Large-Eddy Simulation of Atmospheric Boundary-Layer Flow Over Fluvial-Like Landscapes Using a Dynamic Roughness Model

A recently developed dynamic surface roughness model (Anderson and Meneveau, J Fluid Mech 679:288–314, 2011) for large-eddy simulation (LES) of atmospheric boundary-layer flow over multi-scale topographies is applied to boundary-layer flow over several types of fluvial-like landscapes. The landscapes are generated numerically with simulation of a modified Kardar–Parisi–Zhang equation (Passalacqua et al., Water Resour Res 42:WOD611, 2006). These surfaces possess the fractal-like channel network and anisotropic features often found in real terrains. The dynamic model is shown to lead to accurate flow predictions when the surface-height distributions exhibit power-law scaling (scale invariance) in the prevalent mean flow direction. In those cases, the LES provide accurate predictions (invariant to resolution) of mean velocity profiles. Conversely, some resolution dependence is found for applications in which the landscape’s streamwise spectra do not exhibit pure power-law scaling near wavenumbers corresponding to the LES grid resolution.     

Large-Eddy Simulation of Thermally Stratified Atmospheric Boundary-Layer Flow Using a Minimum Dissipation Model

A generalized form of a recently developed minimum dissipation model for subfilter turbulent fluxes is proposed and implemented in the simulation of thermally stratified atmospheric boundary-layer flows. Compared with the original model, the generalized model includes the contribution of buoyant forces, in addition to shear, to the production or suppression of turbulence, with a number of desirable practical and theoretical properties. Specifically, the model has a low computational complexity, appropriately switches off in laminar and transitional flows, does not require any ad hoc shear and stability corrections, and is consistent with theoretical subfilter turbulent fluxes. The simulation results show remarkable agreement with well-established empirical correlations, theoretical predictions, and field observations in the atmosphere. In addition, the results show very little sensitivity to the grid resolution, demonstrating the robustness of the model in the simulation of the atmospheric boundary layer, even with relatively coarse resolutions.     

A Large-Eddy Simulation Study of Turbulent Flow Over Multiscale Topography

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.     

Large-Eddy Simulation of Flow Over a Vegetation-Like Canopy Modelled as Arrays of Bluff-Body Elements

Turbulent flow over a vegetation canopy under neutral atmospheric conditions is investigated using large-eddy simulation. Each model tree, which consists of a sphere-shaped tree crown and a cylindrical trunk, is fully resolved. The resulting turbulence statistics and the drag force on the vegetation agree well with measurements from the corresponding wind-tunnel experiment described by Böhm et al. (Boundary-Layer Meteorol, 146:393–419, 2013). Statistically, this kind of model canopy exhibits both vegetation and bluff-body-flow characteristics. The time-averaged flow skims over the top of the underlying canopy, forming a low-momentum recirculation zone on the lee-side of the bluff elements, which causes significant dispersive stress within the canopy layer. Two other numerical representations of vegetation canopies, referred to as the drag-element and drag-crown approaches, have also been developed to assess the performance of simulations. Turbulence statistics suggest that the canopy shear layer interferes with wakes behind stems and crowns. The drag-crown approach yields better agreement between numerical results and experimental measurements than does the traditional drag-element approach, thus providing a promising numerical model for simulating canopy turbulence.     

Stably Stratified Boundary-Layer Flow Over Low Hills: A Comparison of Model Results and Field Data

A linear theory of airflow over low hills andthe MSFD–STAB model are comparedwith published observations made at Cooper'sRidge, north–west of Goulburn inNew South Wales, Australia. The MSFD–STABmodel results show good agreementwith field data in weak to moderate stablystratified flow cases. The originallinear theory overpredicts the wind speed-upratio even in weakly stablecases. After some modification, the agreementis greatly improved.     

Wind Flow Over Complex Terrain: A Historical Perspective and the Prospect for Large-Eddy Modelling

The development of our understanding of turbulent flow overcomplex terrain is described. Despite considerable advances, there are still gaps in our knowledge. Large-eddy simulation of such flows is now becoming possible. This may stimulate further advances but it is computationally very demanding. The application of this technique to flow over hills is discussed.     

Large-Eddy Simulation of Flow and Pollutant Dispersion in High-Aspect-Ratio Urban Street Canyons with Wall Model

A large-eddy simulation (LES) with a one-equation subgrid-scale (SGS) model was developed to investigate the flow field and pollutant dispersion inside street canyons of high aspect ratio (AR). A 1/7th power-law wall model was implemented near rigid walls to mitigate the demanding near-wall resolution requirements in LES. This LES model had been extensively validated against experimental results for street canyons of AR = 1 and 2 before it was applied to the cases of AR = 3 and 5. A ground-level passive pollutant line source, located in the middle of the street, was used to simulate vehicular emissions. Three and five vertically aligned primary recirculations were developed in the street canyons of AR 3 and 5, respectively. The ground-level mean wind speed was less than 0.5% of the free stream value, which makes it difficult for the pollutant to be transported upward for removal. High pollutant concentration and variance were found near the buildings where the air flow is upwards. It was found that the velocity fluctuation, pollutant concentration and variance were all closely related to the interactions between the primary recirculations and/or the free surface layer. Several quantities, which are non-linear functions of AR, were introduced to quantify the air quality in street canyons of different configurations.     

A Theoretical Model for the Study of Convective Turbulence Decay and Comparison with Large-Eddy Simulation Data

The development of a theoretical model fora decaying convective boundary layeris considered. The model relies on thedynamical energy spectrumequation in which the buoyancy andinertial transfer terms are retained,and a closure assumptionmade for both. The parameterization for thebuoyancy term is given providing a factorizationbetween the energy source termand its temporal decay. Regarding the inertialtransfer term a hypothesis ofsuperposition is used to describe theconvective energy source and time variationof velocity correlation separately.The solution of the budget equation for theturbulent kinetic energy spectrum is possible,given the three-dimensional initial energyspectrum. This is doneutilizing a version of the Kristensen et al.(see Boundary-Layer Meteorol. 47, 149–193)model valid for non-isotropic turbulence. During thedecay the locus of the spectralpeak remains at about the sameposition as the heat flux decreases.Comparison of the theoretical modelis performed against large-eddy simulationdata for a decaying convectiveboundary layer.     

A New Scheme for the Simulation of Microscale Flow and Dispersion in Urban Areas by Coupling Large-Eddy Simulation with Mesoscale Models

A coupling scheme is proposed for the simulation of microscale flow and dispersion in which both the mesoscale field and small-scale turbulence are specified at the boundary of a microscale model. The small-scale turbulence is obtained individually in the inner and outer layers by the transformation of pre-computed databases, and then combined in a weighted sum. Validation of the results of a flow over a cluster of model buildings shows that the inner- and outer-layer transition height should be located in the roughness sublayer. Both the new scheme and the previous scheme are applied in the simulation of the flow over the central business district of Oklahoma City (a point source during intensive observation period 3 of the Joint Urban 2003 experimental campaign), with results showing that the wind speed is well predicted in the canopy layer. Compared with the previous scheme, the new scheme improves the prediction of the wind direction and turbulent kinetic energy (TKE) in the canopy layer. The flow field influences the scalar plume in two ways, i.e. the averaged flow field determines the advective flux and the TKE field determines the turbulent flux. Thus, the mean, root-mean-square and maximum of the concentration agree better with the observations with the new scheme. These results indicate that the new scheme is an effective means of simulating the complex flow and dispersion in urban canopies.     

A Mixed Spectral-Integration Model for Neutral Mean Wind Flow Over Hills

A linear model for neutral surface-layer flow over orography is presented. The Reynolds-Averaged Navier-Stokes and E– turbulence closure equations are expressed in a terrain-following coordinate system created from a simple analytical expression in the Fourier domain. The perturbation equations are solved spectrally horizontally and by numerical integration vertically. Non-dimensional solutions are stored in look-up tables for quick re-use. Model results are compared to measurements, as well as other authors’ flow models in three test cases. The model is implemented and tested in two-dimensional space; the equations for a full three-dimensional version are presented.     

A New Large-Eddy Simulation Model for Simulating Air Flow and Warm Clouds Above Highly Complex Terrain. Part II: The Moist Model and its Application to Banner Clouds

In Part I the dry version of a new large-eddy simulation (LES) model was presented that is specifically designed to simulate air flow and clouds above highly complex terrain. Here the implemented moisture physics are described and a new method for the generation of turbulent inflow conditions for meteorological LES is proposed. As a typical area of application the new model is applied to simulate banner clouds developing downwind of pyramidal mountain peaks. Banner clouds are shown to be primarily a dynamical phenomenon, and form in the lee of steep mountain peaks as a result of dynamically forced lee upslope flow. Due to the highly asymmetric flow field induced by the extreme orography, banner clouds can form even under horizontally homogeneous initial conditions regarding both moisture and temperature. Thus, additional leeward moisture sources, distinct air masses on both windward and leeward sides, or radiation effects are no prerequisite for banner-cloud formation. The probability of banner-cloud formation increases with increasing obstacle height and steepness and is, to a first approximation, independent of the pyramid’s orientation. Simulations with and without moisture physics reveal that, for the set-up chosen, moisture is of only secondary importance for banner-cloud dynamics. The reinforcement of lee upslope flow and corresponding cloud formation due to latent heat release turns out to be almost negligible. Nevertheless moisture physics are shown to induce a dipole-like structure in the vertical profile of the Brunt-Väisälä frequency, which in turn leads to a moderate increase in leeward turbulence.     

A Simple Model for the Afternoon and Early Evening Decay of Convective Turbulence Over Different Land Surfaces

A simple model to study the decay of turbulent kinetic energy (TKE) in the convective surface layer is presented. In this model, the TKE is dependent upon two terms, the turbulent dissipation rate and the surface buoyancy fluctuations. The time evolution of the surface sensible heat flux is modelled based on fitting functions of actual measurements from the LITFASS-2003 field campaign. These fitting functions carry an amplitude and a time scale. With this approach, the sensible heat flux can be estimated without having to solve the entire surface energy balance. The period of interest covers two characteristic transition sub-periods involved in the decay of convective boundary-layer turbulence. The first sub-period is the afternoon transition, when the sensible heat flux starts to decrease in response to the reduction in solar radiation. It is typically associated with a decay rate of TKE of approximately t ⁻² (t is time following the start of the decay) after several convective eddy turnover times. The early evening transition is the second sub-period, typically just before sunset when the surface sensible heat flux becomes negative. This sub-period is characterized by an abrupt decay in TKE associated with the rapid collapse of turbulence. Overall, the results presented show a significant improvement of the modelled TKE decay when compared to the often applied assumption of a sensible heat flux decreasing instantaneously or with a very short forcing time scale. In addition, for atmospheric modelling studies, it is suggested that the afternoon and early evening decay of sensible heat flux be modelled as a complementary error function.     

A Modulated-Gradient Parametrization for the Large-Eddy Simulation of the Atmospheric Boundary Layer Using the Weather Research and Forecasting Model

The performance of the modulated-gradient subgrid-scale (SGS) model is investigated using large-eddy simulation (LES) of the neutral atmospheric boundary layer within the weather research and forecasting model. Since the model includes a finite-difference scheme for spatial derivatives, the discretization errors may affect the simulation results. We focus here on understanding the effects of finite-difference schemes on the momentum balance and the mean velocity distribution, and the requirement (or not) of the ad hoc canopy model. We find that, unlike the Smagorinsky and turbulent kinetic energy (TKE) models, the calculated mean velocity and vertical shear using the modulated-gradient model, are in good agreement with Monin–Obukhov similarity theory, without the need for an extra near-wall canopy model. The structure of the near-wall turbulent eddies is better resolved using the modulated-gradient model in comparison with the classical Smagorinsky and TKE models, which are too dissipative and yield unrealistic smoothing of the smallest resolved scales. Moreover, the SGS fluxes obtained from the modulated-gradient model are much smaller near the wall in comparison with those obtained from the regular Smagorinsky and TKE models. The apparent inability of the LES model in reproducing the mean streamwise component of the momentum balance using the total (resolved plus SGS) stress near the surface is probably due to the effect of the discretization errors, which can be calculated a posteriori using the Taylor-series expansion of the resolved velocity field. Overall, we demonstrate that the modulated-gradient model is less dissipative and yields more accurate results in comparison with the classical Smagorinsky model, with similar computational costs.     

Numerical Studies with a Regional Atmospheric Climate Model Based on Changes in the Roughness Length for Momentum and Heat Over Antarctica

A regional atmospheric climate model is used toexamine the effect of changes in the roughnesslengths of momentum (_z0m) and heat (_z0h)on the structure of the lower atmosphere and on thesurface energy fluxes over Antarctica. Fourexperiments were carried out in which _z0mand/or _z0h were altered with respect to acontrol experiment. The changes consisted of (1) alowering of _z0m from a field aggregated froma vegetation map with an orographic correction basedon the European Centre for Medium-Range WeatherForecasts _z0m field, to a constant value of10^-3 m; and (2) a lowering of _z0h from a valueequal to _z0m to a constant value of 10^-3 mor a value dependent on the wind speed via a surfacerenewal model. A reduction of _z0m results in theexpected increase in near-surface wind speed. It alsoresults in an increase in the depth of the layer in whichsouth-easterly near-surface winds prevail, and in adecrease in the strength of the large-scale flow overthe continent, in particular in summer. In theescarpment region a decrease of _z0m is foundto result in too high wind speeds. Surface temperatureson average decrease while atmospheric temperaturesincrease, resulting in an increase of near-surfacestatic stability. Changes in roughness lengths donot significantly change the temperature profiles.The surface fluxes, on average found reduced, aremodelled best by using the _z0h based on thesurface renewal method.