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"Atmospheric turbulence Simulation methods."
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Towards Adaptive Grids for Atmospheric Boundary-Layer Simulations
We present a proof-of-concept for the adaptive mesh refinement method applied to atmospheric boundary-layer simulations. Such a method may form an attractive alternative to static grids for studies on atmospheric flows that have a high degree of scale separation in space and/or time. Examples include the diurnal cycle and a convective boundary layer capped by a strong inversion. For such cases, large-eddy simulations using regular grids often have to rely on a subgrid-scale closure for the most challenging regions in the spatial and/or temporal domain. Here we analyze a flow configuration that describes the growth and subsequent decay of a convective boundary layer using direct numerical simulation (DNS). We validate the obtained results and benchmark the performance of the adaptive solver against two runs using fixed regular grids. It appears that the adaptive-mesh algorithm is able to coarsen and refine the grid dynamically whilst maintaining an accurate solution. In particular, during the initial growth of the convective boundary layer a high resolution is required compared to the subsequent stage of decaying turbulence. More specifically, the number of grid cells varies by two orders of magnitude over the course of the simulation. For this specific DNS case, the adaptive solver was not yet more efficient than the more traditional solver that is dedicated to these types of flows. However, the overall analysis shows that the method has a clear potential for numerical investigations of the most challenging atmospheric cases.
Journal Article
Lagrangian Stochastic Modeling of Stratified Atmospheric Boundary Layer
A single-column turbulence model for stratified atmospheric boundary layer (ABL), which solves the transport equations of turbulence probability density function (PDF) using a Lagrangian stochastic modeling (LSM) approach, is proposed in this study. This study adopts previously developed stochastic differential equations (SDEs) for particle velocity and temperature and extends the LSM to simulate inhomogeneous turbulence. The proposed LSM is tested for its ability to fully simulate statistics of inhomogeneous stratified turbulence. In the model, particles evolve by SDEs, and turbulence statistics are calculated by averaging the properties of particles. The model provides a full representation of turbulence PDF and simulates turbulent transport without any modeling assumption. The model performance is evaluated against large-eddy simulation (LES) results in the simulations of convective and stable ABL cases. For the convective ABL, LSM realistically simulates the entrainment process with the temperature and heat flux profiles that closely match with LES. The joint PDF simulated by LSM reproduces a curved and highly skewed shape, and some distinct features, like the asymmetric distribution of vertical velocity and the separation of the PDF in the entrainment zone, are simulated. LSM also reproduces the entrainment enhancement by wind shear in the simulation of sheared convective ABL. The LSM simulation of stable ABL predicts realistic turbulence intensity and mean field profiles, where Gaussian-like PDFs are simulated both in LSM and LES.
Journal Article
Bridging the Transition from Mesoscale to Microscale Turbulence in Numerical Weather Prediction Models
With a focus towards developing multiscale capabilities in numerical weather prediction models, the specific problem of the transition from the mesoscale to the microscale is investigated. For that purpose, idealized one-way nested mesoscale to large-eddy simulation (LES) experiments were carried out using the Weather Research and Forecasting model framework. It is demonstrated that switching from one-dimensional turbulent diffusion in the mesoscale model to three-dimensional LES mixing does not necessarily result in an instantaneous development of turbulence in the LES domain. On the contrary, very large fetches are needed for the natural transition to turbulence to occur. The computational burden imposed by these long fetches necessitates the development of methods to accelerate the generation of turbulence on a nested LES domain forced by a smooth mesoscale inflow. To that end, four new methods based upon finite amplitude perturbations of the potential temperature field along the LES inflow boundaries are developed, and investigated under convective conditions. Each method accelerated the development of turbulence within the LES domain, with two of the methods resulting in a rapid generation of production and inertial range energy content associated to microscales that is consistent with non-nested simulations using periodic boundary conditions. The cell perturbation approach, the simplest and most efficient of the best performing methods, was investigated further under neutral and stable conditions. Successful results were obtained in all the regimes, where satisfactory agreement of mean velocity, variances and turbulent fluxes, as well as velocity and temperature spectra, was achieved with reference non-nested simulations. In contrast, the non-perturbed LES solution exhibited important energy deficits associated to a delayed establishment of fully-developed turbulence. The cell perturbation method has negligible computational cost, significantly accelerates the generation of realistic turbulence, and requires minimal parameter tuning, with the necessary information relatable to mean inflow conditions provided by the mesoscale solution.
Journal Article
Large-Eddy Simulations of Atmospheric Flows Over Complex Terrain Using the Immersed-Boundary Method in the Weather Research and Forecasting Model
Atmospheric flow over complex terrain, particularly recirculation flows, greatly influences wind-turbine siting, forest-fire behaviour, and trace-gas and pollutant dispersion. However, there is a large uncertainty in the simulation of flow over complex topography, which is attributable to the type of turbulence model, the subgrid-scale (SGS) turbulence parametrization, terrain-following coordinates, and numerical errors in finite-difference methods. Here, we upgrade the large-eddy simulation module within the Weather Research and Forecasting model by incorporating the immersed-boundary method into the module to improve simulations of the flow and recirculation over complex terrain. Simulations over the Bolund Hill indicate improved mean absolute speed-up errors with respect to previous studies, as well an improved simulation of the recirculation zone behind the escarpment of the hill. With regard to the SGS parametrization, the Lagrangian-averaged scale-dependent Smagorinsky model performs better than the classic Smagorinsky model in reproducing both velocity and turbulent kinetic energy. A finer grid resolution also improves the strength of the recirculation in flow simulations, with a higher horizontal grid resolution improving simulations just behind the escarpment, and a higher vertical grid resolution improving results on the lee side of the hill. Our modelling approach has broad applications for the simulation of atmospheric flows over complex topography.
Journal Article
Setting Up a Large-Eddy Simulation to Focus on the Atmospheric Surface Layer
Large-eddy simulations (LES) above forests and cities typically constrain the simulation domain to the first 10–20% of the Atmospheric Boundary Layer (ABL), aiming to represent the finer details of the roughness elements and sublayer. These simulations are also commonly driven by a constant pressure gradient term in the streamwise direction and zero stress at the top, resulting in an unrealistic fast decay of the total stress profile. In this study, we investigate five LES setups, including pressure and/or top-shear driven flows with and without the Coriolis force, with the aim of identifying which option best represents turbulence profiles in the atmospheric surface layer (ASL). We show that flows driven solely by pressure not only result in a fast-decaying stress profile, but also in lower velocity variances and higher velocity skewnesses. Top-shear driven flows, on the other hand, better replicate ASL statistics. Overall, we recommend, and provide setup guidance for, simulation designs that include both a large scale pressure forcing and a non-zero stress and scalar flux at the top of the domain, and that also represent the Coriolis force. Such setups retain all the forces used in typical full ABL cases and result in the best match of the profiles of various statistical moments.
Journal Article
Turbulence-Kinetic-Energy Budget in the Urban-Like Boundary Layer Using Large-Eddy Simulation
We describe and explain the turbulent processes at play in the lower part of the urban boundary layer through performing a large-eddy simulation of the flow over an urban-like canopy composed of a staggered array of cubes with a packing density of 25%. The simulation models neutral thermal conditions at a Reynolds number (based on both velocity at the top of the domain and the domain height) of Re=50,000. A dynamic Smagorinsky model is implemented in order to allow for energy backscattering from subgrid scales. A wall refinement of the grid allows resolving the viscous sublayer. Turbulent statistics up to the third order, as well as each term of the turbulence-kinetic-energy budget, are computed individually everywhere in the domain. Results are discussed in relation to experimental and numerical data from the literature in order to describe turbulent energy transfers occurring in the roughness sublayer. The fine grid resolution close to surfaces serves to analyze in depth the three-dimensional distribution of turbulence production inside the urban canopy layer. This analysis in turn leads to discovering areas, never previously documented in an urban-like canopy, of highly positive and highly negative production close to the surface, away from the well-known high production area in the shear layer. Furthermore, evidence of a close link between high and low production areas near the surfaces and singular points in the mean flow is presented, thus laying the groundwork for a simple pre-diagnostic tool to detect turbulence-kinetic-energy production areas near surfaces.
Journal Article
Insights into Atmospheric Predictability through Global Convection-Permitting Model Simulations
Global convection-permitting models enable weather prediction from local to planetary scales and are therefore often expected to transform the weather prediction enterprise. This potential, however, depends on the predictability of the atmosphere, which was explored here through identical twin experiments using the Model for Prediction Across Scales. The simulations were produced on a quasi-uniform 4-km mesh, which allowed the illumination of error growth from convective to global scales. During the first two days, errors grew through moist convection and other mesoscale processes, and the character of the error growth resembled the case of [Formula: see text] turbulence. Between 2 and 13 days, errors grew with the background baroclinic instability, and the character of the error growth mirrored the case of [Formula: see text] turbulence. The existence of an error growth regime with properties similar to [Formula: see text] turbulence confirmed the radical idea of E. N. Lorenz that the atmosphere has a finite limit of predictability, no matter how small the initial error. The global-mean predictability limit of the troposphere was estimated here to be around 2–3 weeks, which is in agreement with previous work. However, scale-dependent predictability limits differed between the divergent and rotational wind component and between vertical levels, indicating that atmospheric predictability is a more complex problem than that of homogeneous, isotropic turbulence. The practical value of global cloud-resolving models is discussed in light of the various aspects of atmospheric predictability.
Journal Article
Implications of Nonlocal Transport and Conditionally Averaged Statistics on Monin–Obukhov Similarity Theory and Townsend’s Attached Eddy Hypothesis
According to Townsend’s hypothesis, so-called wall-attached eddies are the main contributors to turbulent transport in the atmospheric surface layer (ASL). This is also one of the main assumptions of Monin–Obukhov similarity theory (MOST). However, previous evidence seems to indicate that outer-scale eddies can impact the ASL, resulting in deviations from the classic MOST scaling. We conduct large-eddy simulations and direct numerical simulations of a dry convective boundary layer to investigate the impact of coherent structures on the ASL. A height-dependent passive tracer enables coherent structure detection and conditional analysis based on updrafts and subsidence. The MOST similarity functions computed from the simulation results indicate a larger deviation of the momentum similarity function ϕ m from classical scaling relationships compared to the temperature similarity function ϕ h . The conditional-averaged ϕ m for updrafts and subsidence are similar, indicating strong interactions between the inner and outer layers. However, ϕ h conditioned on subsidence follows the mixed-layer scaling, while its updraft counterpart is well predicted by MOST. Updrafts are the dominant contributors to the transport of momentum and temperature. Subsidence, which comprises eddies that originate from the outer layer, contributes increasingly to the transport of temperature with increasing instability. However, u′ of different signs are distributed symmetrically in subsidence unlike the predominantly negative θ′ as instability increases. Thus, the spatial patterns of u′ w′ differ compared to θ′ w′ in regions of subsidence. These results depict the mechanisms for departure from the MOST scaling, which is related to the stronger role of subsidence.
Journal Article
Quantifying methane point sources from fine-scale satellite observations of atmospheric methane plumes
Anthropogenic methane emissions originate from a large number of relatively small point sources. The planned GHGSat satellite fleet aims to quantify emissions from individual point sources by measuring methane column plumes over selected ∼10×10 km2 domains with≤50×50 m2 pixel resolution and 1 %–5 % measurement precision. Here we develop algorithms for retrieving point source rates from such measurements. We simulate a large ensemble of instantaneous methane column plumes at 50×50 m2 pixel resolution for a range of atmospheric conditions using the Weather Research and Forecasting model (WRF) in large eddy simulation (LES) mode and adding instrument noise. We show that standard methods to infer source rates by Gaussian plume inversion or source pixel mass balance are prone to large errors because the turbulence cannot be properly parameterized on the small scale of instantaneous methane plumes. The integrated mass enhancement (IME) method, which relates total plume mass to source rate, and the cross-sectional flux method, which infers source rate from fluxes across plume transects, are better adapted to the problem. We show that the IME method with local measurements of the 10 m wind speed can infer source rates with an error of 0.07–0.17 t h-1+5 %–12 % depending on instrument precision (1 %–5 %). The cross-sectional flux method has slightly larger errors (0.07–0.26 t h-1+8 %–12 %) but a simpler physical basis. For comparison, point sources larger than 0.3 t h-1 contribute more than 75 % of methane emissions reported to the US Greenhouse Gas Reporting Program. Additional error applies if local wind speed measurements are not available and may dominate the overall error at low wind speeds. Low winds are beneficial for source detection but detrimental for source quantification.
Journal Article