region of the channel, events characterized by strong Reynolds shear stress correlated fairly well with areas of high SGS dissipation (both forward and backward). In compressible isotropic turbulence similar results were obtained, independent of fluctuation Mach number.

Piomelli, Ugo↗

NASA NTRS1999

Characterization of Sound Radiation by Unresolved Scales of Motion in Computational Aeroacoustics

Evaluation of the sound sources in a high Reynolds number turbulent flow requires time-accurate resolution of an extremely large number of scales of motion. Direct numerical simulations will therefore remain infeasible for the forseeable future: although current large eddy simulation methods can resolve the largest scales of motion accurately the, they must leave some scales of motion unresolved. A priori studies show that acoustic power can be underestimated significantly if the contribution of these unresolved scales is simply neglected. In this paper, the problem of evaluating the sound radiation properties of the unresolved, subgrid-scale motions is approached in the spirit of the simplest subgrid stress models: the unresolved velocity field is treated as isotropic turbulence with statistical descriptors, evaluated from the resolved field. The theory of isotropic turbulence is applied to derive formulas for the total power and the power spectral density of the sound radiated by a filtered velocity field. These quantities are compared with the corresponding quantities for the unfiltered field for a range of filter widths and Reynolds numbers.

Rubinstein, Robert↗