Effect of Roughness on Surface Boundary Conditions for Large-Eddy Simulation

An important parameterization in large-eddy simulations (LESs) of high- Reynolds-number boundary layers, such as the atmospheric boundary layer, is the specification of the surface boundary condition. Typical boundary conditions compute the fluctuating surface shear stress as a function of the resolved (filtered) velocity at the lowest grid points based on similarity theory. However, these approaches are questionable because they use instantaneous (filtered) variables, while similarity theory is only valid for mean quantities. Three of these formulations are implemented in simulations of a neutral atmospheric boundary layer with different aerodynamic surface roughness. Our results show unrealistic influence of surface roughness on the mean profile, variance and spectra of the resolved velocity near the ground, in contradiction of similarity theory. In addition to similarity-based surface boundary conditions, a recent model developed from an a priori experimental study is tested and it is shown to yield more realistic independence of the results to changes in surface roughness. The optimum value of the model parameter found in our simulations matches well the value reported in the a priori wind-tunnel study.     

Including the Drag Effects of Canopies: Real Case Large-Eddy Simulation Studies

We use the mesoscale meteorological model Meso-NH, taking the drag force of trees into account under stable, unstable and neutral conditions in a real case study. Large-eddy simulations (LES) are carried out for real orography, using a regional forcing model and including the energy and water fluxes between the surface (mostly grass with some hedges of trees) and the atmosphere calculated using a state-of-the-art soil-vegetation-atmosphere-transfer model. The formulation of the drag approach consists of adding drag terms to the momentum equation and subgrid turbulent kinetic energy dissipation, as a function of the foliage density. Its implementation in Meso-NH is validated using Advanced Regional Prediction System simulation results and measurements from Shaw and Schumann (Boundary-Layer Meteorol, 61(1):47?C64, 1992). The simulation shows that the Meso-NH model successfully reproduces the flow within and above homogeneous covers. Then, real case studies are used in order to investigate the three different boundary layers in a LES configuration (resolution down to 2 m) over the ??Lannemezan 2005?? experimental campaign. Thus, we show that the model is able to reproduce realistic flows in these particular cases and confirm that the drag force approach is more efficient than the classical roughness approach in describing the flow in the presence of vegetation at these resolutions.     

The Coupling State of an Idealized Stable Boundary Layer

The coupling state between the surface and the top of the stable boundary layer (SBL) is investigated using four different schemes to represent the turbulent exchange. An idealized SBL is assumed, with fixed wind speed and temperature at its top. At the surface, two cases are considered, first a constant temperature, 20 K lower than the SBL top, and later a constant 2 K h⁻¹ cooling rate is assumed for 10 h after a neutral initial condition. The idealized conditions have been chosen to isolate the influence of the turbulence formulations on the coupling state, and the intense stratification has the purpose of enhancing such a response. The formulations compared are those that solve a prognostic equation for turbulent kinetic energy (TKE) and those that directly prescribe turbulence intensity as a function of atmospheric stability. Two TKE formulations are considered, with and without a dependence of the exchange coefficients on stability, while short and long tail stability functions (SFs) are also compared. In each case, the dependence on the wind speed at the SBL top is considered and it is shown that, for all formulations, the SBL experiences a transition from a decoupled state to a coupled state at an intermediate value of mechanical forcing. The vertical profiles of potential temperature, wind speed and turbulence intensity are shown as a function of the wind speed at the SBL top, both for the decoupled and coupled states. The formulation influence on the coupling state is analyzed and it is concluded that, in general, the simple TKE formulation has a better response, although it also tends to overestimate turbulent mixing. The consequences are discussed.     

Application of Dynamic Subgrid-scale Models for Large-eddy Simulation of the Daytime Convective Boundary Layer over Heterogeneous Surfaces

The sensitivity of large-eddy simulation (LES) to the representation of subgrid-scale (SGS) processes is explored for the case of the convective boundary layer (CBL) developing over surfaces with varying degrees of spatial heterogeneity. Three representations of SGS processes are explored: the traditional constant Smagorinsky–Lilly model and two other dynamic models with Lagrangian averaging approaches to calculate the Smagorinsky coefficient (C _S ) and SGS Prandtl number (Pr). With initial data based roughly on the observed meteorology, simulations of daytime CBL growth are performed over surfaces with characteristics (i.e. fluxes and roughness) ranging from homogeneous, to striped heterogeneity, to a realistic representation of heterogeneity as derived from a recent field study. In both idealized tests and the realistic case, SGS sensitivities are mostly manifest near the surface and entrainment zone. However, unlike simulations over complex domains or under neutral or stable conditions, these differences for the CBL simulation, where large eddies dominate, are not significant enough to distinguish the performance of the different SGS models, irrespective of surface heterogeneity.     

A parameterization of the stable atmospheric boundary layer

Two formulations of the stable atmospheric boundary layer are proposed for use in weather forecasting or climate models. They feature the log-linear profile near the surface, but are free from the associated critical Richardson number. The diffusion coefficients in the Ekman layer are a natural extension of the surface layer. They are locally determined using wind shear in one case and turbulent kinetic energy in the other. The parameterizations are tested in a one-dimensional model simulating the evolution of the nocturnal boundary layer with and without radiative cooling. Both formulations give very similar results, except near the top of the boundary layer where the transition to the free atmosphere is smoother with the wind shear formulation. A distinctive feature of these schemes is that they retain their simulating skill when resolution is reduced. This is verified for a wide range of situations. In practice, this means that there is no need for a large-scale model to have a level below 50 m or so.     

Application of a Large-Eddy Simulation Database to Optimisation of First-Order Closures for Neutral and Stably Stratified Boundary Layers

Large-eddy simulation (LES) is a well-established numerical technique, resolving the most energetic turbulent fluctuations in the planetary boundary layer. By averaging these fluctuations, high-quality profiles of mean quantities and turbulence statistics can be obtained in experiments with well-defined initial and boundary conditions. Hence, LES data can be beneficial for assessment and optimisation of turbulence closure schemes. A database of 80 LES runs (DATABASE64) for neutral and stably stratified planetary boundary layers (PBLs) is applied in this study to optimize first-order turbulence closure (FOC). Approximations for the mixing length scale and stability correction functions have been made to minimise a relative root-mean-square error over the entire database. New stability functions have correct asymptotes describing regimes of strong and weak mixing found in theoretical approaches, atmospheric observations and LES. The correct asymptotes exclude the need for a critical Richardson number in the FOC formulation. Further, we analysed the FOC quality as functions of the integral PBL stability and the vertical model resolution. We show that the FOC is never perfect because the turbulence in the upper half of the PBL is not generated by the local vertical gradients. Accordingly, the parameterised and LES-based fluxes decorrelate in the upper PBL. With this imperfection in mind, we show that there is no systematic quality deterioration of the FOC in the strongly stable PBL provided that the vertical model resolution is better than 10 levels within the PBL. In agreement with previous studies, we found that the quality improves slowly with the vertical resolution refinement, though it is generally wise not to overstretch the mesh in the lowest 500 m of the atmosphere where the observed, simulated and theoretically predicted stably stratified PBL is mostly located. The submission to a special issue of the “Boundary-Layer Meteorology” devoted to the NATO advanced research workshop “Atmospheric Boundary Layers: Modelling and Applications for Environmental Security”.     

A Comprehensive Modelling Approach for the Neutral Atmospheric Boundary Layer: Consistent Inflow Conditions, Wall Function and Turbulence Model

We report on a novel approach for the Reynolds-averaged Navier-Stokes (RANS) modelling of the neutral atmospheric boundary layer (ABL), using the standard k-ek-{\varepsilon} turbulence model. A new inlet condition for turbulent kinetic energy is analytically derived from the solution of the k-ek-{\varepsilon} model transport equations, resulting in a consistent set of fully developed inlet conditions for the neutral ABL. A modification of the standard k-ek-{\varepsilon} model is also employed to ensure consistency between the inlet conditions and the turbulence model. In particular, the turbulence model constant C _μ is generalized as a location-dependent parameter, and a source term is introduced in the transport equation for the turbulent dissipation rate. The application of the proposed methodology to cases involving obstacles in the flow is made possible through the implementation of an algorithm, which automatically switches the turbulence model formulation when going from the region where the ABL is undisturbed to the region directly affected by the building. Finally, the model is completed with a slightly modified version of the Richards and Hoxey rough-wall boundary condition. The methodology is implemented and tested in the commercial code Ansys Fluent 12.1. Results are presented for a neutral boundary layer over flat terrain and for the flow around a single building immersed in an ABL.     

Velocity profiles,the resistance law and the dissipation rate of mean flow kinetic energy in a neutrally and stably stratified planetary boundary layer

The logarithmic + polynomial approximation is suggested for vertical profiles of velocity components in a planetary boundary layer (PBL) at neutral and stable stratification. The resistance law functions A and B are determined on the basis of this approximation, using integral relations derived from the momentum equations, the Monin-Obukhov asymptotic formula for the wind profile in a stably stratified near-surface layer and the known expressions for the PBL depth. This result gives a realistic and convenient method for calculating the surface friction velocity and direction and the total dissipation rate of mean flow kinetic energy in terms of geostrophic velocity, buoyancy flux at the surface, the roughness parameter and the Coriolis parameter. In the course of these derivations a review is given of current views on the main problems of the neutral and stable PBL.     

二阶闭合模式在污染气象学中的某些应用

本文采用二阶闭合的湍流边界层模式,进行一系列数值试验以模拟边界层中连续线源的扩散状况。试验表明:无论在稳定的或不稳定的边界层中,高源的扩散能力都低于低源;在稳定层中,粗糙地表上的大气扩散能力高于光滑表面;在相同风速和地表净辐射情况下,粗糙表面上的大气扩散能力反而低于光滑表面;对流边界层中存在反梯度输送,因而K理论的应用受到限制。试验还表明,修正的Kazanski-Monin参数可能比Monin-Obukhov长度更能反映大气的扩散能力。     

PARAMETERISING SUB-GRID SCALE VERTICAL TRANSPORT IN ATMOSPHERIC MODELS UNDER STATICALLY STABLE CONDITIONS

Five different formulations of the stability functions used forvertical turbulent transfer in atmospheric models are compared in a 1-Dmodel of the nocturnal boundary layer. One of them has a critical valueof the Richardson number around 0.2 and leads to the traditional log-linear profile, while other more empirical formulations maintain sometransfer at values of Ri around 1.0. Although no new observationalevidence is presented, it is suggested that the latter formulations aremore appropriate for use in atmospheric models because the unresolvedvariability inside a model grid box induces some turbulent transfer evenat super-critical values of the mean Ri. The study shows that themagnitude of the stability functions is principally important in theeffective range of Ri values found in the stable boundary layer and thattheir slopes near the origin are less important. This permits the use inatmospheric models of a simple explicit function of Ri containing asingle parameter, with results similar to those obtained with earlier morecomplex formulations. The results of the simulation with the 1-D model are used toexamine the errors introduced by the relatively thick surface layers of most atmospheric models, in which, for the stable case, the traditionalassumption of constancy of the fluxes with height is often clearlyviolated. When a height variation of the fluxes is introduced in surface-layer formulations, the error in the magnitude of the surface fluxes isdecreased with some of the formulations but not all of them. This lackof sensitivity is explained by a compensation mechanism in which theassumed decrease of the fluxes with height implies a correspondingdecrease of the Obukhov length which acts in the oppositedirection, reducing, and sometimes eliminating, the adverse effect of theunrealistic specification of the fluxes. It may be argued that thiscompensation mechanism also explains the wide range of validity of theMoini-Obukhov similarity theory.     

Large-Eddy Simulation of the stably-stratified atmospheric boundary layer

Large-Eddy Simulation of stable boundary layers (SBLs) has been considered particularly difficult, indeed perhaps impossible with present computational resources. Here we present a new series of successful simulations of SBLs over uniform, flat terrain, using an approach previously successful for neutral and convective conditions, and showing that essentially the same model can handle all three main dry types of atmospheric boundary layer. We consider both technical requirements for successful and accurate SBL simulations and the observed characteristics of the simulated SBL. We discuss the evolution (in some cases to quasi-steady states) and compare with theory and experimental data. Effects of static-stability on the flow are analyzed using one-point and two-point statistics. Results show the development of a shear-driven SBL, with little sign of distinctively wavelike motions. The flow statistics are found to be consistent with local scaling, and that framework is used to compare with other data and theoretical models.     

Radiative Processes in the Stable Boundary Layer: Part II. The Development of the Nocturnal Boundary Layer

The interaction between radiation and turbulence in the stable boundary layer over land is explored using an idealized model, with a focus on the surface layer after the evening transition. It is shown that finer vertical resolution is required in transitional boundary layers than in developed ones. In very light winds radiative cooling determines the temperature profile, even if similarity functions without a critical Richardson number are used; standard surface similarity theory applied over thick layers then yields poor forecasts of near-surface air temperatures. These points are illustrated with field data. Simulations of the developing nocturnal boundary layer are used to explore the wider role of radiation. Comparatively, radiation is less significant within the developed stable boundary layer than during the transition; although, as previous studies have found, it remains important towards the top of the stable layer and in the residual layer. Near the ground, reducing the surface emissivity below one is found to yield modest relative radiative warming rather than intense cooling, which reduces the potential importance of radiation in the developed surface layer. The profile of the radiative heating rate may be strongly dependent on other processes, leading to quite varied behaviour.     

The exchange coefficients for latent and sensible heat flux over lakes: Dependence upon atmospheric stability

Components of the energy budget of a small lake were estimated over the autumnal cooling period. Measured values of the stored thermal energy and radiative heating were used to evaluate several bulk formulae for sensible and latent heat transfer. Over 50–100 day intervals, bulk formulae for latent and sensible heat flux without stability corrections were as good as formulae that incorporated such corrections; both satisfactorily reproduced the measured heat storage data. Over shorter (daily to weekly) time-scales, predictions incorporating stability corrections were superior to those without stability corrections. Over daily periods when the atmosphere was nearly neutral or was unstable, a formulation for sensible and latent heat transfer designed for small-scale systems (cooling ponds and reservoirs) agreed closely with the usual large-scale (oceanic) bulk formulations. The corrections for stability in the small-scale formulation are based on laboratory and theoretical studies of free convection; the stability correction in the large-scale formulation uses a bulk Richardson number in a manner consistent with flux-profile theory. Both agreed with the measured data for the unstable and near-neutral cases. Under stable atmospheric conditions (in a daily average sense), both formulations underestimated the measured fluxes     

Parameterization of the surface-layer exchange coefficients for atmospheric models

A new surface-flux parameterization is presented and its impact on climate simulations with the Canadian Centre for Climate Modelling and Analysis (CCCMA) general circulation model (GCM) is discussed. The parameterization is based on the Monin-Obukhov similarity theory using well established flux-profile relationships for the unstable conditions. However, recently proposed new relationships are used in stable conditions. The new formulation allows different roughness lengths for heat and momentum, and gives transfer coefficients that are in agreement with Monin-Obukhov similarity theory. It also includes a parameterization for the free-convective boundary layer, which often occurs over warm surfaces within light winds. In circumstances where the surface layer is not neutrally stratified the proposed flux parameterization yields surface transfer coefficients that are different from those resulting from the standard surface flux formulation used in the GCM. The most marked effects of implementing the new formulation in the GCM are found over land and adjacent oceanic regions in winter where significant differences are found in the surface heat and moisture fluxes and surface temperatures.     

Shallow gravity flows over the Ekström ice shelf

Wind and temperature profiles measured near the Antarctic Georg von Neumayer Station in January and February 1983 are analysed with respect to situations of low cloud cover. In these situations, shallow inversions develop in the period of low sun elevation. The structure of these inversions in comparison with those in midlatitudes is explained by considering the heat fluxes near the ground, the influence of surface friction over different terrain roughness and for different Coriolis parameters.One effect of stabilisation over the Ekström ice shelf is the development of shallow gravity-influenced flows. The flow dynamics are discussed by means of a scale analysis. The results show that gravity is of considerable influence; however, it will not dominate the other forces. Strictly speaking, the flow is not katabatic for the scale considered. The Froude numbers of the flow approach values similar to those of nocturnal inversions during cooling periods. Thus it seems that the modelling methods for midlatitude stable planetary boundary layers (PBLs) will be successful in explaining antarctic boundary layers as well.     

Wind-Tunnel Simulation of the Wake of a Large Wind Turbine in a Stable Boundary Layer. Part 1: The Boundary-Layer Simulation

Measurements have been made in both a neutral and a stable boundary layer as part of an investigation of the wakes of wind turbines in an offshore environment, in the EnFlo stratified flow wind tunnel. The working section is long enough for the flow to have become very nearly invariant with streamwise distance. In order to be systematic, the flow profile generators of Irwin-type spires and surface roughness were the same for both neutral and stable conditions. Achieving the required profiles by adjusting the flow generators, even for neutral flow, is a highly iterative art, and the present results indicate that it will be no less iterative for a stable flow (as well as there being more conditions to meet), so this was not attempted in the present investigation. The stable-case flow conformed in most respects to Monin–Obukhov similarity in the surface layer. A linear temperature profile was applied at the working section inlet, resulting in a near-linear profile in the developed flow above the boundary layer and ‘strong’ imposed stability, while the condition at the surface was ‘weak’. Aerodynamic roughness length (mean velocity) was not affected by stability even though the roughness Reynolds number ${<}1$ , while the thermal roughness length was much smaller, as is to be expected. The neutral case was Reynolds-number independent, and by inference, the stable case was also Reynolds-number independent.     

The position of the lowest levels in the boundary layer of atmospheric circulation models

Abstract

The error associated with the position of the lowest wind level in atmospheric boundary‐layer modelling is studied in connection with vertical resolutions typical of parametrization schemes for atmospheric circulation models. The test case is the neutrally stratified steady‐state boundary layer. Finite‐difference and finite‐element schemes of two types are used: in one case the lowest wind level is centred with respect to the surface and the lowest internal level where the shear stress is calculated, in the other case the lowest wind level is set very close to the surface (5 m). It is found that schemes of the latter type underestimate the friction force at the lowest level and consequently overestimate the wind and the surface stress. This error is largest at low resolution since it is due to the uncentring of the lowest wind level with respect to the stress levels. The error in schemes of the former type is different, and is associated with the determination of the surface stress from a wind at a height that may exceed the extent of the surface layer. For all neutral cases, this error can be made small by adding a corrective term to the traditional logarithmic formulation. This paper shows that considerably more error is generated by uncentred differencing than by deepening the surface layer.     

The wind field in the nonlinear multilayer planetary boundary layer

By use of the small parameter expansion method, the nonlinear planetary boundary layer (PBL) is studied in this paper. The PBL is divided into the surface layer and the Ekman layer, which is divided into several sublayers. In the surface-layer, the eddy coefficient K is taken as a linear function of height; in the Ekman layer, different constant K values are taken within different sublayers: these values are determined from O'Brien's formula (O'Brien, 1970) approximately. Under the upper and lower boundary conditions and the continuity conditions of the wind velocities and turbulent stresses at each boundary between sublayers, analytical expressions for wind velocity in all sublayers and the vertical velocity at the top of the PBL are obtained. A specific example of steady axisymmetrical circular high and low pressure areas is analysed, and some new conclusions are obtained. The results are in better agreement with reality than previous results. This example also shows that the vertical velocity at the top of the PBL caused by friction approaches zero near the center of a high or low pressure system for this model, but attains its maximum absolute values near the center of the high or low pressure area for Wu's (1984) model. This is due to the fact that in our model, the geostrophic wind speed near the center of this specific vortex approaches zero, which causes the wind shear and the friction effect to be very weak. Therefore the wind distribution in the PBL is very sensitive to the type of eddy coefficient.     

Boundary-Layer Adjustment Over Small-Scale Changes of Surface Heat Flux

Four months of eddy correlation data collected over a grass field and a nearby sage brush community are analyzed to examine the adjustment of the boundary-layer structure as it flows from the heated brush to the snow-covered grass. The grass site includes a 34-m tower with seven levels of eddy correlation data. The midday heat flux over the snow-covered grass and bare ground surfaces is often downward particularly with melting conditions, while the corresponding heat flux over the brush is almost always upward. For most of these cases, a stable internal boundary layer over the snow is well defined in terms of vertical profiles of the buoyancy flux over the snow-covered grass. The stable internal boundary layer is generally embedded within a deeper layer of flux divergence corresponding to increasing upward heat flux with height above the internal boundary layer. With thin snow cover, the surface heat flux over the grass is weak upward due to heating of grass protruding above the snow so that the flow adjusts to a decrease of the upward surface heat flux in the downwind direction. This common case of an adjusting boundary layer contrasts with the formation of an internal boundary layer due to a change of sign of the surface heat in flux the downwind direction. The adjustment of the boundary layer to the decrease of the surface heat flux leads to vertical divergence of the upward heat flux in contrast to the usual heated boundary layer over homogeneous surfaces. The consequences of the cooling due to the vertical divergence of the heat flux are discussed in terms of the heat budget of the adjusting and internal boundary layers.