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NASA NTRS1999

Large Eddy Simulation of Cirrus Clouds

The Regional Atmospheric Modeling System (RAMS) with mesoscale interactive nested-grids and a Large-Eddy Simulation (LES) version of RAMS, coupled to two-moment microphysics and a new two-stream radiative code were used to investigate the dynamic, microphysical, and radiative aspects of the November 26, 1991 cirrus event. Wu (1998) describes the results of that research in full detail and is enclosed as Appendix 1. The mesoscale nested grid simulation successfully reproduced the large scale circulation as compared to the Mesoscale Analysis and Prediction System's (MAPS) analyses and other observations. Three cloud bands which match nicely to the three cloud lines identified in an observational study (Mace et al., 1995) are predicted on Grid #2 of the nested grids, even though the mesoscale simulation predicts a larger west-east cloud width than what was observed. Large-eddy simulations (LES) were performed to study the dynamical, microphysical, and radiative processes in the 26 November 1991 FIRE 11 cirrus event. The LES model is based on the RAMS version 3b developed at Colorado State University. It includes a new radiation scheme developed by Harrington (1997) and a new subgrid scale model developed by Kosovic (1996). The LES model simulated a single cloud layer for Case 1 and a two-layer cloud structure for Case 2. The simulations demonstrated that latent heat release can play a significant role in the formation and development of cirrus clouds. For the thin cirrus in Case 1, the latent heat release was insufficient for the cirrus clouds to become positively buoyant. However, in some special cases such as Case 2, positively buoyant cells can be embedded within the cirrus layers. These cells were so active that the rising updraft induced its own pressure perturbations that affected the cloud evolution. Vertical profiles of the total radiative and latent heating rates indicated that for well developed, deep, and active cirrus clouds, radiative cooling and latent heating could be comparable in magnitude in the cloudy layer. This implies that latent heating cannot be neglected in the construction of a cirrus cloud model. The probability density function (PDF) of w was analyzed to assist in the parameterization of cloud-scale velocities in large-scale models. For the more radiatively-driven, thin cirrus case, the PDFs are approximately Gaussian. However, in the interior of the deep, convectively unstable case, the PDFs of w are multi-modal and very broad, indicating that parameterizing cloud-scale motions for such clouds can be very challenging. The results of this research are described in detail in a paper submitted to the Journal of Atmospheric Science (Wu and Cotton, 1999), which is enclosed as Appendix 2. Using soundings extracted from a mesoscale simulation of the November 26, 1991 cirrus event, the radiative effects on vapor deposition/sublimation of ice crystals was studied using a two-dimensional cloud-resolving model (CRM) version of RAMS, coupled to an explicit bin-resolving microphysics. The CRM simulations of the November 26, 1991 cirrus event demonstrate that the radiative impact on the diffusional growth (or sublimation) of ice crystals is significant. In this case, the ice particles experienced radiative warming. Model results show that radiative feedbacks in the diffusional growth of ice particles can be very complex. Radiative warming of an ice particle will restrict the particle's diffusional growth. In the case of radiative warming, ice particles larger than a certain size will experience so much radiative warming that surface ice saturation vapor pressures become large enough to cause sublimation of the larger crystals, while smaller crystals are growing by vapor deposition. However, ice mass production can be enhanced in the case of radiative cooling of an ice particle. For the November 26, 1991 cirrus event, radiative feedback results in significant reduction in the total ice mass, especially in the production of large ice crystals, and consequently, both radiative and dynamic properties of the cirrus cloud are significantly affected. A complete description of this research has been submitted as a paper to the Journal of Atmospheric Science (Wu et al., 1999), and included as Appendix 3.

Wu, Ting↗
NASA NTRS1997

Annual Research Briefs

This report contains the 1997 annual progress reports of the research fellows and students supported by the Center for Turbulence Research (CTR). Titles include: Invariant modeling in large-eddy simulation of turbulence; Validation of large-eddy simulation in a plain asymmetric diffuser; Progress in large-eddy simulation of trailing-edge turbulence and aeronautics; Resolution requirements in large-eddy simulations of shear flows; A general theory of discrete filtering for LES in complex geometry; On the use of discrete filters for large eddy simulation; Wall models in large eddy simulation of separated flow; Perspectives for ensemble average LES; Anisotropic grid-based formulas for subgrid-scale models; Some modeling requirements for wall models in large eddy simulation; Numerical simulation of 3D turbulent boundary layers using the V2F model; Accurate modeling of impinging jet heat transfer; Application of turbulence models to high-lift airfoils; Advances in structure-based turbulence modeling; Incorporating realistic chemistry into direct numerical simulations of turbulent non-premixed combustion; Effects of small-scale structure on turbulent mixing; Turbulent premixed combustion in the laminar flamelet and the thin reaction zone regime; Large eddy simulation of combustion instabilities in turbulent premixed burners; On the generation of vorticity at a free-surface; Active control of turbulent channel flow; A generalized framework for robust control in fluid mechanics; Combined immersed-boundary/B-spline methods for simulations of flow in complex geometries; and DNS of shock boundary-layer interaction - preliminary results for compression ramp flow.

Spinks, Debra↗
NASA NTRS1998

Cloud Scaling Properties and Cloud Parameterization

Cloud liquid and cloud traction variability is studied as a function of horizontal scale in the ECMWF forecast model during several 10-day runs at the highest available model resolution, recently refined from approximately 60 km (T213) down to approximately 20 km (T639). At higher resolutions, model plane-parallel albedo biases are reduced, so that models may be tuned to have larger, more realistic, cloud liquid water amounts, However, the distribution of cloud liquid assumed -within- each gridbox, for radiative and thermodynamic computations, depends on ad hoc assumptions that are not necessarily consistent with observed scaling properties, or with scaling properties produced by the model at larger scales. To study the larger-scale cloud properties, ten locations on the Earth are chosen to coincide with locations having considerable surface data available for validation, and representing a variety of climatic regimes, scaling exponents are determined from a range or scales down to model resolution, and are re-computed every three hours, separately for low, medium and high clouds, as well as column-integrated cloudiness. Cloud variability fluctuates in time, due to diurnal, synoptic and other' processes, but scaling exponents are found to be relatively stable. various approaches are considered for applying computed cloud scaling to subgrid cloud distributions used for radiation, beyond simple random or maximal overlap now in common use. Considerably more work is needed to compare model cloud scaling with observations. This will be aided by increased availability of high-resolution surface, aircraft and satellite data, and by the increasing resolution of global models,

Cahalan, R. F.↗
NASA NTRS1997

Time-Domain Filtering for Spatial Large-Eddy Simulation

An approach to large-eddy simulation (LES) is developed whose subgrid-scale model incorporates filtering in the time domain, in contrast to conventional approaches, which exploit spatial filtering. The method is demonstrated in the simulation of a heated, compressible, axisymmetric jet, and results are compared with those obtained from fully resolved direct numerical simulation. The present approach was, in fact, motivated by the jet-flow problem and the desire to manipulate the flow by localized (point) sources for the purposes of noise suppression. Time-domain filtering appears to be more consistent with the modeling of point sources; moreover, time-domain filtering may resolve some fundamental inconsistencies associated with conventional space-filtered LES approaches.

Pruett, C. David↗
NASA NTRS1999

On Taylor-Series Approximations of Residual Stress

Although subgrid-scale models of similarity type are insufficiently dissipative for practical applications to large-eddy simulation, in recently published a priori analyses, they perform remarkably well in the sense of correlating highly against exact residual stresses. Here, Taylor-series expansions of residual stress are exploited to explain the observed behavior and "success" of similarity models. Until very recently, little attention has been given to issues related to the convergence of such expansions. Here, we re-express the convergence criterion of Vasilyev [J. Comput. Phys., 146 (1998)] in terms of the transfer function and the wavenumber cutoff of the grid filter.

Pruett, C. David↗
NASA NTRS1998

Influence of Soil Heterogeneity on Mesoscale Land Surface Fluxes During Washita '92

The influence of soil heterogeneity on the partitioning of mesoscale land surface energy fluxes at diurnal time scales is investigated over a 10(exp 6) sq km domain centered on the Little Washita Basin, Oklahoma, for the period June 10 - 18, 1992. The sensitivity study is carried out using MM5/PLACE, the Penn State/NCAR MM5 model enhanced with the Parameterization for Land-Atmosphere-Cloud Exchange or PLACE. PLACE is a one-dimensional land surface model possessing detailed plant and soil water physics algorithms, multiple soil layers, and the capacity to model subgrid heterogeneity. A series of 12-hour simulations were conducted with identical atmospheric initialization and land surface characterization but with different initial soil moisture and texture. A comparison then was made of the simulated land surface energy flux fields, the partitioning of net radiation into latent and sensible heat, and the soil moisture fields. Results indicate that heterogeneity in both soil moisture and texture affects the spatial distribution and partitioning of mesoscale energy balance. Spatial averaging results in an overprediction of latent heat flux, and an underestimation of sensible heat flux. In addition to the primary focus on the partitioning of the land surface energy, the modeling effort provided an opportunity to examine the issue of initializing the soil moisture fields for coupled three-dimensional models. For the present case, the initial soil moisture and temperature were determined from off-line modeling using PLACE at each grid box, driven with a combination of observed and assimilated data fields.

Jasinski, Michael F.↗
NASA NTRS1999

Ocean Turbulence: Mesoscale Modeling in Isopycnal Coordinates the role of the Spectrum of Vertical Shear - Part 4

We study the tracer subgrid term in isopycnal coordinates, S(sub I). We employ two ingredients: the experimental data on vertical spectra of ocean turbulence measured by Gargett et al.(1981) and the stochastic approach recently developed by Dukowicz and Smith (1997). Our result confirms that S(sub I) is made of two parts: an advection and a diffusion term. However, the tracer bolus velocity u** consists of two terms u** = u(sub 1) + u(sub 2) while in the GM model there is only a term related to u(sub 1) which is shown to be: u(sub 1) = k(bar-q)(sup -1)(delta)(sub rho) where bar-q is the thickness weighted average potential vorticity, a result in agreement with the recent suggestions by Treguier et al. (1997), Lee et al. (1997) and Greatbatch (1998). The second component u(sub 2) IS new. We compute it in the geostrophic approximation using the Gargett et al. data (1981) on ocean vertical turbulence. We find that u(sub 2) much greater than u(sub 1) and that u(sub 2) is orthogonal to u(sub 1).

Canuto, V. M.↗
NASA NTRS1998

The Vertical Extent of the Influence of the Land Surface Boundary on the Atmosphere Above

Heterogeneities in the land surface type on scales smaller than the typical General Circulation Model (GMC) grid size have long presented a challenge to properly modelling the impact of the subgrid scale variability on the grid scale. In particular, at some height above the heterogeneous vegetated surface the atmospheric properties (temperature, humidity, for example) become homogenized. This is an issue with implications for climate modelling as well as for the optimal use of field data for climate studies. There is evidence that the influence of the soil and/or vegetation properties extends well beyond the atmospheric surface layer. The present study is aimed at understanding the implications of this influence for a GCM's description of the coupling at the earth-atmosphere interface.

Molod, Andrea↗
NASA NTRS1999

Large-Eddy Simulation of Aeroacoustic Applications

This report summarizes work accomplished under a one-year NASA grant from NASA Langley Research Center (LaRC). The effort culminates three years of NASA-supported research under three consecutive one-year grants. The period of support was April 6, 1998, through April 5, 1999. By request, the grant period was extended at no-cost until October 6, 1999. Its predecessors have been directed toward adapting the numerical tool of large-eddy simulation (LES) to aeroacoustic applications, with particular focus on noise suppression in subsonic round jets. In LES, the filtered Navier-Stokes equations are solved numerically on a relatively coarse computational grid. Residual stresses, generated by scales of motion too small to be resolved on the coarse grid, are modeled. Although most LES incorporate spatial filtering, time-domain filtering affords certain conceptual and computational advantages, particularly for aeroacoustic applications. Consequently, this work has focused on the development of subgrid-scale (SGS) models that incorporate time-domain filters.

Pruett, C. David↗
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 NTRS2000

A Catchment-Based Approach to Modeling Land Surface Processes in a GCM: Parameter Estimation and Model Demonstration - Part 2

The viability of a new catchment-based land surface model (LSM) developed for use with general circulation models is demonstrated. First, simple empirical functions -- tractable enough for operational use in the LSM -- are established that faithfully capture the control of topography on the subgrid variability of soil moisture and the surface water budget, as predicted by theory. Next, the full LSM is evaluated offline. Using forcing and validation datasets developed for PILPS Phase 2c, the minimally calibrated model is shown to reproduce observed evaporation and runoff fluxes successfully in the Red-Arkansas River Basin. A complementary idealized study that employs the range of topographic variability seen over North America demonstrates that the simulated surface water budget does vary strongly with topography, which can, by itself, induce variations in annual evaporation as high as 20%.

Ducharne, Agnes↗
NASA NTRS2000

A Catchment-Based Approach to Modeling Land Surface Processes in a GCM: Model Structure - Part 1

A new strategy for modeling the land surface component of the climate system is described. The strategy is motivated by an arguable deficiency in most state-of-the-art land surface models (LSMs), namely the disproportionately higher emphasis given to the formulation of one-dimensional, vertical physics relative to the treatment of horizontal heterogeneity in surface properties -- particularly subgrid soil moisture variability and its effects on runoff generation. The new strategy calls for the partitioning of the continental surface into a mosaic of hydrologic catchments, delineated through analysis of high-resolution surface elevation data. The effective "grid" used for the land surface is therefore not specified by the overlying atmospheric grid. Within each catchment, the variability of soil moisture is related to characteristics of the topography and to three bulk soil moisture variables through a well-established model of catchment processes. This modeled variability allows the partitioning of the catchment into several areas representing distinct hydrological regimes, wherein distinct (regime-specific) evaporation and runoff parameterizations are applied. Care is taken to ensure that the deficiencies of the catchment model in regions of little to moderate topography are minimized.

Koster, Randal D.↗
NASA NTRS2000

SAO and Kelvin Waves in the EuroGRIPS GCMS and the UK Meteorological Offices Analyses

This work is an intercomparison of four tropospheric-stratospheric climate models, the Unified Model (UM) of the U.K. Meteorological Office (UKMO), the model of the Free University in Berlin (FUB). the ARPEGE-climat model of the National Center for Meteorological Research (CNRM), and the Extended UGAMP GCM (EUGCM) of the Center for Global Atmospheric Modelling (CGAM), against the UKMO analyses. This comparison has been made in the framework of the "GSM-Reality Intercomparison Project for SPARC" (GRIPS). SPARC (Stratospheric Processes and their Role in Climate) aims are to investigate the effects of the middle atmosphere on climate and the GRIPS purpose is to organized a comprehensive assessment of current Middle Atmosphere-Climate Models (MACMs). The models integrations were made without identical contraints e.g. boundary conditions, incoming solar radiation). All models are able to represent the dominant features of the extratropical circulation. In this paper, the structure of the tropical winds and the strengths of the Kelvin waves are examined. Explanations for the differences exhibited. between the models. as well as between models and analyses, are also proposed. In the analyses a rich spectrum of waves (eastward and westward) is present and contributes to drive the SAO (SemiAnnual Oscillation) and the QBO (Quasi-Biennal Oscillation). The amplitude of the Kelvin waves is close to the one observed in UARS (Upper Atmosphere Research Satellite) data. In agreement with observations, the Kelvin waves generated in the models propagate into the middle atmosphere as wave packets which underlines convective forcing origin. In most models, slow Kelvin waves propagate too high and are hence overestimated in the upper stratosphere and in the mesosphere, except for the UM which is more diffusive. These waves are not sufficient to force realistic westerlies of the QBO or SAO westerly phases. If the SAO is represented by all models only two of them are able to generate westerlies between 10 hPa and 50 hPa. The importance of the role played by subgrided gravity waves is more and more recognized. Actually, the EUGCM which includes a parametrization of gravity waves with a non-zero phase speed is able to simulate. with however some unrealistic features, clear easterly to westerly transitions as well as westerlies downward propagations. Thermal damping is also important in the westerlies forcing in the stratosphere. The model ARPEGE-climat shows more westerlies in the stratosphere than tile other three models probably due to the use of a simplified scheme to predict the ozone distribution in the middle atmosphere.

Amodei, M.↗
NASA NTRS1999

El Nino and the Global Ocean Observing System

Until a decade ago, an often-quoted expression in oceanography is that very few observations are recorded throughout the ocean. Now, the sentiment is no longer valid in the uppermost 10% of the tropical Pacific Ocean nor at the surface of the global ocean. One of the remarkable legacies of the 1985-1994 Tropical Oceans Global Atmosphere (TOGA) Program is an in situ marine meteorological and upper oceanographic measurement array throughout the equatorial Pacific to monitor the development and maintenance of El Nino episodes. The TOGA Observing System, which initially consisted of moored- and drifting-buoy arrays, a network of commercial ships, and coastal and island stations, now includes a constellation of satellites and data-assimilating models to simulate subsurface oceanographic conditions. The El Nino and La Nina tropical Pacific Ocean observing system represents the initial phase of an integrated global ocean observing system. Remarkable improvements have been made in ocean model simulation of subsurface currents, but some problems persist. For example, the simulation of the South Equatorial Current (SEC) remains an important challenge in the 2S-2N Pacific equatorial wave guide. During El Nino the SEC at the equator is reduced and sometimes the direction is reversed, becoming eastward. Both conditions allow warm water stored in the western Pacific to invade the eastern region, creating an El Nino episode. Assimilation of data is a tenet of faith to correct simulation errors caused by deficiencies in surface fluxes (especially wind stress) and parameterizations of subgrid-scale physical processes. In the first of two numerical experiments, the Pacific SEC was simulated with and without assimilation of subsurface temperature data. Along the equator, a very weak SEC occurred throughout the eastern Pacific, independent of assimilation of data. However, as displayed in the diagram, in the western Pacific there was no satisfactory agreement between the two simulations. To help determine reliability of the simulated SEC in the western Pacific, current measurements recorded during the 9-19 October 1994 voyage of the French research vessel L'Atalante are also shown in the diagram. With data assimilation, the simulated SEC was in much better agreement with L'Atalante observations. The simulated SEC with data assimilation was far from perfect, in part because of the sparsity of subsurface temperature observations. In the next experiment, TOPEX/POSEIDON sea surface height data in combination with subsurface temperatures will be assimilated to assess further improvement of the simulation of the SEC.

Halpern, David↗
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.↗
NASA NTRS2000

SST Variation Due to Interactive Convective-Radiative Processes

The recent linking of Cloud-Resolving Models (CRMs) to Ocean-Mixed Layer (OML) models has provided a powerful new means of quantifying the role of cloud systems in ocean-atmosphere coupling. This is due to the fact that the CRM can better resolve clouds and cloud systems and allow for explicit cloud-radiation interaction. For example, Anderson (1997) applied an atmospheric forcing associated with a CRM simulated squall line to a 3-D OML model (one way or passive interaction). His results suggested that the spatial variability resulting from the squall forcing can last at least 24 hours when forced with otherwise spatially uniform fluxes. In addition, the sea surface salinity (SSS) variability continuously decreased following the forcing, while some of the SST variability remained when a diurnal mixed layer capped off the surface structure. The forcing used in the OML model, however, focused on shorter time (8 h) and smaller spatial scales (100-120 km). In this study, the 3-D Goddard Cumulus Ensemble Model (GCE; 512 x 512 x 23 cu km, 2-km horizontal resolution) is used to simulate convective active episodes occurring in the Western Pacific warm pool and Eastern Atlantic regions. The model is integrated for seven days, and the simulated results are coupled to an OML model to better understand the impact of precipitation and changes in the planetary boundary layer upon SST variation. We will specifically examine and compare the results of linking the OML model with various spatially-averaged outputs from GCE simulations (i.e., 2 km vs. 10-50 km horizontal resolutions), in order to help understand the SST sensitivity to multi-scale influences. This will allow us to assess the importance of explicitly simulated deep and shallow clouds, as well as the subgrid-scale effects (in coarse-model runs) upon SST variation. Results using both 1-D and 2-D OML models will be evaluated to assess the effects of horizontal advection.

Tao, W.-K.↗
NASA NTRS2000

Inferring Small Scale Dynamics from Aircraft Measurements of Tracers

The millions of ER-2 and DC-8 aircraft measurements of long-lived tracers in the Upper Troposphere/Lower Stratosphere (UT/LS) hold enormous potential as a source of statistical information about subgrid scale dynamics. Extracting this information however can be extremely difficult because the measurements are made along a 1-D transect through fields that are highly anisotropic in all three dimensions. Some of the challenges and limitations posed by both the instrumentation and platform are illustrated within the context of the problem of using the data to obtain an estimate of the dissipation scale. This presentation will also include some tutorial remarks about the conditional and two-point statistics used in the analysis.

Sparling, L. C.↗
NASA NTRS2000

CVS Filtering of 3D Turbulent Mixing Layers Using Orthogonal Wavelets

Coherent Vortex Simulation (CVS) filtering has been applied to Direct Numerical Simulation (DNS) data of forced and unforced time-developing turbulent mixing layers. CVS filtering splits the turbulent flow into two orthogonal parts, one corresponding to coherent vortices and the other to incoherent background flow. We have shown that the coherent vortices can be represented by few wavelet modes and that these modes are sufficient to reproduce the vorticity probability distribution function (PDF) and the energy spectrum over the entire inertial range. The remaining incoherent background flow is homogeneous, has small amplitude, and is uncorrelated. These results are compared with those obtained for the same compression rate using large eddy simulation (LES) filtering. In contrast to the incoherent background flow of CVS filtering, the LES subgrid scales have a much larger amplitude and are correlated, which makes their statistical modeling more difficult.

Schneider, Kai↗