Field Experimental Study of Dynamic Smagorinsky Models in the Atmospheric Surface Layer

The accuracy of large-eddy simulation (LES) of stratified flows is significantly influenced by sub-grid scale (SGS) stress and scalar flux models. In this study, two-dimensional high-resolution velocity and scalar (density) data (simultaneously obtained using a combined Particle Image Velocimetry and Planar Laser Induced Fluorescence technique) in a horizontal turbulent stratified jet are used to examine the SGS parameters and the performance of SGS models. The profiles of SGS dissipation of kinetic energy indicate that the flow has more capability to sustain its structure in the stable region (upper mixing layer) of stratified jet. The backscatter is observed from the components of the SGS dissipation of kinetic energy and SGS dissipation of scalar variance in the stable stratification region of jet in the high-Ri case. The SGS dissipation of kinetic energy and of scalar variance are shown strong dependence on the stability status of local flow field, which experience the ascending and descending as the stability parameter increases. In the SGS model tests, the scale-invariant dynamic model shows better performance of predicting Display FormulaCs2 than classic Smagorinsky model and scale-dependent dynamic model. From the current study, the SGS turbulent Prandtl number is suggested as constant (e.g., Pr ≃ 0.46) to a achieve a good simulation of scalar field in engineering applications to economize the computational cost.© 2013 ASME

A field experiment – the Snow Horizontal Array Turbulence Study (SnoHATS) – has been performed over an extensive glacier in Switzerland in order to study small-scale turbulence in the stable atmospheric surface layer, and to investigate the role, dynamics and modelling of the subgrid scales (SGSs) in the context of large-eddy simulations. Thea prioridata analysis aims at comparing the role and behaviour of the SGSs under stable conditions with previous studies under neutral or unstable conditions. It is found that the SGSs in a stable surface layer remain an important sink of temperature variance and turbulent kinetic energy from the resolved scales and carry a significant portion of the fluxes when the filter scale is larger than the distance to the wall. The fraction of SGS fluxes (out of the total fluxes) is found to be independent of stability. In addition, the stress–strain alignment is similar to the alignment under neutral and unstable conditions. The model coefficients vary considerably with stability but in a manner consistent with previous findings, which also showed that scale-dependent dynamic models can capture this variation. Furthermore, the variation of the coefficients for both momentum and heat SGS fluxes can be shown to be better explained by stability parameters based on vertical gradients, rather than vertical fluxes. These findings suggest that small-scale turbulence dynamics and SGS modelling under stable conditions share many important properties with neutral and convective conditions, and that a unified approach is thus possible. This paper concludes with a discussion of some other challenges for stable boundary-layer simulations that are not encountered in the neutral or unstable cases.

On the relevance of the type of contraction of the Germano identity in the new integral-based dynamic Smagorinsky model

Large-eddy simulation (LES), coupled with a wind-turbine model, is used to investigate the characteristics of a wind-turbine wake in a neutral turbulent boundary-layer flow. The tuning-free Lagrangian scale-dependent dynamic subgrid-scale (SGS) model is used for the parametrisation of the SGS stresses. The turbine-induced forces (e.g., thrust, lift and drag) are parametrised using two models: (a) the ‘standard’ actuator-disk model (ADM-NR), which calculates only the thrust force and distributes it uniformly over the rotor area; and (b) the actuator-disk model with rotation (ADM-R), which uses the blade-element theory to calculate the lift and drag forces (that produce both thrust and rotation), and distribute them over the rotor disk based on the local blade and flow characteristics. Simulation results are compared to high-resolution measurements collected with hot-wire anemometry in the wake of a miniature wind turbine at the St. Anthony Falls Laboratory atmospheric boundary-layer wind tunnel. In general, the characteristics of the wakes simulated with the proposed LES framework are in good agreement with the measurements in the far-wake region. The ADM-R yields improved predictions compared with the ADM-NR in the near-wake region, where including turbine-induced flow rotation and accounting for the non-uniformity of the turbine-induced forces appear to be important. Our results also show that the Lagrangian scale-dependent dynamic SGS model is able to account, without any tuning, for the effects of local shear and flow anisotropy on the distribution of the SGS model coefficient.

Phenomena such as large-scale shear, buoyancy, and the proximity to the ground surface significantly affect interactions among scales in atmospheric boundary layer turbulent flows. Hence, these phenomena impact parameters that enter subgrid-scale (SGS) parameterizations used in large eddy simulations (LES) of the atmospheric boundary layer. The effects of these phenomena upon SGS parameters have, to date, been studied mostly as functions of the global state of the flow. For instance, the Smagorinsky coefficient has been measured as a function of the mean shear and stability condition of the atmosphere as determined from the average surface heat and momentum fluxes. However, in LES the global average field values are often difficult to determine a priori and the SGS parameters ideally must be expressed as a function of local flow variables that characterize the instantaneous flow phenomena. With the goal of improving the Smagorinsky closure, in this study several dimensionless parameters characterizing the local structure and important dynamical characteristics of the flow are defined. These local parameters include enstrophy, vortex stretching, self-amplification of strain rate, and normalized temperature gradient and all are defined in such a way that they remain bounded under all circumstances. The dependence of the Smagorinsky coefficient on these local parameters is studied a priori from field data measured in the atmospheric surface layer and, as a reference point, from direct numerical simulation of neutrally buoyant, isotropic turbulence. To capture the local effects in a statistically meaningful fashion, conditional averaging is used. Results show various important and interrelated trends, such as significant increases of the coefficient in regions of large strain-rate self-amplification and vortex stretching. Results also show that the joint dependence on the parameters is rather complicated and cannot be described by products of functions that depend on single parameters. Dependence on locally defined parameters is expected to improve the SGS model by sensitizing it to local flow conditions and by enabling possible generalizations of the dynamic model based on conditional averaging.

A method for performing nested grid calculations with a large-eddy simulation code is described. A common numerical method is used for all meshes, and the grid architecture consists of a single outer or coarse grid, and nested or fine grids, which overlap in some common region. Inter-grid communication matches the velocity, pressure and potential temperature fields in the overlap region. Resolved and sub-grid scale (SGS) turbulent fluxes and kinetic energy on the fine grid are averaged to the coarse grid using a conservation rule equivalent to Germano's identity used to develop dynamic SGS models. Simulations of a slightly convective, strong shear planetary boundary layer were carried out with varying surface-layer resolutions. Grid refinements in the (x, y, z) directions of up to (5, 5, 2) times were employed. Two-way interaction solutions on the coarse and fine meshes are successfully matched in the overlap region on an instantaneous basis, and the turbulent motions on the fine grid blend smoothly into the coarse grid across the grid interface. With surface-layer grid nesting, significant increases in resolved eddy fluxes and variances are found. The energy-scale content of the vertical velocity, and hence vertical turbulent fluxes, appear to be most influenced by increased grid resolution. Vertical velocity spectra show that the dominant scale shifts towards higher wavenumbers (smaller scales) and the magnitude of the peak energy is increased by more than a factor of 3 with finer resolution. Outside of the nested region the average heat and momentum fluxes and spectra are slightly influenced by the fine resolution in the surface layer. From these results we conclude that fine resolution is required to resolve the details of the turbulent motions in the surface layer. At the same time, however, increased resolution in the surface layer does not appreciably alter the ensemble statistics of the resolved and SGS motions outside of the nested region.

The effects of the subgrid-scale (SGS) turbulence and SGS models on the one-point joint probability density function (JPDF) of resolvable-scale velocity are studied using its transport equation. It is shown that the SGS stress evolves the JPDF through the conditional means of the SGS stress and its production rate conditional on the resolvable-scale velocity, which must be reproduced by the SGS model in order for large-eddy simulation (LES) to reproduce the JPDF. Measurements are conducted in an axisymmetric turbulent jet using an array consisting of three X-wire probes to obtain filtered variables for analysing the conditional means. Data for three filter scales show that both the conditional SGS stress and the conditional SGS stress production rate depend strongly on the resolvable-scale velocity. While the magnitude of the conditional SGS stress decreases with the filter scale, that of the conditional SGS stress production does not, suggesting persistent effects on the resolvable-scale velocity JPDF. Therefore, the SGS model must be able to reproduce the conditional SGS stress production even for inertial-range filter scales. The conditional production of SGS normal stress (energy transfer) has some negative values, indicating conditional backscatter of SGS energy. This provides direct evidence that for LES to reproduce the JPDF it is essential for the SGS models to predict (conditional) backscatter. The Smagorinsky model is capable of predicting the qualitative features of the conditional SGS stress but not those of the conditional SGS stress production, especially the conditional backscatter. The present study links the resolvable-scale statistics to the dynamics of the SGS stress, providing impetus for further study of the SGS dynamics.

A new dynamic subgrid-scale (SGS) mixed model is proposed for large-eddy simulation of turbulent flows. This model is based on the decomposition of the SGS stress terms into the modified Leonard, modified cross and modified SGS Reynolds stress terms. In this model, the modified Leonard term is computed explicitly. The modified cross term and modified SGS Reynolds stress are assumed to be proportional to a new term, the form of which is comparable to the generalized central moment, derived as an extension of the filtered Bardina model proposed by Horiuti [J. Phys. Soc. Jpn. 66, 91 (1997)]. Using a linear combination of this new term with the Smagorinsky model for the modified SGS Reynolds stress, the proposed model contains two model parameters, which are computed dynamically. Two formulations for the test-filtered SGS stress reported by Zang et al. [Phys. Fluids A 5, 3186 (1993)] and Vreman et al. [Phys. Fluids 6, 4057 (1994)] are compared, and the compatibility of the SGS models with the standard dynamic SGS model procedure is discussed. The proposed model is assessed for incompressible channel and mixing layer flows, in comparison with the dynamic Smagorinsky model of Germano et al. [Phys. Fluids A 3, 1760 (1991)], the dynamic mixed model of Zang et al. and the dynamic two-parameter mixed model of Salvetti and Banerjee [Phys. Fluids 7, 2831 (1995)]. In the “a priori” test, the proposed model gave the closest agreement with the modified cross term as well as the modified SGS Reynolds stress term. It is shown that the proposed term represents a more general model of the SGS stress than the modified Leonard term and yields a more accurate approximation. These SGS models are tested further in actual LES of channel and mixing layer flows (“a posteriori” test). The results were consistent with those of the “a priori” tests; the proposed model yielded the most accurate results. In the proposed model, the SGS quantities were predominantly represented using the new term, and the contribution of the Smagorinsky model was minimal. The two parameters contained in the model were determined locally in space on a point-by-point basis.

In this paper, a modified projection method is combined with a self‐adaptive time step procedure to develop numerical scheme for large eddy simulation (LES) of low Ma number turbulent reactive flows. The projection method introduced by Chorin is modified in this study to satisfy the simulation requirement of low Ma number reactive flow. The time step in this computation is automatically determined according to the time scales of both chemical reaction and turbulent fluctuations. This enables the simulation to capture detailed flow structures with less computational time. Numerical simulation of methane–air jet flames is carried out as an example to validate the developed numerical scheme. The mechanism of a simplified 4‐step chemical kinetics is applied for the methane–air reaction. The dynamic model is adopted for the turbulent motion of sub‐grid scale (SGS). The dynamic similarity model is used as the SGS model for the reaction rate. The LES results satisfactorily depict the ignition process of the turbulent jet flames and illustrate lucid and detailed coherent structures of the fully developed turbulent reactive jet flow. The LES results also exhibit the mechanism and characteristics of local extinction. The method developed in this study provides an effective way to capture more flow details with less computational time. In addition the method also helps one to investigate the mechanism of ignition and local extinction in jet flames. Copyright © 2008 John Wiley & Sons, Ltd.

In the present study, a dynamic global subgrid-scale eddy diffusivity model for large eddy simulation of scalar transport in complex turbulent flows is proposed by generalizing the dynamic global subgrid-scale eddy viscosity model [Phys. Fluids, 18 125109 (2006) and Phys. Fluids, 22 075106 (2010)]. The global model coefficient in the subgrid-scale model is determined by a dynamic procedure based on the Germano identity such that the model coefficient is globally constant in space but varies only in time. Large eddy simulations of passive scalar transport in turbulent channel flow, turbulent boundary layer, and turbulent ribbed channel flow are conducted and the proposed model shows an excellent performance for all the flows considered. Since the proposed model requires no ad hoc clipping and/or averaging over a homogeneous direction, it can be readily applied to large eddy simulation of scalar transport in complex turbulent flows.

Most natural landscapes are characterized by multiscale (often multifractal) topography with well-known scale-invariance properties. For example, the spectral density of landscape elevation fields is often found to have a power-law scaling behaviour (with a -2 slope on a log-log scale) over a wide span of spatial scales, typically ranging from tens of kilometres down to a few metres. Even though the effect of topography on the atmospheric boundary layer (ABL) has been the subject of numerous studies, few have focussed on multiscale topography. In this study, large-eddy simulation (LES) is used to investigate boundary-layer flow over multiscale topography, and guide the development of parametrizations needed to represent the effects of subgrid-scale (SGS) topography in numerical models of ABL flow. Particular emphasis is placed on the formulation of an effective roughness used to account for the increased aerodynamic roughness associated with SGS topography. The LES code uses the scale-dependent Lagrangian dynamic SGS model for the turbulent stresses and a terrain-following coordinate transformation to explicitly resolve the effects of the topography at scales larger than the LES resolution. The terrain used in the simulations is generated using a restricted solid-on-solid landscape evolution model, and it is characterized by a -2 slope of the elevation power spectrum. Results from simulations performed using elevation fields band-pass filtered at different spatial resolutions indicate a clear linear relation between the square of the effective roughness and the variance of elevation.

A spectral tensor model is presented for turbulent fluctuations of wind velocity components and temperature, assuming uniform vertical gradients in mean temperature and mean wind speed. The model is built upon rapid distortion theory (RDT) following studies by Mann and by Hanazaki and Hunt, using the eddy lifetime parameterization of Mann to make the model stationary. The buoyant spectral tensor model is driven via five parameters: the viscous dissipation rate ε, length scale of energy-containing eddies L, a turbulence anisotropy parameter , gradient Richardson number (Ri) representing the local atmospheric stability, and the rate of destruction of temperature variance . Model output includes velocity and temperature spectra and associated cospectra, including those of longitudinal and vertical temperature fluxes. The model also produces two-point statistics, such as coherences and phases of velocity components and temperature. The statistics of uniformly sheared and stratified turbulence from the model are compared with atmospheric observations taken from the Horizontal Array Turbulence Study (HATS) field program, and model results fit observed one-dimensional spectra quite well. For highly unstable stratification, however, the model has deficiencies at low wavenumbers that limit its prediction of longitudinal velocity component spectra at scales on the order of 0.6 km. The model predicts coherences well for horizontal separations but overestimates vertical coherence with increasing separation. Finally, it is shown that the RDT output can deviate from Monin–Obukhov similarity theory.

A simulation of a diurnal cycle of atmospheric boundary layer (ABL) flow over a homogeneous terrain is performed using large‐eddy simulation (LES) with the Lagrangian scale‐dependent dynamic subgrid‐scale model. The surface boundary condition is derived from the field observations of surface heat flux from the HATS experiment (Horst et al., 2004; Kleissl et al., 2004). The simulation results display good general agreement with previous modeling and experimental studies with regard to characteristic features such as growth of the convective boundary layer by entrainment, nocturnal jet, and multilayered flow structure of the nocturnal regime. To gain a better understanding of the physical parameters affecting the statistics of the flow, we study the dependence of a subgrid parameter (dynamic Smagorinsky coefficient), resolved turbulent kinetic energy, and resolved vertical velocity variance upon atmospheric stability. The profiles of these turbulent variables plotted as a function of Obukhov length show “hysteretic” behavior that implies nonunique dependence. The subsequent use of local Richardson number as the scaling parameter shows a decrease in this “hysteresis,” but there is an increased scatter in the profiles with increasing height. Conversely, profiles plotted as a function of local Obukhov length (based on the fluxes at the local vertical level) show almost no hysteresis, confirming the validity of Nieuwstadt's local scaling hypothesis. Although the local scaling hypothesis was formulated for the stable boundary layer, we find that it applies to the entire stability range of the diurnal cycle.

A large-eddy simulation of the three-dimensional shear-driven cavity flow was carried out at a high Reynolds number where the subgrid scale turbulence was represented by a dynamic model. Lilly's expression was tested for determining Smagorinsky's coefficient in the model without ad hoc measures such as ensemble-averaging or filtering. However, zero cut-off of negative total viscosity was necessary to maintain stable solutions. A discretized filter function is derived for the test filter. Good qualitative and quantitative agreement with published experimental data was obtained indicating that the dynamic model performed quite well. The cavity flow at Reynolds number of 104 is transitional. The highest turbulent production levels not only occurred within the downstream eddy region of the cavity, but also along the upper half of the downstream wall.

The subgrid-scale (SGS) stress in the atmospheric surface layer is studied using measurement data. Field measurements employing a novel array technique were conducted to provide data for obtaining resolvable- and subgrid-scale variables. We analyse the conditional SGS stress and the conditional stress production rate conditional on the resolvable-scale velocity, which must be reproduced by the SGS model for large-eddy simulation (LES) to predict correctly the one-point resolvable-scale velocity statistics. The results show that both buoyancy and shear play important roles in the physics of the SGS stress. Strong buoyancy and vertical shear associated with updrafts and positive streamwise velocity fluctuations cause conditional forward energy transfer and strong anisotropy in the conditional SGS stress. Downward returning flows associated with large convective eddies result in conditional energy backscatter and much less anisotropic SGS stress. Predictions of the conditional SGS stress and the conditional stress production rate predicted using several SGS models are compared with measurements. None of those models are able to predict correctly the trends of both statistics. The Smagorinsky and one nonlinear model under-predict the anisotropy and the variations of the anisotropy, whereas the other nonlinear model and the mixed model over-predict both. The deficiencies of the SGS models that cause inaccurate LES statistics, such as the over-prediction of the mean shear and under-prediction of the vertical velocity skewness, are identified. The present study shows that analyses of conditional SGS stress and conditional SGS stress production provide a systematic approach for studying SGS physics and evaluating SGS models and can potentially be used to target specific aspects of LES that are important for a given application.