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Bowen Zhou and Fotini Katopodes Chow
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Takenobu Michioka and Fotini Katopodes Chow

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This paper presents high-resolution numerical simulations of the atmospheric flow and concentration fields accompanying scalar transport and diffusion from a point source in complex terrain. Scalar dispersion is affected not only by mean flow, but also by turbulent fluxes that affect scalar mixing, meaning that predictions of scalar transport require greater attention to the choice of numerical simulation parameters than is typically needed for mean wind field predictions. Large-eddy simulation is used in a mesoscale setting, providing modeling advantages through the use of robust turbulence models combined with the influence of synoptic flow forcing and heterogeneous land surface forcing. An Eulerian model for scalar transport and diffusion is implemented in the Advanced Regional Prediction System mesoscale code to compare scalar concentrations with data collected during field experiments conducted at Mount Tsukuba, Japan, in 1989. The simulations use horizontal grid resolution as fine as 25 m with up to eight grid nesting levels to incorporate time-dependent meteorological forcing. The results show that simulated ground concentration values contain significant errors relative to measured values because the mesoscale wind typically contains a wind direction bias of a few dozen degrees. Comparisons of simulation results with observations of arc maximum concentrations, however, lie within acceptable error bounds. In addition, this paper investigates the effects on scalar dispersion of computational mixing and lateral boundary conditions, which have received little attention in the literature—in particular, for high-resolution applications. The choice of lateral boundary condition update interval is found not to affect time-averaged quantities but to affect the scalar transport strongly. More frequent updates improve the simulated ground concentration values. In addition, results show that the computational mixing coefficient must be set to as small a value as possible to improve scalar dispersion predictions. The predicted concentration fields are compared as the horizontal grid resolution is increased from 190 m to as fine as 25 m. The difference observed in the results at these levels of grid refinement is found to be small relative to the effects of computational mixing and lateral boundary updates.

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Bowen Zhou and Fotini Katopodes Chow

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This numerical study investigates the nighttime flow dynamics in Owens Valley, California. Nested high-resolution large-eddy simulation (LES) is used to resolve stable boundary layer flows within the valley. On 17 April during the 2006 Terrain-Induced Rotor Experiment, the valley atmosphere experiences weak synoptic forcings and is largely dominated by buoyancy-driven downslope and down-valley flows. Tower instruments on the valley floor record a continuous decrease in temperature after sunset, except for a brief warming episode. This transient warming event is modeled with good magnitude and temporal precision with LES. Analysis of the LES flow field confirms the event to be the result of a slope to valley flow transition, as previously suggested by researchers based on field observations. On the same night, a northerly cold airflow from the Great Basin is channeled through a pass on the eastern valley sidewall. The current plunges into the stable valley atmosphere, overshooting the altitude of its neutral buoyancy, and generating a large-scale oscillatory motion. The resulting cross-valley flow creates strong vertical shear with the down-valley flow in the lower layers of the atmosphere. A portion of the cross-valley flow is captured by a scanning lidar. The nested LES is in good agreement with the lidar-recorded radial velocity. Furthermore, the LES is able to resolve Kelvin–Helmholtz waves, and ejection and sweep events at the two-layer interface, which lead to top-down vertical mixing.

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Bowen Zhou and Fotini Katopodes Chow

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The nighttime stable atmospheric boundary layer over real terrain is modeled with nested high-resolution large-eddy simulations (LESs). The field site is located near Leon, Kansas, where the 1999 Cooperative Atmosphere–Surface Exchange Study took place. The terrain is mostly flat with an average slope of 0.5°. The main topographic feature is a shallow valley oriented in the east–west direction. The night of 5 October is selected to study intermittent turbulence under prevailing quiescent conditions. Brief turbulent periods triggered by shear-instability waves are modeled with good magnitude and temporal precision with a dynamic reconstruction turbulence closure. In comparison, conventional closures fail to excite turbulent motions and predict a false laminar flow. A plausible new intermittency mechanism, previously unknown owing to limited spatial coverage of field instruments at this site, is unveiled with the LESs. Turbulence can be generated through gravity wave breaking over a stagnant cold-air bubble in the valley upwind of the main tower. The bubble is preceded by the formation of a valley cold-air pool due to down-valley drainage flows during the evening transition. The bubble grows in depth by entraining cold down-valley and downslope flows from below and is eroded by shear-induced wave breaking on the top. The cyclic process of formation and erosion is repeated during the night, leading to sporadic turbulent bursting.

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Bowen Zhou and Fotini Katopodes Chow

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Large-eddy simulation (LES) of the stably stratified atmospheric boundary layer is performed using an explicit filtering and reconstruction approach with a finite difference method. Turbulent stresses are split into the resolvable subfilter-scale and subgrid-scale stresses. The former are recovered from a reconstruction approach, and the latter are represented by a dynamic eddy-viscosity model. The resulting dynamic reconstruction model (DRM) can sustain resolved turbulence with less stringent resolution requirements than conventional closure models, even under strong atmospheric stability. This is achieved by proper representation of subfilter-scale (SFS) backscatter of turbulent kinetic energy (TKE). The flow structure and turbulence statistics for the moderately stable boundary layer (SBL) are analyzed with high-resolution simulations. The DRM simulations show good agreement with established empirical formulations such as flux and gradient-based surface similarity, even at relatively coarse resolution. Similar results can be obtained with traditional closure models at the cost of higher resolution. SBL turbulence under strong stability is also explored. Simulations show an intermittent presence of elevated TKE below the low-level jet. Overall, the explicit filtering and reconstruction approach is advantageous for simulations of the SBL. At coarse resolution, it can extend the working range of LES to stronger stability, while maintaining agreement to similarity theory; at fine resolution, good agreement with theoretical formulations provides confidence in the results and allows for detailed investigation of the flow structure under moderate to strong stability conditions.

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Fotini Katopodes Chow and Robert L. Street

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The evaluation of turbulence closure models for large-eddy simulation (LES) has primarily been performed over flat terrain, where comparisons with theory and observations are simplified. The authors have previously developed improved closure models using explicit filtering and reconstruction, together with a dynamic eddy-viscosity model and a near-wall stress term. This dynamic reconstruction model (DRM) is a mixed model, combining scale-similarity and eddy-viscosity components. The DRM gave improved results over standard eddy-viscosity models for neutral boundary layer flow over flat but rough terrain, yielding the expected logarithmic velocity profiles near the wall. The results from the studies over flat terrain are now extended to flow over full-scale topography. The test case is flow over Askervein Hill, an isolated hill in western Scotland, where a field campaign was conducted in 1983 with the purpose of capturing wind data representing atmospheric episodes under near-neutral stratification and steady wind conditions. This widely studied flow provides a more challenging test case for the new turbulence models because of the sloping terrain and separation in the lee of the hill. Since an LES formulation is used, a number of simulation features are different than those typically used in the Askervein literature. The simulations are inherently unsteady, the inflow conditions are provided by a separate turbulent flow database, and (uniquely herein) ensemble averages of the turbulent flow results are used in comparisons with field data. Results indicate that the DRM can improve the predictions of flow speedup and especially turbulent kinetic energy (TKE) over the hill when compared with the standard TKE-1.5 model. This is the first study, to the authors’ knowledge, in which explicit filtering and reconstruction (scale similarity) and dynamic turbulence models have been applied to full-scale simulations of the atmospheric boundary layer over terrain. Simulations with the lowest level of reconstruction are straightforward. Increased levels of reconstruction, however, present difficulties when used with a dynamic eddy-viscosity model. An alternative mixed model is proposed to avoid the complexities associated with the dynamic procedure and to allow higher levels of reconstruction; this mixed model combines a standard TKE-1.5 eddy-viscosity closure with velocity reconstruction to form a simple and efficient turbulence model that gives good results for both mean flow and turbulence over Askervein Hill. The results indicate that significant improvements in LES over complex terrain can be obtained by the use of mixed models that combine scale-similarity and eddy-viscosity components.

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Fotini Katopodes Chow, Branko Kosović, and Stevens Chan

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The ability to determine the source of a contaminant plume in urban environments is crucial for emergency-response applications. Locating the source and determining its strength based on downwind concentration measurements, however, are complicated by the presence of buildings that can divert flow in unexpected directions. High-resolution flow simulations are now possible for predicting plume evolution in complex urban geometries, where contaminant dispersion is affected by the flow around individual buildings. Using Bayesian inference via stochastic sampling algorithms with a high-resolution computational fluid dynamics model, an atmospheric release event can be reconstructed to determine the plume source and release rate based on point measurements of concentration. Event-reconstruction algorithms are applied first for flow around a prototype isolated building (a cube) and then using observations and flow conditions from Oklahoma City, Oklahoma, during the Joint Urban 2003 field campaign. Stochastic sampling methods (Markov chain Monte Carlo) are used to extract likely source parameters, taking into consideration measurement and forward model errors. In all cases the steady-state flow field generated by a 3D Navier–Stokes finite-element code (FEM3MP) is used to drive thousands of forward-dispersion simulations. To enhance computational performance in the inversion procedure, a reusable database of dispersion simulation results is created. It is possible to successfully invert the dispersion problems to determine the source location and release rate to within narrow confidence intervals even with such complex geometries. The stochastic methodology here is general and can be used for time-varying release rates and reactive flow conditions. The results of inversion indicate the probability of a source being found at a particular location with a particular release rate, thus inherently reflecting uncertainty in observed data or the lack of enough data in the shape and size of the probability distribution. A composite plume showing concentrations at the desired confidence level can also be constructed using the realizations from the reconstructed probability distribution. This can be used by emergency responders as a tool to determine the likelihood of concentration at a particular location being above a threshold value.

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Elijah Goodfriend, Fotini Katopodes Chow, Marcos Vanella, and Elias Balaras

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Increasing computational power has enabled grid resolutions that support large-eddy simulation (LES) of the atmospheric boundary layer. These simulations often use grid nesting or adaptive mesh refinement to refine the grid in regions of interest. LES generates errors at grid refinement interfaces, such as resolved energy accumulation, that may compromise solution accuracy. In this paper, the authors test the ability of two LES formulations and turbulence closures to mitigate errors associated with the use of LES on nonuniform grids for a half-channel approximation to a neutral atmospheric boundary layer simulation. Idealized simulations are used to examine flow across coarse–fine and fine–coarse interfaces, as would occur in a two-way nested configuration or with block structured adaptive mesh refinement. Specifically, explicit filtering of the advection term and the mixed model are compared to a standard LES formulation with an eddy viscosity model. Errors due to grid interfaces are evaluated by comparison to uniform grid solutions. It is found that explicitly filtering the advection term provides significant benefits, in that it allows both mass and momentum to be conserved across grid refinement interfaces. The mixed model reduces unphysical perturbations generated by wave reflection at the interfaces. These results suggest that the choice of LES formulation and turbulence closure can be used to help control grid refinement interface errors in atmospheric boundary layer simulations.

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Francis L. Ludwig, Fotini Katopodes Chow, and Robert L. Street

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This paper demonstrates the importance of high-quality subfilter-scale turbulence models in large-eddy simulations by evaluating the resolved-scale flow features that result from various closure models. The Advanced Regional Prediction System (ARPS) model was used to simulate neutral flow over a 1.2-km square, flat, rough surface with seven subfilter turbulence models [Smagorinsky, turbulent kinetic energy (TKE)-1.5, and five dynamic reconstruction combinations]. These turbulence models were previously compared with similarity theory. Here, the differences are evaluated using mean velocity statistics and the spatial structure of the flow field. Streamwise velocity averages generally differ among models by less than 0.5 m s−1, but those differences are often significant at a 95% confidence level. Flow features vary considerably among models. As measured by spatial correlation, resolved flow features grow larger and less elongated with height for a given model and resolution. The largest differences are between dynamic models that allow energy backscatter from small to large scales and the simple eddy-viscosity closures. At low altitudes, the linear extent of Smagorinsky and TKE-1.5 structures exceeds those of dynamic models, but the relationship reverses at higher altitudes. Ejection, sweep, and upward momentum flux features differ among models and from observed neutral atmospheric flows, especially for Smagorinsky and TKE-1.5 coarse-grid simulations. Near-surface isopleths separating upward fluxes from downward are shortest for the Smagorinsky and TKE-1.5 coarse-grid simulations, indicating less convoluted turbulent interfaces; at higher altitudes they are longest. Large-eddy simulation (LES) is a powerful simulation tool, but choices of grid resolution and subfilter model can affect results significantly. Physically realistic dynamic mixed models, such as those presented here, are essential when using LES to study atmospheric processes such as transport and dispersion—in particular at coarse resolutions.

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Jingyi Bao, Fotini Katopodes Chow, and Katherine A. Lundquist

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The Weather Research and Forecasting (WRF) Model is increasingly being used for higher-resolution atmospheric simulations over complex terrain. With increased resolution, resolved terrain slopes become steeper, and the native terrain-following coordinates used in WRF result in numerical errors and instability. The immersed boundary method (IBM) uses a nonconformal grid with the terrain surface represented through interpolated forcing terms. Lundquist et al.’s WRF-IBM implementation eliminates the limitations of WRF’s terrain-following coordinate and was previously validated with a no-slip boundary condition for urban simulations and idealized terrain. This paper describes the implementation of a log-law boundary condition into WRF-IBM to extend its applicability to general atmospheric complex terrain simulations. The implementation of the improved WRF-IBM boundary condition is validated for neutral flow over flat terrain and the complex terrain cases of Askervein Hill, Scotland, and Bolund Hill, Denmark. First, comparisons are made to similarity theory and standard WRF results for the flat terrain case. Then, simulations of flow over the moderately sloped Askervein Hill are used to demonstrate agreement between the IBM and terrain-following WRF results, as well as agreement with observations. Finally, Bolund Hill simulations show that WRF-IBM can handle steep topography (standard WRF fails) and compares well to observations. Overall, the new WRF-IBM boundary condition shows improved performance, though the leeside representation of the flow can be potentially further improved.

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