A Fine-Scale <Emphasis Type="Italic">k</Emphasis>−ε Model for Atmospheric Flow over Heterogeneous Landscapes

A multi-purpose model for small-scale atmospheric flows over heterogeneous landscapes is being developed. The aim of this research is to build a tool able to predict the dynamical (wind, turbulence) and diffusive (gases, particles) fields over landscapes characterised by heterogeneous plant cover. In its present stage of development the model is based on the numerical integration of neutral atmospheric flow equations, using an energy-dissipation closure scheme and over a domain that may include vegetation layers. Three validation cases of the model are presented: (i) response of the airflow to a change in surface roughness; (ii) airflow within and above a horizontally homogeneous plant canopy; (iii) airflow over two complex forest-to-clearing and clearing-to-forest transitions. All simulations provide results in good agreement with the experimental data, except for turbulent kinetic energy just after a clearing-to-forest transition. This result is not surprising for a statistical k– model in a flow region characterised by strong distorsion and intermittent turbulence. However the overall good performance of the model is promising for environmental research at fine scales over heterogeneous landscapes.     

Simulation of Ekman Boundary Layers by Large Eddy Model with Dynamic Mixed Subfilter Closure

Theoretical analysis of boundary layer turbulence has suggested a feasibility of sufficiently accurate turbulence resolving simulations at relatively coarse meshes. However, large eddy simulation (LES) codes, which employ traditional eddy-viscosity turbulence closures, fail to provide adequate turbulence statistics at coarse meshes especially within a surface layer. Manual tuning of parameters in these turbulence closures may correct low order turbulence statistics but severely harms spectra of turbulence kinetic energy (TKE). For more than decade, engineering LES codes successfully employ dynamic turbulence closures. A dynamic Smagorinsky turbulence closure (DSM) has been already tried in environmental LES. The DSM is able to provide adequate turbulence statistics at coarse meshes but it is not completely consistent with the LES equations. This paper investigates applicability of an advanced dynamic mixed turbulence closure (DMM) to simulations of Ekman boundary layers of high Reynolds number flows. The DMM differs from the DSM by explicit calculation of the Leonard term in the turbulence stress tensor. The Horizontal Array Turbulence Study (HATS) field program has revealed that the Leonard term is indeed an important component of the real turbulence stress tensor. This paper presents validation of a new LES code LESNIC. The study shows that the LES code with the DMM provides rather accurate low order turbulence statistics and the TKE spectra at very coarse meshes. These coarse LES maintain more energetic small scale fluctuations of velocity especially within the surface layer. This is critically important for success of simulations. Accurate representation of higher order turbulence statistics, however, requires essentially better LES resolution. The study also shows that LES of the Ekman boundary layer cannot be directly compared with conventionally neutral atmospheric boundary layers. The depth of the boundary layer is an important scaling parameter for turbulence statistics.     

Subgrid-Scale Modeling of Reacting Scalar Fluxes in Large-Eddy Simulations of Atmospheric Boundary Layers

In large-eddy simulations of atmospheric boundary layer turbulence, the lumped coefficient in the eddy-diffusion subgrid-scale (SGS) model is known to depend on scale for the case of inert scalars. This scale dependence is predominant near the surface. In this paper, a scale-dependent dynamic SGS model for the turbulent transport of reacting scalars is implemented in large-eddy simulations of a neutral boundary layer. Since the model coefficient is computed dynamically from the dynamics of the resolved scales, the simulations are free from any parameter tuning. A set of chemical cases representative of various turbulent reacting flow regimes is examined. The reactants are involved in a first-order reaction and are injected in the atmospheric boundary layer with a constant and uniform surface flux. Emphasis is placed on studying the combined effects of resolution and chemical regime on the performance of the SGS model. Simulations with the scale-dependent dynamic model yield the expected trends of the coefficients as function of resolution, position in the flow and chemical regime, leading to resolution-independent turbulent reactant fluxes.     

Flows through forest canopies in complex terrain

Recent progress on boundary layer flow within and above tall forest canopies in complex terrain is reviewed from the perspective of developing methods to interpret carbon dioxide fluxes from tower measurements in real terrain. Two examples of complex terrain are considered in detail: a forest edge, which exemplifies nonuniform forests, and hilly terrain, which can lead to drainage currents at night. Dynamical arguments show that, when boundary layer winds approach a forest edge, the mean wind adjusts on a length scale of approximately 3L(c), where L(c) is the canopy drag length scale, which depends inversely on the leaf area density of the forest. Over a further distance that also scales on L(c), turbulence in the flow adjusts, and the mixing and transport in the canopy approaches the homogeneous limit. Even low hills change the neutral flow within and above the forest canopy substantially. When the canopy is tall, pressure gradients drive flow up both the upwind and downwind slopes of the hill, leading to an ejection of air out of the top of the canopy just downwind of the crest. This flow at the crest can then advect scalar out of the top of the forest, leading to large variations in the flux of scalar across the hill. At night, when the air near the ground cools and becomes stably stratified, turbulence within the canopy can collapse, even when the flow above the canopy remains turbulent. This leads to a decoupling of the air motions within the canopy from those above. The air above the canopy can then continue to pass up and over the hill, as it does in the neutral case, but at the same time, air within the canopy drains down the hill slopes as drainage currents. These analyses will help us understand when flux towers are reliably measuring the net ecosystem exchange and suggest ways of correcting the flux tower data in more complex situations.     

Wind-induced pressure at a tunnel portal

In order to properly size the mechanical ventilation system of a tunnel, it is essential to estimate the wind-driven pressure difference that might rise between its two portals. In this respect, we explore here the pressure distribution over a tunnel portal under the influence of an incident atmospheric boundary layer and, in particular, its dependency on wind direction and on tunnel geometry. Reduced scale models of generic configurations of a tunnel portal are studied in an atmospheric wind tunnel. Pressure distributions over the front section of different open cavities are measured with surface taps, which allows us to infer the influence of the tunnel aspect ratio and wind direction on a pressure coefficient \(C_{P}\), defined as a spatially and time averaged non-dimensional pressure. Experiments reveal that the magnitude of the coefficient \(C_{P}\), as a function of the wind direction, is significantly influenced by the portal height-to-width ratio and almost insensitive to its length. The experimental data set is completed by hot-wire anemometry measurements providing vertical distribution of velocity statistics. The same configurations are simulated by numerically solving the Reynolds-averaged Navier–Stokes equations, adopting the standard \(k - \varepsilon\) turbulence model. Despite some discrepancies between numerical and experimental estimates of some flow parameters (namely the turbulent kinetic energy field), the numerical estimates of the pressure coefficients \(C_{P}\) show very good agreement with experimental data. The latter is also compared to the predictions of an analytical model, based on the estimate of a spatially averaged velocity within an infinitely long street canyon. The results of the model, which takes into account varying canyon aspect ratios, are in reasonable agreement with experimental data for all cases studied. Notably, its predictions are significantly better than those provided by the simple analytical relations usually adopted as a reference in tunnel ventilation studies.     

Canopy-wake dynamics and wind sheltering effects on Earth surface fluxes

The atmospheric boundary layer adjustment at the abrupt transition from a canopy (forest) to a flat surface (land or water) is investigated in a wind tunnel experiment. Detailed measurements examining the effect of canopy turbulence on flow separation, reduced surface shear stress and wake recovery are compared to data for the classical case of a solid backward-facing step. Results provide new insights into the interpretation for flux estimation by eddy-covariance and flux gradient methods and for the assessment of surface boundary conditions in turbulence models of the atmospheric boundary layer in complex landscapes and over water bodies affected by canopy wakes. The wind tunnel results indicate that the wake of a forest canopy strongly affects surface momentum flux within a distance of 35–100 times the step or canopy height, and mean turbulence quantities require distances of at least 100 times the canopy height to adjust to the new surface. The near-surface mixing length in the wake exhibits characteristic length scales of canopy flows at the canopy edge, of the flow separation in the near wake and adjusts to surface layer scaling in the far wake. Components of the momentum budget are examined individually to determine the impact of the canopy wake. The results demonstrate why a constant flux layer does not form until far downwind in the wake. An empirical model for surface shear stress distribution from a forest canopy to a clearing or lake is proposed.     

Comparison of atmospheric modelling systems simulating the flow,turbulence and dispersion at the microscale within obstacles

Three different modelling techniques to simulate the pollutant dispersion in the atmosphere at the microscale and in presence of obstacles are evaluated and compared. The Eulerian and Lagrangian approaches are discussed, using RAMS6.0 and MicroSpray models respectively. Both prognostic and diagnostic modelling systems are considered for the meteorology as input to the Lagrangian model, their differences and performances are investigated. An experiment from the Mock Urban Setting Test field campaign observed dataset, measured within an idealized urban roughness, is used as reference for the comparison. A case in neutral conditions was chosen among the available ones. The predicted mean flow, turbulence and concentration fields are analysed on the basis of the observed data. The performances of the different modelling approaches are compared and their specific characteristics are addressed. Given the same flow and turbulence input fields, the quality of the Lagrangian particle model is found to be overall comparable to the full-Eulerian approach. The diagnostic approach for the meteorology shows a worse agreement with observations than the prognostic approach but still providing, in a much shorter simulation time, fields that are suitable and reliable for driving the dispersion model.     

Mixing at a sediment concentration interface in turbulent open channel flow

In this work we address the role of turbulence on mixing of clear layer of fluid with sediment-laden layer of fluid at a sediment concentration interface. This process can be conceived as the entrainment of sediment-free fluid into the sediment-laden layer, or alternatively, as the transport of sediment into the top sediment-free flow. This process is governed by four parameters—Reynolds number of the flow \(Re_\tau\), non-dimensional settling velocity of the sediment (proxy for sediment size) \(\tilde{V}\), Richardson number \(Ri_\tau\) and Schmidt number Sc. For this work we have performed direct numerical simulations for fixed Reynolds and Schmidt numbers while varying the values of Richardson number and particle settling velocity. In the simple model considered here, the flow’s momentum and turbulence pre-exists over the entire layer of fluid, while the sediment is initially confined to a layer close to the bed. Mixing of sediment-free fluid with the sediment-laden layer is associated primarily with upward transport of sediment and buoyancy. There is no simultaneous upward transport of fluid momentum and turbulence into the sediment-free fluid layer, which is already in motion and turbulent. The analysis performed shows that the ability of the flow to transport a given sediment size decreases with the distance from the bottom, and thus only fine enough sediment particles are transported across the sediment concentration interface. For these cases, the concentration profiles evolve to a final steady state in good agreement with the well-known Rouse profile. The approach towards the Rouse profile happens through a transient self-similar state. This behavior of the flow is not seen for larger particles. Detailed analysis of the three dimensional structure of the sediment concentration interface shows the mechanisms by which sediment particles are lifted up by tongues of sediment-laden fluid with positive correlation between vertical velocity and sediment concentration. Finally, the mixing ability of the flow is addressed by monitoring the time evolution of the center of mass of the sediment-laden layer and the vertical location of the sediment-free/sediment-laden interface.     

The performance of RAMS in representing the convective boundary layer structure in a very steep valley

Data from a comprehensive field study in the Riviera Valley of Southern Switzerland are used to investigate convective boundary layer structure in a steep valley and to evaluate wind and temperature fields, convective boundary layer height, and surface sensible heat fluxes as predicted by the mesoscale model RAMS. Current parameterizations of surface and boundary layer processes in RAMS, as well as in other mesoscale models, are based on scaling laws strictly valid only for flat topography and uniform land cover. Model evaluation is required to investigate whether this limits the applicability of RAMS in steep, inhomogeneous terrain. One clear-sky day with light synoptic winds is selected from the field study. Observed temperature structure across and along the valley is nearly homogeneous while wind structure is complex with a wind speed maximum on one side of the valley. Upvalley flows are not purely thermally driven and mechanical effects near the valley entrance also affect the wind structure. RAMS captured many of the observed boundary layer characteristics within the steep valley. The wind field, temperature structure, and convective boundary layer height in the valley are qualitatively simulated by RAMS, but the horizontal temperature structure across and along the valley is less homogeneous in the model than in the observations. The model reproduced the observed net radiation, except around sunset and sunrise when RAMS does not take into account the shadows cast by the surrounding topography. The observed sensible heat fluxes fall within the range of simulated values at grid points surrounding the measurement sites. Some of the scatter between observed and simulated turbulent sensible heat fluxes are due to sub-grid scale effects related to local topography.     

RANS simulation of neutral atmospheric boundary layer flows over complex terrain by proper imposition of boundary conditions and modification on the k-ε model

In this study, a modelling methodology is proposed for RANS simulations of neutral Atmospheric Boundary Layer (ABL) flows on the basis of the standard k-ε model, which allows the adoption of an arbitrary shear stress model. This modelling methodology is first examined in the context of an open flat terrain in an empty domain to ascertain there are no substantial changes in the prescribed profiles. The results show that relatively good homogeneity can be achieved with this modelling methodology for various sets of inflow boundary profiles. In addition, to extend the solutions derived from the standard k-ε model to RNG k-ε model, the RNG k-ε model is in detail assembly and tuned. Finally, the topographic effects on surface wind speeds over a complex terrain are assessed with the combined use of the proposed methodology and the modified RNG model. The numerical results are in good agreement with wind tunnel testing results and long-term field observations. A discussion of the effects of horizontal homogeneity and turbulence models on the simulated wind flows over a complex terrain is also given.     

Analytical evaluation of mesoscale fluxes and pressure field

Terrain in natural areas is never homogeneous: there may be a variety of vegetation types and patches of vegetated and unvegetated areas which can modify the mesoscale atmospheric flow. Moreover, horizontal thermal inhomogeneities in the planetary boundary layer are a well known source of mesoscale circulation systems such as land and sea breezes, mountain-valley winds, and urban heat island circulations. Since those phenomena are not resolved in regional scale numerical models, therefore an analytic procedure able to evaluate the relative importance of mesoscale and turbulent heat fluxes associated with surface thermal heterogeneities is of crucial importance in the optic of developing a parameterization of mesoscale effects generated by these heterogeneities for use in larger scale models. In the present paper we analyze how small a horizontal variation in surface heating can be and still produce a significant mesoscale circulation, how the heat and momentum fluxes associated to mesoscale flows can penetrate deeply into the mid-troposphere, and how they modify tropospheric relevant climate parameters, such as the atmospheric static stability. In addition, we evaluate the terms of the pressure gradient force, nonlinear and linear, non-hydrostatic and hydrostatic, as function of time and space scales of the mesoscale flow. The present paper is mainly a review of analytical results, the numerical comparison and verification using RAMS is in progress.     

Simulation of exchange flow between open water and floating vegetation using a modified RNG <Emphasis Type="Italic">k</Emphasis>-<Emphasis Type="Italic">ε</Emphasis> turbulence model

The paper focuses on the numerical simulation of the exchange flow between open water and floating vegetation, which plays an important role in maintaining the ecological balance by transporting nutrient matter. The simulation was conducted using a new solver developed upon OpenFOAM. A modified RNG k-ε turbulence model, which is expected to model both the high- and low-Reynolds number flows correctly, was used to determine the eddy viscosity. Several particular terms were added into the momentum equations and turbulence model equations to model the effects of vegetation and buoyancy. Among these terms, the term for the effect of vegetation in the ε-equation was re-modelled. The model was validated by properly predicting the profiles of mean velocity and turbulent kinetic energy for flows through suspended canopies. The density flow between open and vegetated water was simulated with the same conditions as those of the experiment conducted by Zhang and Nepf. The predicted results agreed well with the experimental data and provided more detailed information of such exchange flow. The convection between the root layer and the layer beneath the roots, which was not observed in the experiment, was observed in the numerical simulation.     

Part I : <Emphasis Type="Italic">a priori</Emphasis> study of erosion and deposition with large eddy simulation of turbulent flow over multiple 2D sandy Gaussian hills

The micro-scale prediction of sand trapping or take-off over hilly terrains is a crucial issue in semi-arid regions for soil depletion. In this context, large eddy simulations around one or several hills are performed in order to provide statistical parameters to characterize the flow at micro-scales and provide data for mesoscale modelling. We focus on the determination of recirculation zones since they play an important role in solid particle erosion or entrapment. A new wall modeling adapted from Huang et al. (J Turbul 17:1–24, 2016) for rough boundary layers is found to improve the prediction of the recirculation zone length downstream of an isolated hill and is used for all the numerical cases presented here. A geometrical parameterization of the recirculation zones is proposed. When the recirculation region is assumed to have an ellipsoidal shape, the total surface of the recirculation can be obtained from this new parameterization and easily extrapolated to more general dune configurations. Numerical results are compared with experiments performed in our laboratory (Simoëns et al. in Procedia IUTAM 17:110–118, 2015) and good agreement is achieved. We explore general aerodynamic cases deduced from the urban canopy scheme of Oke (Energy Build 11:103–113, 1988). In this scheme the momentum and mass exchange between the upper layer and the space between hills is sorted according to the streamwise hill spacing within three basic cases of skimming, wake or isolated flow. The study of the recirculation zones, the mean velocity and Reynolds stress profiles around an isolated or two consecutive hills with different distances shows that the double hill configuration with 3H separation behaves as much as a whole to the upcoming flow. The vortex formed between the crests does not strongly affect the overall evolution of the outer flow. By an a priori prediction of the preferential zones of erosion and accumulation of fictive particles, it is shown that isolated dunes present more deposition and less erosion than two-hill configurations. The results presented in this study will be discussed in the presence of Lagrangian transport of sand particles above 2D Gaussian hills in future work.     

Turbulent flow over a D-section bluff body: a numerical benchmark

Environmental Fluid Mechanics - A numerical benchmark of different turbulence closures was performed to investigate the turbulent wake flow behind a submerged D-shaped bluff body. The numerical...     

Mass conservation and atmospheric dynamics in the Regional Atmospheric Modeling System (RAMS)

This paper examines the spatio-temporal patterns of atmospheric carbon dioxide transport predicted by the Regional Atmospheric Modeling System (RAMS). Forty-eight hour simulations over northern New England incorporating a simple representation of the diurnal summertime surface carbon dioxide forcing arising from biological activity indicate that, in its native formulation, RAMS exhibits a significant degree of mass non-conservation. Domain-wide rates of non-physical mass gain and mass loss are as large as three percent per day which translates into approximately eleven parts per million per day for carbon dioxide — enough to rapidly dilute the signature of carbon dioxide fluxes arising from biological activity. Analysis shows that this is due to the approximation used by RAMS to compute the Exner function. Substitution of the exact, physically complete equation improves mass conservation by two orders of magnitude. In addition to greatly improving mass conservation, use of the complete Exner function equation has a substantial impact on the spatial pattern of carbon dioxide predicted by the model, yielding predictions differing from a conventional RAMS simulation by as much as forty parts per million. Such differences have important implications both for comparisons of modeled atmospheric carbon dioxide concentrations to observations and for carbon dioxide inversion studies, which use estimates of atmospheric transport of carbon dioxide in conjunction with measurements of atmospheric carbon dioxide concentrations to infer the spatio-temporal distribution of surface carbon dioxide fluxes. Furthermore, use of the complete Exner function equation affects the vertical velocity and water mixing ratio fields, causing significant changes in accumulated precipitation over the region.     

Flow and drag force around a free surface piercing cylinder for environmental applications

This paper investigates flows around a free surface piercing cylinder with Froude number F > 0.5 and Reynolds number around Re = 50,000. The aim of this work is to gain a better understanding of the flow behaviour in environmental systems such as fishways. The advances are based upon experimental and numerical results. Several flow discharges and slopes are tested to obtain both subcritical and supercritical flows. The drag force exerted on the cylinder is measured with the help of a torque gauge while the velocity field is obtained using particle velocimetry. For the numerical part, two URANS turbulence models are tested, the k-\(\omega\) SST and the RNG k-\(\varepsilon\) models using the OpenFOAM software suite for subcritical cases, and then compared with the corresponding experimental results. With fishways applications in mind, the changes in drag coefficient \(C_d\) versus Froude number and water depth are studied and experimental correlations proposed. We conclude that the most suitable URANS turbulence model for reproducing this kind of flow is the k-\(\omega\) SST model.     

Large-Eddy Simulations of the Atmospheric Boundary Layer Using a New Subgrid-Scale Model – I. Slightly unstable and neutral cases

Subgrid-scale (SGS) modeling is a long-standing problem and a critical component in the large-eddy simulation (LES) of atmospheric boundary layer. A variety of SGS models with different levels of sophistication have been proposed for different needs, such as Smagorinsky's (1963) eddy viscosity model, Mason and Thomson's (1992) stochastic backscattering model, and Sullivan et al.'s (1994) near surface model. A modified Smagorinsky SGS model has been used in the LES version of Terminal Area Simulation System (TASS-LES). It has successfully simulated the buoyancy-dominated, convective atmospheric boundary layer flows, while simulations of the shear-dominated, slightly unstable, neutral, and stably stratified boundary layer flows are not so good. For the later, we used a simpler version of Sullivan et al.'s subgrid-scale model in which turbulent kinetic energy equation is not included and the model is still the first-order closure. A momentum profile matching approach is adopted in the proposed model. A series of simulations for shear-dominated, slightly unstable and neutral boundary layers are performed using different subgrid-scale models and different grid resolutions. The results are compared with those of Sullivan et al. (1994) and with empirical similarity relations for the surface layer. The simulations with the new SGS model appear to be far more satisfactory than those with the modified Smagorinsky model.     

Effect of initial excess density and discharge on constant flux gravity currents propagating on a slope

The effect of the upstream conditions on propagation of gravity current over a slope is investigated using three-dimensional numerical simulations. The current produced by constant buoyancy flux, is simulated using a large eddy simulation solver. The dense saline solution used at the inlet is the driving force of the flow. Higher replenishment of the current is possible either by a high inflow discharge or high initial fractional density excess. In the simulations, it is observed that these two parameters affect the flow in different ways. Results show that the front speed of the descending current is proportional to the cube root of buoyancy flux, $(g_o^{\prime } Q)^{1/3}$ , which agrees with the previous experimental and numerical observations. The height of the tail of the current grows linearly in the streamwise direction. Formation of a strong shear layer at the boundary of mixed upper layer and dense lower layer is observed within the body and the tail of the current. Over the tail of the current far enough from the inlet, the vertical velocity and density profiles are compared to the ones from an experimental study. Distance from the bed to the point of maximum velocity increases with an increase in inflow discharge, while it remains practically unchanged with increasing initial fractional excess density in the simulations. Even though the velocity profiles are in good agreement, some discrepancies are observed in fractional excess density profiles among experimental and numerical results. Possible reasons for these discrepancies are discussed. Generally, gravity current type of flows could be expressed in layer-integrated formulation of governing equations. However, layer integration introduces several constants, commonly known as shape factors, to the equations of motion. The values of these shape factors are calculated based on simulation results and compared to the values from experiments and to the favorably used ‘top hat’ assumption.