Subgrid-scale Turbulent Kinetic Energy Research Articles

A conditional deep learning model for super-resolution reconstruction of small-scale turbulent structures in particle-Laden flows

Super-resolution reconstruction of turbulent flows using deep learning has gained significant attention, yet challenges remain in accurately capturing physical small-scale structures. This study introduces the Conditional Enhanced Super-Resolution Generative Adversarial Network (CESRGAN) for reconstructing high-resolution turbulent velocity fields from low-resolution inputs. CESRGAN consists of a conditional discriminator and a conditional generator, the latter being called CoGEN. CoGEN incorporates subgrid-scale (SGS) turbulence kinetic energy as conditional information, improving the recovery of small-scale turbulent structures with the desired level of energy. By being aware of SGS turbulence kinetic energy, CoGEN is relatively insensitive to the degree of detail in the input. As shown in the paper, its advantages become more pronounced when the model is applied to heavily filtered input. We evaluate the model using direct numerical simulation (DNS) data of forced homogeneous isotropic turbulence. The analysis of Q-criterion isosurfaces, energy spectra, and probability density functions shows that the proposed CoGEN reconstructs fine-scale vortical structures more precisely and captures turbulent intermittency better compared to the traditional generator. Particle-pair dispersion simulations validate the physical fidelity of CoGEN-reconstructed fields, closely matching DNS results across various Stokes numbers and filtering levels. This paper demonstrates how incorporating available physical information enhances super-resolution models for turbulent flows.

Challenges of high-fidelity air quality modeling in urban environments – PALM sensitivity study during stable conditions

Abstract. Urban air quality is an important part of human well-being, and its detailed and precise modeling is important for efficient urban planning. In this study the potential sources of errors in large eddy simulation (LES) runs of the PALM model in stable conditions for a high-traffic residential area in Prague, Czech Republic, with a focus on street canyon ventilation, are investigated. The evaluation of the PALM model simulations against observations obtained during a dedicated campaign revealed unrealistically high concentrations of modeled air pollutants for a short period during a winter inversion episode. To identify potential reasons, the sensitivities of the model to changes in meteorological boundary conditions and adjustments of model parameters were tested. The model adaptations included adding the anthropogenic heat from cars, setting a bottom limit of the subgrid-scale turbulent kinetic energy (TKE), adjusting the profiles of parameters of the synthetic turbulence generator in PALM, and limiting the model time step. The study confirmed the crucial role of the correct meteorological boundary conditions for realistic air quality modeling during stable conditions. Besides this, the studied adjustments of the model parameters proved to have a significant impact in these stable conditions, resulting in a decrease in concentration overestimation in the range 30 %–66 % while exhibiting a negligible influence on model results during the rest of the episode. This suggested that the inclusion or improvement of these processes in PALM is desirable despite their negligible impact in most other conditions. Moreover, the time step limitation test revealed numerical inaccuracies caused by discretization errors which occurred during such extremely stable conditions.

Large eddy simulation of plunging solitary wave: Understanding the breaking and turbulent mechanisms along shoaling region

A large eddy simulation (LES) is conducted to investigate the distribution of turbulence kinetic energy (TKE) under a plunging solitary wave over a 1:15 slope. This study provides a novel contribution to the field by examining the roles of resolved and sub-grid scale TKE in plunging solitary waves at the different stages of wave breaking. Furthermore, comparing the performances of two sub-grid scale (SGS) models in simulating the distribution of TKE was carried out to identify their performances. The separate investigation of these components in the context of wave breaking and recognizing the importance of an appropriate sub-grid scale model to consider the effects of small-scale eddies provide a significant advancement in understanding coastal morphological changes and nearshore sediment transport. Both the zero-equation and one-equation SGS models demonstrated acceptable performance in simulating water surface and kinematic properties. The one-equation SGS model, however, provided more accurate results on TKE transport during the breaking process and as the wave approaches its collapsing point. The study’s results reveal that an SGS model’s inability to simulate TKE transport (such as in the zero equation model) leads to inaccurate simulations of the TKE level and breaking location in the breaking zone. Additionally, the results of the one-equation model demonstrated that the maximum horizontal fluid velocity around the wavefront surface is a better predictor of breaking wave onset than the horizontal fluid velocity at the wave crest.

Analysis of combustion cyclic variation in a lean burn spark-ignited engine using large eddy simulation

The low-temperature combustion technique improves engine efficiency by reducing the thermal and exhaust losses. The representative method of low-temperature combustion technique is lean burn. However, lean burn has been limited because it increases the cycle-to-cycle variation (CCV) owing to poor initial ignition stability. To overcome the low initial ignition stability, increasing the spark energy intensity and strengthening the tumble motion have been proposed. Therefore, lean burn engines with ignition stability are being rapidly developed recently. In this study, the result of the LES simulation of a lean burn engine showed the importance of ignition delay increased more than that of a conventional gasoline engine. With the importance of ignition delay in lean burn condition, the sources of the ignition delay were analyzed. The primary ignition delay sources were the flow velocity near the spark plug and the subgrid-scale turbulent kinetic energy. Next, the parameters affecting the 5% mass fraction burned (MFB) duration were analyzed by comparing five characteristic cycles. Also, factors that decreased the correlation coefficient were analyzed by comparing with the outlying cycle. As a result of analyzing the cycle with a significant change in MFB 5 and MFB 50 ranking, the burn duration was found to be affected by curl TKE, SGS TKE, large-scale flow motion, and air–fuel ratio. Finally, methods to reduce CCV were proposed. The first method was to increase tumble X+ and tumble X- using pistons that enhance the wall flow. Consequently, the coefficient of variance (COV) during the ignition delay was reduced by 27%. The second method involved changing the injector target to enhance tumble Y. The enhanced tumble Y reduced the COV of burn duration by 11%.

Non-equilibrium extension of the explicit algebraic subgrid-scale stress model with application to turbulent channel flow at low Reynolds numbers

An extension of the explicit algebraic subgrid-scale (SGS) stress model (EASSM) of Marstorp et al. [J. Fluid Mech. 639, 403–432 (2009)] is proposed to account for the non-local equilibrium between the production, P, and viscous dissipation, ϵ, of the SGS turbulent kinetic energy in its formulation. The original derivation of the EASSM uses the equilibrium assumption P=ϵ, whereas in the current new derivation, a cubic algebraic equation is extracted for P/ϵ from the modeled transport equation for the SGS stress anisotropy, which can be solved to improve the EASSM predictions with less than 4% additional computational costs per time step. The performance of the extended EASSM is assessed in large-eddy simulation of plane turbulent channel flow at Reτ=587 and 179 for a wide range of resolutions, where deviations from the local equilibrium assumption are expected at the vicinity of the walls. The enhanced EASSM formulation lowers resolution dependence of the model predictions and improves its predictions at low resolutions. The improvements affected major one-point turbulence statistics of interest, such as the wall shear stress, mean velocity, Reynolds stresses, and SGS dissipation as well as the two-point velocity correlations and premultiplied spanwise spectra of the streamwise velocity. The predicted mean P/ϵ also reasonably agrees with the filtered direct numerical simulation data.

Quantitative analysis on implicit large eddy simulation

Current research conducts the quantitative comparisons between implicit large eddy simulation (iLES) and explicit eddy-viscosity large eddy simulation (eLES). iLES and eLES in a compressible Taylor–Green vortex problem are implemented with a fourth-order finite-volume gas kinetic scheme. Compared with the key statistical quantities of direct numerical simulation, iLES outweighs eLES on the exactly same unresolved grids. With DNS solution, a priori analysis of compressible filtered subgrid-scale (SGS) turbulent kinetic energy ρ¯Ksgsf is performed. Forward and backward filtered SGS turbulent kinetic energy transfer coexists. The ensemble turbulent kinetic energy Ek is on the order of o(104) to o(102) of ensemble filtered SGS turbulent kinetic energy Ksgsf. The ensemble dominant physical dissipation rate ε1 is approximately 20 times larger than the ensemble filtered SGS dissipation rate −τijfS̃ijf. Then, for iLES and eLES, the total dissipation rate is decomposed into the resolved physical dissipation rate εphy, modeling SGS dissipation rate εsgsmod, and numerical SGS dissipation rate εsgsnum. Quantitative comparisons on the modeling SGS dissipation rate and numerical SGS dissipation rate in iLES and eLES are evaluated. The numerical dissipation in iLES can be treated as the built-in SGS dissipation, which accounts for the reasonable performance of iLES. While the explicit modeling SGS dissipation in eLES pollutes the resolved turbulent structures in such low-Reynolds number turbulence. The next generation of large eddy simulation on unresolved grids must take into account both the built-in numerical SGS dissipation and its competition explicit modeling SGS dissipation.

A Study of Large-eddy Simulation using Statistical and Machine Learning Techniques

The numerical solution of Navier-Stokes (N-S) equations has been found useful in various disciplines during its development, especially in recent years. However, a large-eddy simulation method has been developed to model the subgrid-scale dissipation rate by closing the Navier-Stokes equations. Because the instantaneous and time-averaged statistic characteristics of the subgrid-scale turbulent kinetic energy and dissipation have been studied by large eddy simulation. The purpose of this study is to check the statistical and machine learning of the subgrid-scale energy dissipation. As we know that the current turbulence theory states that the vortex stretching mechanism transports energy from large to small scales and leads to a high energy dissipation rate in a turbulent flow. Hence, a vortex-stretching-based subgrid-scale model is considered regarding the square of the velocity gradient to detect the playing role of the vortex stretching mechanism. The study in this article has shown a two-step process. Considering a posteriori statistic of the velocity gradient is analyzed through higher-order statistics and joint probability density function. Secondly, a machine learning approach is studied on the same data. The results of the vortex-stretching-based subgrid-scale model are then compared with the other two dynamic subgrid models, such as the localized dynamic kinetic energy equation model and the TKE-based Deardorff model. The results suggest that the vortex-stretching-based model can detect the significant subgrid-scale dissipation of small-scale motions and predict satisfactory turbulence statistics of the velocity gradient tensor.

Transport and modeling of subgrid-scale turbulent kinetic energy in channel flows

To develop a more convenient subgrid-scale (SGS) model that performs well even in coarse grid cases, we investigate the transport and modeling of SGS turbulent kinetic energy (hereafter SGS energy) in turbulent channel flows based on the stabilized mixed model (SMM). In this paper, we try to increase the convenience of the SMM by replacing the modeled transport equation for the SGS energy with an algebraic model. The SMM quantitatively adequately predicts the total turbulent kinetic energy of the direct numerical simulation (DNS) even in coarse grid cases. For both the filtered DNS (fDNS) and large-eddy simulation (LES), the statistically averaged production term balances with the dissipation in the region away from the wall in the SGS energy transport equation. In contrast, we reveal that the correlation coefficient between the production and dissipation terms is high for the modeled transport equation in LES, whereas that for the fDNS is low. Based on the high correlation or local equilibrium between the production and dissipation observed in the LES, we demonstrate the reduction of the SMM into a zero-equation SMM (ZE-SMM). We construct a new damping function based on the grid-scale Kolmogorov length to reproduce the near-wall behavior of the algebraic model for the SGS energy. The ZE-SMM provides quantitatively the same performance as the original SMM that employs the SGS energy transport model. This result suggests that the local equilibrium model for the SGS energy provides the equivalent performance as the transport model in wall-bounded turbulent flows even in coarse grid cases.

Non-Equilibrium Time-Relaxation Kinetic Model for Compressible Turbulence Modeling

For the first time, the non-equilibrium time-relaxation kinetic model (NTRKM) is proposed for compressible turbulence modeling on unresolved grids. Within the non-equilibrium time-relaxation framework, NTRKM is extended in the form of modified Bhatnagar-Gross-Krook model. Based on the first-order Chapman-Enskog expansion, NTRKM connects with the six-variable macroscopic governing equations. The first five governing equations correspond to the conservative laws in mass, momentum and total energy, while the sixth equation governs the evolution of unresolved turbulence kinetic energy Kutke. The unknowns in NTRKM, including turbulent relaxation time and source term, are determined by essential gradient-type assumption and standard dynamic modeling approach. Current generalized kinetic model on unresolved grids consequently offers a profound mesoscopic understanding for one-equation subgrid-scale turbulence kinetic energy Ksgs model in compressible large eddy simulation. To solve NTRKM accurately and robustly, a non-equilibrium gas-kinetic scheme is developed, which succeeds the well-established gas-kinetic scheme for simulating Navier-Stokes equations. Three-dimensional decaying compressible isotropic turbulence and temporal compressible plane mixing layer on unresolved grids are simulated to evaluate the generalized kinetic model and non-equilibrium gas-kinetic scheme. The performance of key turbulent quantities up to second-order statistics confirms that NTRKM is comparable with the widely-used eddy-viscosity Smagorinsky model (SM) and dynamic Smagorinsky model (DSM). Specifically, compared with the DNS solution in temporal compressible plane mixing layer, the performance of NTRKM is much closer with DSM and better than SM. This study provides a workable approach for compressible turbulence modeling on unresolved grids.

Reformulation and improvement of a universal subgrid eddy viscosity model based on the multiscale framework

A universal multiscale Smagorinsky model (UMSM) is established for the large eddy simulation (LES) of wall-bounded turbulent flows by reformulating a universal subgrid eddy viscosity model presented by Gu et al. (Europhysics Letter 94(3):34003,2011). The UMSM is adapted to the LES of wall-bounded turbulent flows by integrating the “small-all” form of the multiscale Smagorinsky model with the dynamic subgrid characteristic length, controlled by subgrid-scale (SGS) motions. The dynamic subgrid characteristic length is determined by the characteristic wave number, which is calculated from a new energy-weighted-mean method when the SGS turbulent kinetic energy and the dissipation wave number are known. The dissipation wave number is derived from the SGS turbulent kinetic energy spectrum equation and the total dissipation rate spectrum equation. The UMSM is used to simulate the fully developed channel flow and the turbulent flow past a square cylinder. The dynamic subgrid characteristic length, as a counterpart of Germano’s procedure, evaluates the rapidly fluctuating small-scale behavior and spatial variations of turbulent characteristics. The results for fully developed channel flow show that the errors in the streamwise velocity and the velocity fluctuations change slowly. The flat nature of the UMSM error across different multiscale Smagorinsky coefficients (Cs’) indicates that the model is relatively insensitive to the value of Cs′. Additionally, the UMSM is less sensitive to grid resolution since more details of turbulence fluctuations are captured on the same grid-points compared to the RVBMM (Journal of Computational Physics, 234:79-107,2013) and DSM (Journal of Fluid Mechanics 319:353-385,1996). Overall, the proposed model and the DSM exhibit similar behavior, and both LES formulations provide good agreement with reference data from direct numerical simulations. However, the UMSM is more computationally efficient, being 17% faster than the dynamic Smagorinsky model.

Three dimensional high-order gas-kinetic scheme for supersonic isotropic turbulence II: Coarse-graining analysis of compressible Ksgs budget

The direct numerical simulation (DNS) of compressible isotropic turbulence up to the supersonic regime with Mat=1.2 has been investigated by the high-order gas-kinetic scheme (HGKS) (Cao et al. (2019) [8]). In this study, the DNS on a much higher initial turbulent Mach number up to Mat=2.0 is performed by HGKS, which confirms the super robustness of HGKS. The coarse-graining analysis of subgrid-scale (SGS) turbulent kinetic energy Ksgs budget is fully analyzed for constructing one-equation SGS model in the compressible large eddy simulation (LES). The exact compressible SGS turbulent kinetic energy Ksgs transport equation is derived with density weighted filtering process. Based on the compressible Ksgs transport equation, the coarse-graining processes are implemented on three sets of unresolved grids with the Box filter. The coarse-graining analysis of compressible Ksgs budgets shows that all unresolved source terms are dominant in the current system. Especially, the magnitude of SGS pressure-dilation term is on the order of SGS solenoidal dissipation term within the initial acoustic time scale. Therefore, the SGS pressure-dilation term cannot be neglected as that in the previous work. The delicate coarse-graining analysis of SGS diffusion terms in compressible Ksgs equation also confirms that both the fluctuation velocity triple correlation term and the pressure-velocity correlation term are dominant terms. The current analysis provides an indication on the order of magnitude of all SGS terms in compressible Ksgs budget, which provides a solid basis for compressible LES modeling of high Mach number turbulent flow.

Numerical simulation of flow over a passive disturbance and backward-facing step

This research aimed to simulate the flow past a rib and backward-facing step (BFS). The Reynolds and sub-grid-scale (SGS) stresses were modelled. These models consisted of k–ɛ, Smagorinksy-Lilly, SGS turbulence kinetic energy (kSGS ), dynamic SGS and wall-adapting local eddy-viscosity (WALE) which implemented in Open FOAM. The simulation was carried out to compare against the experiment in literatures which gave a high Reynolds number of 15,500. The simulation results showed that the k–ɛ model provided the best prediction of the turbulent flow over a passive disturbance and BFS. The absence of rib was carried out to compare with the presence of the rib. It was found that the rib positions had affected to flow reattachment behind the BFS.

A Novel Canopy Drag Coefficient Model for Analyzing Urban Wind Environments Based on the Large Eddy Simulation

It is very challenging to capture the drag effects for the computational fluid dynamics numerical simulations of the urban canopy wind environment. This study proposed a novel canopy drag coefficient model for accurate analysis of the urban wind environment based on a large eddy simulation, where the drag coefficients varied with quantitatively identified canopy parameters along with the height. Four computational parameters, namely the average kinetic energy, turbulent kinetic energy, sub-grid scale turbulent kinetic energy, and sub-grid scale dissipation, were incorporated into the conventional drag coefficient. The Meixi Lake International Community in Changsha, China, was considered as a case study. The inlet boundary conditions were provided by the Weather Research and Forecasting model, and the proposed drag coefficient model was utilized to simulate the wind field characteristics. The results showed that the drag coefficient was relatively large near the ground, and it decreased with the increase of height overall. The decay rate of the drag coefficient below 0.4 times the building was significantly higher than the other areas. Finally, compared with the field measurement data, the proposed model had good accuracy of the simulated wind field compared to previous approaches, thus offering a reliable model for analyzing the urban wind environment.

A hybrid dynamic Smagorinsky model for large eddy simulation

A hybrid dynamic subgrid-scale model (HDSM) pertaining to Large-eddy simulation (LES) has been developed. The coefficient obtained by German dynamic Smagorinsky model (DSM) was integrated with a new dynamic coefficient, based on the dynamic subgrid characteristic length and controlled by the subgrid-scale (SGS) motions. In HDSM, the characteristic wave number determining the characteristic length of the dynamic subgrid is calculated from a new energy weighted mean method when the subgrid scale turbulent kinetic energy and the dissipation wave number are known. The dissipation wave-number is derived from the SGS turbulent kinetic energy spectrum equation. The total dissipation rate spectrum equation is based on the Pao energy spectrum and local equilibrium assumption. The dynamic subgrid characteristic length could take into account the rapidly fluctuating small scale behaviours and the spatial variation of turbulent characteristics. HDSM was used to simulate the fully developed channel and turbulent flow past a circular cylinder, and to determine the impact of the dam-break flow on downstream structure. The HDSM is robust in respect to anisotropic mesh and is less sensitive to grid resolution, and would accurately describe the energy transfer from large-scale to SGS fluctuations and capture more fluctuations of turbulence with same meshes compared to the DSM.

An assessment on the performance of sub-grid scale models of large eddy simulation in modeling bubbly flows

An Euler-Euler large eddy simulation (LES) of transient gas-liquid turbulence flow in a bubble column was conducted to investigate the adaptiveness of various sub-grid scale (SGS) models. The performance of three SGS models, respectively the standard Smagorinsky model, the wall-adapting local eddy (WALE) model and the Dynamic model, on the predictions of bubbly flow was studied. Comparison between SGS models for time-averaged and transient velocities, gas void fraction, power spectrum density (PSD), SGS turbulent dissipation, SGS turbulent kinetic energy, and Reynolds stress is conducted. The transient multi-scale irregular vortex structures, fluctuation characteristics of liquid motion and spiral floating motion of bubbles can be well captured by LES. The Dynamic model and WALE model with CW = 0.325 give reasonably better agreement with the time-averaged experimental data. The transient fluctuation behavior of gas-liquid turbulent flow can be correctly captured by the current Euler-Euler LES model, whatever the SGS model. The classical −5/3 law of PSD of vertical liquid velocity is hold properly in the low frequency region. The slope of PSD is around −25/3 at the high frequency region. The Smagorinsky model and WALE model are sensitive to the model constant, at least for the energy transfer of high frequency. The molecular dissipation is negligible compared to the SGS turbulent dissipation. The Dynamic model gives higher predictions for fluctuation amplitude and time-averaged values of both SGS turbulent dissipation rate profile and SGS turbulent kinetic energy profile than other SGS models. A certain calculation time is needed to reach the dynamic stable state in LES, and the specific time is related to the scale of the calculation model.

A-priori Direct Numerical Simulation assessment of models for generalized sub-grid scale turbulent kinetic energy in turbulent premixed flames

Abstract The fidelity of Large Eddy Simulation (LES) in the context of turbulent premixed combustion modelling depends on the complex coupling between turbulence and chemical reactions occurring at the unresolved scale. Although LES of combustion systems is becoming increasingly popular, the closures for sub-grid scale (SGS) stresses have mostly been derived assuming constant density flows. Similar to the unclosed scalar flux, the behaviour of the SGS stresses depends on the balance between heat release and turbulence, and it has been shown recently that counter-gradient transport (CGT) can occur for the stress tensor when the isotropic part of the stress tensor is not properly accounted for. This leads to a negative correlation between the predictions obtained from an eddy viscosity type model and the stresses obtained from Direct Numerical Simulation (DNS). In the present work the modelling of the isotropic part of the stress tensor, closely related to the generalised sub-grid scale kinetic energy, is considered in detail. To this end the interplay between SGS dilatation effects and unresolved velocity fluctuations is analysed using a-priori DNS analysis of turbulent, statistically planar flames with different values of global Lewis number and heat release parameter. Well-known models for generalised sub-grid scale kinetic energy have been assessed in the context of turbulent premixed combustion and detailed physical explanations for their behaviour have been provided. Further, the effects of SGS dilatation rate on the anisotropy of the SGS stresses have been highlighted using a variant of the Lumley triangle.

Assessment of subgrid-scale stress statistics in non-premixed turbulent wall-jet flames

ABSTRACTWe investigate the heat-release effects on the characteristics of the subgrid-scale (SGS) stress tensor and SGS dissipation of kinetic energy and enstrophy. Direct numerical simulation data of a non-premixed reacting turbulent wall-jet flow with and without substantial heat release is employed for the analysis. This study comprises, among others, an analysis of the eigenvalues of the resolved strain rate and SGS stress tensors, to identify the heat-release effects on their topology. An assessment of the alignment between the eigenvectors corresponding to the largest eigenvalues of these two tensors is also given to provide further information for modelling of the SGS stress tensor. To find out the heat-release effects on the dynamics of the turbulent kinetic energy and enstrophy dissipation, probability density functions (PDFs) and mean values are analysed. The mean SGS shear stress and turbulent kinetic energy both slightly increase in the buffer layer and substantially decrease further away from the wall, due to the heat-release effects. Contrary to the kinetic energy, heat release decreases the mean SGS dissipation of enstrophy in the near-wall region. Moreover, differences in the shapes of the PDFs between the isothermal and exothermic cases indicate changes in the intermittency level of both SGS dissipations. Heat release also increases the SGS stress anisotropy in the near-wall region. Although, the structure of the mean resolved strain-rate tensor only marginally differs between the isothermal and exothermic cases in the near-wall region, substantial differences are observed in the jet area, where compressibility effects are important and heat-release effects are found to promote compression states. The differences in the relative alignment between the SGS stress and resolved strain-rate tensors in the isothermal and exothermic cases are discussed in connection with the differences in the SGS dissipation of kinetic energy.

Particle subgrid scale modelling in large-eddy simulations of particle-laden turbulence

This study is concerned with particle subgrid scale (SGS) modelling in large-eddy simulations (LESs) of particle-laden turbulence. Although many particle-laden LES studies have neglected the effect of the SGS on the particles, several particle SGS models have been proposed in the literature. In this research, the approximate deconvolution method (ADM) and the stochastic models of Fukagata et al. (Dynamics of Brownian particles in a turbulent channel flow, Heat Mass Transf. 40 (2004), 715–726) Shotorban and Mashayek (A stochastic model for particle motion in large-eddy simulation, J. Turbul. 7 (2006), 1–13) and Berrouk et al. (Stochastic modelling of inertial particle dispersion by subgrid motion for LES of high Reynolds number pipe flow, J. Turbul. 8 (2007), pp. 1–20) are analysed. The particle SGS models are assessed using both a priori and a posteriori simulations of inertial particles in a periodic box of decaying, homogeneous and isotropic turbulence with an initial Reynolds number of Reλ = 74. The model results are compared with particle statistics from a direct numerical simulation (DNS). Particles with a large range of Stokes numbers are tested using various filter sizes and stochastic model constant values. Simulations with and without gravity are performed to evaluate the ability of the models to account for the crossing trajectory and continuity effects. The results show that ADM improves results but is only capable of recovering a portion of the SGS turbulent kinetic energy. Conversely, the stochastic models are able to recover sufficient SGS energy, but show a large range of results dependent on the Stokes number and filter size. The stochastic models generally perform best at small Stokes numbers, but are unable to predict preferential concentration.

Nesting Turbulence in an Offshore Convective Boundary Layer Using Large-Eddy Simulations

The applicability of the one-way nesting technique for numerical simulations of the heterogeneous atmospheric boundary layer using the large-eddy simulation (LES) framework of the Weather Research and Forecasting model is investigated. The focus of this study is on LES of offshore convective boundary layers. Simulations were carried out using two subgrid-scale models (linear and non-linear) with two different closures [diagnostic and prognostic subgrid-scale turbulent kinetic energy (TKE) equations]. We found that the non-linear backscatter and anisotropy model with a prognostic subgrid-scale TKE equation is capable of providing similar results when performing one-way nested LES to a stand-alone domain having the same grid resolution but using periodic lateral boundary conditions. A good agreement is obtained in terms of velocity shear and turbulent fluxes, while velocity variances are overestimated. A streamwise fetch of 14 km is needed following each domain transition in order for the solution to reach quasi-stationary results and for the velocity spectra to generate proper energy content at high wavelengths, however, a pile-up of energy is observed at the low-wavelength portion of the spectrum on the first nested domain. The inclusion of a second nest with higher resolution allows the solution to reach effective grid spacing well within the Kolmogorov inertial subrange of turbulence and develop an appropriate energy cascade that eliminates most of the pile-up of energy at low wavelengths. Consequently, the overestimation of velocity variances is substantially reduced and a considerably better agreement with respect to the stand-alone domain results is achieved.

Modeling microphysical effects of entrainment in clouds observed during EUCAARI-IMPACT field campaign

Abstract. This paper discusses aircraft observations and large-eddy simulation (LES) modeling of 15 May 2008, North Sea boundary-layer clouds from the EUCAARI-IMPACT field campaign. These clouds are advected from the northeast by the prevailing lower-tropospheric winds and featured stratocumulus-over-cumulus cloud formations. An almost-solid stratocumulus deck in the upper part of the relatively deep, weakly decoupled marine boundary layer overlays a field of small cumuli. The two cloud formations have distinct microphysical characteristics that are in general agreement with numerous past observations of strongly diluted shallow cumuli on one hand and solid marine stratocumulus on the other. Based on the available observations, a LES model setup is developed and applied in simulations using a novel LES model. The model features a double-moment warm-rain bulk microphysics scheme combined with a sophisticated subgrid-scale scheme allowing local prediction of the homogeneity of the subgrid-scale turbulent mixing. The homogeneity depends on the characteristic time scales for the droplet evaporation and for the turbulent homogenization. In the model, these scales are derived locally based on the subgrid-scale turbulent kinetic energy, spatial scale of cloudy filaments, mean cloud droplet radius, and humidity of the cloud-free air entrained into a cloud, all predicted by the LES model. The model reproduces contrasting macrophysical and microphysical characteristics of the cumulus and stratocumulus cloud layers. Simulated subgrid-scale turbulent mixing within the cumulus layer and near the stratocumulus top is on average quite inhomogeneous, but varies significantly depending on the local conditions.