Subgrid-scale Fluxes Research Articles

A Priori Test of Scale-Similarity Parameterizations for Subgrid-Scale Fluxes in Convective Storms

Abstract This study evaluates a parameterization scheme for subgrid-scale (SGS) fluxes based on the scale-similarity assumption and employing a large-eddy simulation of an idealized back-building convective system. In this parameterization, the SGS fluxes are decomposed into the “Leonard term,” which depends only on the resolved scale components, the “Reynolds term,” which depends only on the SGS components, and the “cross term,” which corresponds to the interaction between the resolved scale and SGS components. Assuming a linear relationship between the Leonard term and the Reynolds and cross terms, SGS fluxes are expressed as the product of an empirical coefficient and the Leonard term. The Leonard term reasonably represents the SGS flux derived by a smooth filter operation, including the countergradient vertical SGS transport of potential temperature, which cannot be represented by a traditional eddy-diffusivity model. The dependence of the empirical coefficient on filter width is also evaluated. This dependence is related mainly to the Reynolds term, the magnitude of which varies widely with the filter width. The estimation based on the spectral decomposition of the Reynolds term explains the obtained dependence of the empirical coefficient for the vertical flux on filter width. In contrast, the variation of the empirical coefficient with filter width is not required to obtain the horizontal flux. For the parameterization of SGS fluxes in kilometer-scale models that use finite difference or volume methods, the Leonard term is expressed by the horizontal gradient of variables on a discrete grid. The Leonard term on a discrete grid also accurately represents the amplitude and spatial pattern of the SGS flux. Significance Statement Kilometer-scale numerical weather prediction models can reproduce deep convection explicitly. However, they cannot reproduce smaller inner structures within this deep convection. Therefore, a parameterization scheme that can express the nature of the transport associated with such structures is required. Using a large-eddy simulation with a horizontal resolution sufficient to express such inner structures, we evaluated a parameterization based on the scale similarity assumption, including an empirical coefficient. Based on spectral decomposition, we quantitatively estimated the relationship between the empirical coefficient and grid spacing. Our results provide guidance in selecting the value of the empirical coefficient in this parameterization.

Learning Closed‐Form Equations for Subgrid‐Scale Closures From High‐Fidelity Data: Promises and Challenges

AbstractThere is growing interest in discovering interpretable, closed‐form equations for subgrid‐scale (SGS) closures/parameterizations of complex processes in Earth systems. Here, we apply a common equation‐discovery technique with expansive libraries to learn closures from filtered direct numerical simulations of 2D turbulence and Rayleigh‐Bénard convection (RBC). Across common filters (e.g., Gaussian, box), we robustly discover closures of the same form for momentum and heat fluxes. These closures depend on nonlinear combinations of gradients of filtered variables, with constants that are independent of the fluid/flow properties and only depend on filter type/size. We show that these closures are the nonlinear gradient model (NGM), which is derivable analytically using Taylor‐series. Indeed, we suggest that with common (physics‐free) equation‐discovery algorithms, for many common systems/physics, discovered closures are consistent with the leading term of the Taylor‐series (except when cutoff filters are used). Like previous studies, we find that large‐eddy simulations with NGM closures are unstable, despite significant similarities between the true and NGM‐predicted fluxes (correlations >0.95). We identify two shortcomings as reasons for these instabilities: in 2D, NGM produces zero kinetic energy transfer between resolved and subgrid scales, lacking both diffusion and backscattering. In RBC, potential energy backscattering is poorly predicted. Moreover, we show that SGS fluxes diagnosed from data, presumed the “truth” for discovery, depend on filtering procedures and are not unique. Accordingly, to learn accurate, stable closures in future work, we propose several ideas around using physics‐informed libraries, loss functions, and metrics. These findings are relevant to closure modeling of any multi‐scale system.

On a proper tensorial subgrid heat flux model for LES

In this work, we aim to shed light on the following research question: can we find a subgrid-scale (SGS) heat flux model with good physical and numerical properties, such that we can obtain satisfactory predictions for buoyancy-driven turbulence at high Rayleigh numbers? This is motivated by our previous findings showing the limitations of existing SGS heat flux models for LES. On one hand, the most popular models rely on the eddy-diffusivity assumption despite their well-known lack of accuracy in a priori studies. On the other hand, the gradient model, which is the leading term of the Taylor series of the SGS flux, is much more accurate a priori but cannot be used as a standalone model since it produces a finite-time blow-up. In this context, we firstly aim to reconcile accuracy and stability for the gradient model. To do so, it is expressed as a linear combination of regularized (smoother) forms of the convective operator. The new alternative form can indeed be viewed as an approximate deconvolution of the exact SGS flux. Moreover, it facilitates the mathematical analysis of the gradient model, neatly identifying those terms that may cause numerical instabilities, leading to a new unconditionally stable non-linear model that can indeed be viewed as a stabilized version of the gradient model. In this way, we expect to combine the good a priori accuracy of the gradient model with the stability required in practical numerical simulations.

Univariate Flux Partition Functions for Planetary Boundary Layer Schemes at Gray Zone Resolutions

Abstract When the horizontal grid spacing of a numerical weather prediction model approaches kilometer scale, the so-called gray zone range, turbulent fluxes in the convective boundary layer (CBL) are partially resolved and partially subgrid scale (SGS). Knowledge of the partition between resolved and SGS turbulent fluxes is key to building scale-adaptive planetary boundary layer (PBL) schemes that are capable of regulating the SGS fluxes with varying grid spacing. However, flux partition depends not only on horizontal grid spacing, but also on local height, bulk stability of the boundary layer, and the particular turbulent flux. Such multivariate functions are difficult to construct analytically, so their implementations in scale-adaptive PBL schemes always involve certain levels of approximation that can lead to inaccuracies. This study introduces a physically based perspective for the flux partition functions that greatly simplifies their implementation with high accuracy. By introducing an appropriate scaling length λ that accounts for both height and bulk stability dependencies, the dimensionality of the partition functions is reduced to a single dimensionless group. Based on the analysis of a comprehensive large-eddy simulation dataset of the CBL, it is further shown that λ’s height and bulk stability dependencies can be separately represented by a similarity length scale and a stability coefficient. The resulting univariate partition functions are incorporated into a traditional first-order PBL scheme as a proof of concept. Our results show that the augmented scheme well-reproduces the SGS fluxes at gray zone resolutions. Significance Statement Flux partition functions are a key component in most scale-adaptive planetary boundary layer (PBL) schemes developed for kilometer- and subkilometer-resolution numerical weather prediction models. They regulate the parameterized turbulent fluxes as a function of horizontal grid spacing, while they also depend on height and atmospheric stability. Such multivariate dependencies forbid simple analytical expressions, and as a result, partition functions implemented in scale-adaptive PBL schemes are generally simplified at the cost of accuracy in previous works. This study investigates the possibility of constructing partition functions that are both accurate and easy to parameterize. Utilizing a physically based length scale, univariate partition functions are built, evaluated, and put into a conventional PBL scheme to improve the gray zone turbulence parameterization.

Nonlinear diffusion‐limited two‐dimensional colliding‐plume simulations with very high‐order numerical approximations

AbstractAtmospheric numerical models play a crucial role in operational weather forecasting, as well as in improving our understanding of atmospheric dynamics via research studies. Maximising their accuracy is of paramount importance. Use of advective flux schemes greater than O7 in atmospheric models is largely undocumented, with no studies considering O3–O17 fluxes with formal accuracy‐preserving high‐order interpolation, pressure gradient/divergence, and subgrid‐scale (SGS) turbulent fluxes. Higher‐order numerical approximations can reduce truncation, amplitude and phase errors, and potentially improve model accuracy and effective resolution. Here, simulations are presented using very‐high‐order O3–O17 fluxes, with/without high‐order O2–O18 Lagrangian interpolations, pressure gradient/divergence approximations, and SGS turbulent fluxes for a two‐dimensional, highly‐viscous (Re ∼ 100) diffusion‐limited, nonlinear colliding‐plumes problem using 25–200 m spatial resolutions. The highest‐order flux schemes coupled with higher‐order interpolations, pressure gradient/divergence and SGS flux approximations produced the best solutions, with higher‐order fluxes and interpolations being most important. Overall solution convergence of order about O1–O2 with mode‐split (fast sound/slow advective waves) O3 Runge–Kutta temporal schemes was negatively impacted by order at most O1 temporal convergence with SGS fluxes, divergence damping, and especially spatial filters, compared to about order O3 convergence with these inactivated. While very‐high‐order schemes were shown to improve solution accuracy, few cost‐effective higher‐order highly‐viscous test problem solutions (higher order vs finer resolution) were found using theoretical floating‐point operations (FPO) with Courant‐Friedrichs‐Lewy (CFL)‐limited or constant stable Courant number‐based time steps. However, employing central processing unit (CPU) time, rather than FPOs, demonstrated there was reduced computational burden using higher‐order approximations. We conclude that O9–O17 flux schemes with or without high‐order (≥O4) interpolations, pressure gradient/divergence approximations, and SGS fluxes can improve atmospheric model solution accuracy, without prohibitive computation costs, compared to O3–O7 flux with O2 interpolations, pressure gradient/divergence approximations, and SGS fluxes.

Modifications to Three‐Dimensional Turbulence Parameterization for Tropical Cyclone Simulation at Convection‐Permitting Resolution

AbstractAdequate representation of the subgrid‐scale (SGS) turbulent fluxes associated with convective clouds in the eyewall and rainbands above the boundary layer is important for simulating the formation of tropical cyclone (TC) dynamic and thermal structure, as well as the evolution and intensification of the TC. Two sets of benchmark large‐eddy simulations (LESs) for an idealized TC during the rapid intensification and mature stages were conducted. The turbulent transport above the boundary layer in the TC eyewall and rainbands exhibits a remarkable countergradient characteristic, which is poorly represented by the traditional eddy‐diffusivity closure. In contrast, the H‐gradient closure based on the horizontal gradients of the resolved variables is capable of accurately capturing the countergradient features and exhibiting a spatial distribution of SGS fluxes that mimics much better the coarse‐grained fluxes from the LES benchmarks. Moreover, the H‐gradient closure allows for the backscatter transfer of energy. By implementing the H‐gradient closure into a three‐dimensional turbulence parameterization, the TC simulated using the modified parameterization bears closer resemblance to the LES benchmarks in terms of the spatial distribution of SGS fluxes, TC intensity, primary and secondary circulations, and cloud morphology.

Artificial-neural-network-based nonlinear algebraic models for large-eddy simulation of compressible wall-bounded turbulence

In this paper, we propose artificial-neural-network-based (ANN-based) nonlinear algebraic models for the large-eddy simulation (LES) of compressible wall-bounded turbulence. An innovative modification is applied to the invariants and the tensor bases of the nonlinear algebraic models through using the local grid widths along each direction to normalise the corresponding gradients of the flow variables. Furthermore, the dimensionless model coefficients are determined by the ANN method. The modified ANN-based nonlinear algebraic model (MANA model) has much higher correlation coefficients and much lower relative errors than the dynamic Smagorinsky model (DSM), Vreman model and wall-adapting local eddy-viscosity model in the a priori test. The significantly more accurate estimations of the mean subgrid-scale (SGS) fluxes of the kinetic energy and temperature variance are also obtained by the MANA models in the a priori test. Furthermore, in the a posteriori test, the MANA model can give much more accurate predictions of the flow statistics and the mean SGS fluxes of the kinetic energy and the temperature variance than other traditional eddy-viscosity models in compressible turbulent channel flows with untrained Reynolds numbers, Mach numbers and grid resolutions. The MANA model has a better performance in predicting the flow statistics in supersonic turbulent boundary layer. The MANA model can well predict both direct and inverse transfer of the kinetic energy and temperature variance, which overcomes the inherent shortcoming that the traditional eddy-viscosity models cannot predict the inverse energy transfer. Moreover, the MANA model is computationally more efficient than the DSM.

Variations of Subgrid-Scale Turbulent Fluxes in the Dry Convective Boundary Layer at Gray Zone Resolutions

Abstract In the numerical gray zone of the convective boundary layer (CBL), the horizontal resolution is comparable to the size of organized convective circulation. As turbulence becomes partially resolved, gridscale variations of the subgrid-scale (SGS) turbulent fluxes become significant compared to the mean. Previously, such variations have often been ignored in scale-adaptive planetary boundary layer (PBL) schemes developed for the gray zone. This study investigates these variations with respect to height and resolution based on large-eddy simulations. It is found that SGS fluxes exhibit maximum variability at the center of the gray zone, where the resolved and the SGS mean fluxes are approximately equal. A simple analytical model is used to associate such characteristic variations to the nonlinear interactions of the dominant energy-containing mode of CBL turbulence. Examination of the horizontal distribution of the SGS fluxes reveals their preferential location over the updraft edges surrounding the core. A priori analysis further suggests the ability of a scale-similarity closure to reproduce the unique spatial patterns of the SGS fluxes at gray zone resolutions. Four scale-adaptive PBL schemes are evaluated focusing on their representations of the modeled SGS flux variability. Their shared shortcomings as a result of their gradient diffusion–based formulation are exposed. This study suggests that a mixed model consisting of a scale-adaptive PBL scheme to represent the mean, and a scale-similarity component to account for gridscale variability to be advantageous for the gray zone. Significance Statement As Gresho and Lee’s famous quote on numerical schemes goes, “Don’t suppress the wiggles. They’re telling you something!” In the numerical gray zone, where the grid spacing is comparable to the characteristic length scale of the flow, turbulence is partially resolved. The “wiggles” (or gridscale variability) reflecting the resolved heterogeneity of turbulent fluxes is an outstanding feature of the gray zone. However, they are often overlooked as error bars to the mean. This study uncovers the significance of these error bars, and characterizes and explains their variations with height and grid spacing. A suitable model that captures such variations is investigated to help build better planetary boundary layer schemes.

Effect of heat source on kinetic energy transfer in compressible homogeneous shear turbulence

The effects of heat sources on kinetic energy transfer in compressible homogeneous shear turbulence are studied using numerical simulations at turbulent Mach numbers 0.1 and 0.4 for two levels of heat source. It is found that the strong heat source can significantly enhance both positive and negative components of subgrid-scale (SGS) kinetic energy flux and pressure–dilatation. After adding a strong heat source, compression motions enhance the positive SGS flux, and expansion motions enhance the negative SGS flux at a low turbulent Mach number. According to the Helmholtz decomposition, we found that the solenoidal and dilatational components of pressure–dilatation and SGS kinetic energy flux are increased greatly by a strong heat source at a low turbulent Mach number. The solenoidal mode plays a dominant role in the kinetic energy transfer process, but the contribution of the dilatational mode is not negligible. The dilatational component of the production term is increased by a strong heat source at a low turbulent Mach number, providing the main source of kinetic energy to the dilatational mode. The strong heat source also enhances the kinetic energy exchange between solenoidal mode and dilatational mode through nonlinear advection at a low turbulent Mach number. Moreover, the strong heat source enhances pressure anisotropy, redistribution of the kinetic energy of two transverse components, and energy transfer from internal energy to the kinetic energy through pressure–dilatation term. At a high turbulent Mach number, the strong heat source has little impact on the solenoidal and dilatational components of kinetic energy transfer terms.

Impacts of Cumulus Convection and Turbulence Parameterizations on the Convection-Permitting Simulation of Typhoon Precipitation

Abstract Convection-permitting resolutions, which refer to kilometer-scale horizontal grid spacings, have become increasingly popular in regional numerical weather prediction and climate studies. However, this resolution range is in the gray zone for the simulation of convection, where conventional cumulus convection and subgrid-scale (SGS) turbulence parameterizations are inadequate for such grid spacings due to invalid assumptions and simplifications. Recent studies demonstrated that the magnitudes of SGS fluxes of momentum and scalars are comparable to those of resolved fluxes at convection-permitting resolutions and that horizontal SGS components are as important as the vertical SGS component. Thus, it appears necessary to adapt available schemes to model the SGS effects of convective motions for the gray zone. Here, we investigated the efficacy of separately parameterizing the vertical and horizontal SGS effects in improving the convection-permitting simulation of Typhoon Vicente (2012). To represent the vertical SGS turbulence effect, we evaluated the Grell-3, Tiedtke, and multiscale Kain–Fritsch (MSKF) schemes in the Weather Research and Forecasting (WRF) Model; the MSKF scheme is scale adaptive, whereas the other two are conventional cumulus schemes. For horizontal SGS turbulence, we evaluated the effects of the traditional Smagorinsky scheme and our newly developed reconstruction and nonlinear anisotropy (RNA) model, which models not only downgradient diffusion but also backscatter. We found that the simulation combining the MSKF and RNA schemes exhibits the best skill in predicting precipitation, especially rainfall extremes. The advantages are rooted in the MSKF scheme’s scale-awareness and parameterized cloud–radiation feedback and in the backscatter-enabling capability of the RNA model. Significance Statement Operational numerical weather prediction and some climate simulations have approached kilometer-scale horizontal resolutions, called convection-permitting resolutions. However, details of convective storms are not well represented at these resolutions, and small-scale fluid motions can potentially impact the overall simulation performance. In practice, the effects of such unresolved turbulent eddies were once neglected. We suggest representing these effects in the vertical and horizontal directions with an adaptive cumulus convection parameterization and an advanced turbulence model, respectively, which significantly improve the simulation of tropical cyclones. This framework allows us to adapt convection schemes developed by the mesoscale modeling community and turbulence schemes studied by large-eddy simulation groups for representing three-dimensional turbulence in the convection-permitting regime.

Artificial neural network-based subgrid-scale models for LES of compressible turbulent channel flow

Fully connected neural networks (FCNNs) have been developed for the closure of subgrid-scale (SGS) stress and SGS heat flux in large-eddy simulations of compressible turbulent channel flow. The FCNN-based SGS model trained using data with Mach number Ma=3.0 and Reynolds number Re=3000 was applied to situations with different Mach numbers and Reynolds numbers. The input variables of the neural network model were the filtered velocity gradients and temperature gradients at a single spatial grid point. The a priori test showed that the FCNN model had a correlation coefficient larger than 0.91 and a relative error smaller than 0.43, with much better reconstructions of SGS unclosed terms than the dynamic Smagorinsky model (DSM). In a posteriori test, the behavior of the FCNN model was marginally better than that of the DSM in predicting the mean velocity profiles, mean temperature profiles, turbulent intensities, total Reynolds stress, total Reynolds heat flux, and mean SGS flux of kinetic energy, and outperformed the Smagorinsky model.

Mixing and energy transfer in compressible Rayleigh-Taylor turbulence for initial isothermal stratification

In compressible Rayleigh--Taylor instability, flow compressibility plays an important role in the generation of large-scale kinetic energy, which mainly comes from the conversion of potential energy for small stratification parameter (Sr) and conversion of internal energy through pressure-dilatation work for large Sr. The latter leads to bubble heights increasing rapidly and bubbles that are bigger at large Sr. The overall statistics of normalized subgrid-scale (SGS) flux of kinetic energy is nearly independent of Sr, but the reverse SGS flux increases significantly with increase of Sr. The compression motions enhance direct SGS flux and the expansion motions strengthen the reverse SGS flux.

Density-unweighted subgrid-scale models for large-eddy simulations of compressible turbulence

Density-unweighted methods in large-eddy simulations (LES) of turbulence have received little attention, and the modeling of unclosed terms using density-unweighted methods even less. We investigate the density-unweighted subgrid-scale (SGS) closure problem for LES of decaying compressible isotropic turbulence at initial turbulent Mach numbers 0.4 and 0.8. Compared to the LES with Favre (density-weighted) filtering, there are more unclosed SGS terms for density-unweighted LES, which can be reconstructed using different SGS models, including the gradient model (GM), approximate deconvolution model (ADM), dynamic Smagorinsky model (DSM), dynamic mixed model (DMM), and the dynamic iterative approximate deconvolution (DIAD) models proposed by Yuan et al. “Dynamic iterative approximate deconvolution models for large-eddy simulation of turbulence,” Phys. Fluids 33, 085125 (2021). We derive GM models suitable for density-unweighted methods. We also, for the first time, apply the DIAD model to investigate compressible turbulence. In the a priori tests, the correlation coefficients of the GM, ADM, and DIAD models are larger than 0.9. Particularly, the correlation coefficients of DIAD models exceed 0.98 and the relative errors are below 0.2, which is superior to that in other SGS models. In the a posteriori tests of the density-unweighted LES, the DIAD model shows great advantages over other SGS models (including GM, ADM, DSM, and DMM models) in predicting the various statistics and structures of compressible turbulence, including the velocity spectrum, probability density functions (PDFs) of SGS fluxes and the instantaneous spatial structures of SGS heat flux, SGS kinetic energy flux, and vorticity.

Evaluation of flamelet/progress variable model for the applications in supersonic combustion using hybrid RANS/LES approach

The Flamelet/Progress Variables (FPV) model coupled with large eddy simulation (LES) has been performed to appraise its applicability and performance for supersonic hydrogen combustion, based on the simulations of strut based scramjet and cavity based combustors. For the two typical schemes involved in the present work, the validation of the numerical solver compiled by in-house code is realized by the comparisons with the experimental measurements including temperature, velocity, and wall pressure. The methods for calculating mixture fraction variance in the framework of LES are also investigated and examined in both cases. It can be observed that the diffusion combustion mode is in the dominant state for the whole reactive zone in both cases, where the FPV model is physically compatible. Through the comparisons of the scale similarity method and the transport equation method for calculating mixture fraction variance, the importance of calculating this sub-grid turbulent scalar flux is emphasized. The results show that the mixture fraction variance calculated by the scale similarity model is locally high, but its diffusion is insufficient, which makes the local temperature of the combustion flow field overpredicted and concentrated. On the contrary, the transport equation of the mixture fraction variance can overcome this problem and improve the combustion prediction accuracy, thus, it is more recommended if the computing resources are guaranteed. Qualitatively, the Flamelet/Progress Variables (FPV) model with the large eddy simulation approach can accurately capture the structure and characteristics of the supersonic combustion flow field.

Contribution of flow topology to the kinetic energy flux in hypersonic turbulent boundary layer

The contribution of various flow topologies to the subgrid-scale (SGS) flux of kinetic energy in hypersonic turbulent boundary layer for different Mach numbers and wall temperature ratios is investigated by direct numerical simulation. In the far-wall region (approximately y+=y/δν>50, where y is the wall-normal location and δν is the viscous length scale), the volume fractions of flow topologies unstable focus/compressing (UFC) and stable focus/stretching (SFS) increase with the increase in filter width, resulting in the dominance of UFC and SFS in the inertial range; while in the near-wall region, the volume fractions of flow topologies unstable/saddle/saddle (UN/S/S), stable node/saddle/saddle (SN/S/S), stable focus/compressing (SFC), and unstable focus/stretching (UFS) increase with the increase in filter width, leading to the majority of UN/S/S and SN/S/S in the inertial range. In the inertial range, the SGS flux of kinetic energy is mainly contributed by UFC and SFS far from the wall (approximately y+>50) and is primarily contributed by UN/S/S and SN/S/S near the wall. The wall temperature has a significant effect on the contributions of various flow topologies in the near-wall region. As the wall temperature decreases, the contributions by SN/S/S and SFC to the SGS kinetic energy flux increase in the compression region, and those by UN/S/S and UFS increase in the expansion region. Moreover, the direct transfer of fluctuating kinetic energy from large scales to small scales is mainly characterized by UN/S/S, SFS, and SFC in the compression region, while the reverse transfer of fluctuating kinetic energy is primarily characterized by UFC, SN/S/S, and UFS in the expansion region.

Sensitivity of Pollutant Concentrations to the Turbulence Schemes of a Dispersion Modelling Chain over Complex Orography

Atmospheric circulation over mountainous regions is more complex than over flat terrain due to the interaction of flows on various scales: synoptic-scale flows, thermally-driven mesoscale winds and turbulent fluxes. In order to faithfully reconstruct the circulation affecting the dispersion and deposition of pollutants in mountainous areas, meteorological models should have a sub-kilometer grid spacing, where turbulent motions are partially resolved and the parametrizations of the sub-grid scale fluxes need to be evaluated. In this study, a modelling chain based on the Weather Research and Forecasting (WRF) model and the chemical transport model Flexible Air Quality Regional Model (FARM) is applied to estimate the pollutant concentrations at a 0.5 km horizontal resolution over the Aosta Valley, a mountainous region of the northwestern Alps. Two pollution episodes that occurred in this region are reconstructed: one summer episode dominated by thermally-driven winds, and one winter episode dominated by synoptic-scale flows. Three WRF configurations with specific planetary boundary layer and surface layer schemes are tested, and the numerical results are compared with the surface measurements of meteorological variables at twenty-four stations. For each WRF configuration, two different FARM runs are performed, with turbulence-related quantities provided by the SURface-atmosphere interFace PROcessor or directly by WRF. The chemical concentrations resulting from the different FARM runs are compared with the surface measurements of particulate matter of less than 10 µm in diameter and nitrogen dioxide taken at five air quality stations. Furthermore, these results are compared with the outputs of the modelling chain employed routinely by the Aosta Valley Environmental Protection Agency, based on FARM driven by COSMO-I2 (COnsortium for Small-scale MOdelling) at 2.8 km horizontal grid spacing. The pollution events are underestimated by the modelling chain, but the bias between simulated and measured surface concentrations is reduced using the configuration based on WRF turbulence parametrizations, which imply a reduced dispersion.

Effect of wall temperature on the kinetic energy transfer in a hypersonic turbulent boundary layer

The effect of wall temperature on the transfer of kinetic energy in a hypersonic turbulent boundary layer for different Mach numbers and wall temperature ratios is studied by direct numerical simulation. A cold wall temperature can enhance the compressibility effect in the near-wall region through increasing the temperature gradient and wall heat flux. It is shown that the cold wall temperature enhances the local reverse transfer of kinetic energy from small scales to large scales, and suppresses the local direct transfer of kinetic energy from large scales to small scales. The average filtered spatial convection and average filtered viscous dissipation are dominant in the near-wall region, while the average subgrid-scale flux of kinetic energy achieves its peak value in the buffer layer. It is found that the wall can suppress the inter-scale transfer of kinetic energy, especially for the situation of a cold wall. A strong local reverse transfer of fluctuating kinetic energy is identified in the buffer layer in the inertial range. Helmholtz decomposition is applied to analyse the compressibility effect on the subgrid-scale flux of kinetic energy. A strong transfer of the solenoidal component of fluctuating kinetic energy is identified in the buffer layer, while a significant transfer of the dilatational component of fluctuating kinetic energy is observed in the near-wall region. It is also shown that compression motions have a major contribution to the direct transfer of fluctuating kinetic energy, while expansion motions play a marked role in the reverse transfer of fluctuating kinetic energy.

Data-driven fractional subgrid-scale modeling for scalar turbulence: A nonlocal LES approach

Filtering the passive scalar transport equation in the large-eddy simulation (LES) of turbulent transport gives rise to the closure term corresponding to the unresolved scalar flux. Understanding and respecting the statistical features of subgrid-scale (SGS) flux is a crucial point in robustness and predictability of the LES. In this work, we investigate the intrinsic nonlocal behavior of the SGS passive scalar flux through studying its two-point statistics obtained from the filtered direct numerical simulation (DNS) data for passive scalar transport in homogeneous isotropic turbulence (HIT). Presence of long-range correlations in true SGS scalar flux urges to go beyond the conventional local closure modeling approaches that fail to predict the non-Gaussian statistical features of turbulent transport in passive scalars. Here, we propose an appropriate statistical model for microscopic SGS motions by taking into account the filtered Boltzmann transport equation (FBTE) for passive scalar. In FBTE, we approximate the filtered equilibrium distribution with an α-stable Lévy distribution that essentially incorporates a power-law behavior to resemble the observed nonlocal statistics of SGS scalar flux. Generic ensemble-averaging of such FBTE lets us formulate a continuum level closure model for the SGS scalar flux appearing in terms of fractional-order Laplacian that is inherently nonlocal. Through a data-driven approach, we infer the optimal version of our SGS model using the high-fidelity data for the two-point correlation function between the SGS scalar flux and filtered scalar gradient, and sparse linear regression. In an a priori test, the optimal fractional-order model yields a promising performance in reproducing the probability distribution function (PDF) of the SGS dissipation of the filtered scalar variance compared to its true PDF obtained from the filtered DNS data.

Development of a large-eddy simulation subgrid model based on artificial neural networks: a case study of turbulent channel flow

Abstract. Atmospheric boundary layers and other wall-bounded flows are often simulated with the large-eddy simulation (LES) technique, which relies on subgrid-scale (SGS) models to parameterize the smallest scales. These SGS models often make strong simplifying assumptions. Also, they tend to interact with the discretization errors introduced by the popular LES approach where a staggered finite-volume grid acts as an implicit filter. We therefore developed an alternative LES SGS model based on artificial neural networks (ANNs) for the computational fluid dynamics MicroHH code (v2.0). We used a turbulent channel flow (with friction Reynolds number Reτ=590) as a test case. The developed SGS model has been designed to compensate for both the unresolved physics and instantaneous spatial discretization errors introduced by the staggered finite-volume grid. We trained the ANNs based on instantaneous flow fields from a direct numerical simulation (DNS) of the selected channel flow. In general, we found excellent agreement between the ANN-predicted SGS fluxes and the SGS fluxes derived from DNS for flow fields not used during training. In addition, we demonstrate that our ANN SGS model generalizes well towards other coarse horizontal resolutions, especially when these resolutions are located within the range of the training data. This shows that ANNs have potential to construct highly accurate SGS models that compensate for spatial discretization errors. We do highlight and discuss one important challenge still remaining before this potential can be successfully leveraged in actual LES simulations: we observed an artificial buildup of turbulence kinetic energy when we directly incorporated our ANN SGS model into a LES simulation of the selected channel flow, eventually resulting in numeric instability. We hypothesize that error accumulation and aliasing errors are both important contributors to the observed instability. We finally make several suggestions for future research that may alleviate the observed instability.

Interscale kinetic energy transfer in chemically reacting compressible isotropic turbulence

Abstract