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Publication# Theoretical and numerical studies of atmospheric boundary-layer flows over complex terrain

Résumé

Atmospheric boundary-layer (ABL) flows over complex terrain have been the focus of active research, given their impact on weather and climate variability. Surface complexity is understood in a broad sense and includes variation in roughness properties, inclination of the underlying surface, presence of heterogeneous forcing mechanisms (e.g., buoyancy, humidity), to name but a few. Most assumptions of classical boundary-layer similarity theory do not hold under such conditions, complicating matters from both a measurement and modeling perspective. Here, a combination of analytical and numerical approaches are used to address two among the most relevant problems: turbulent slope flows, and ABL flows over multi-scale rough surfaces. The first part of the thesis focuses on slope flows: the building blocks of local weather in mountainous regions. To understand the system conceptually, a closed-form analytic solution to the Prandtl slope flow model is first derived, prescribing transfer coefficients in accordance to the O'Brien K-theory model. Profiles are characterized by stark variations in both phase and amplitude of extrema compared to the classic constant-K and a more recent solution, valid within the Wentzel-Kramers-Brillouin theory, shedding new light on this long-standing geophysical problem. In addition, direct numerical simulation is used to study the turbulent structure of anabatic and katabatic flows, and to describe the sensitivity of the solution to variations in the parameter space, within the conceptual framework of the Prandtl model. Variations in the sloping angle from the vertical wall setup are shown to induce a progressive departure of averaged profiles between the two flow regimes, ultimately resulting in stark differences at gentle sloping angles. The thermodynamical mechanisms responsible for sustaining mean and turbulent kinetic energy are used to further distinguish between flow regimes, and to propose a qualitative partition of the boundary layer in slope flows. The DNS setup is additionally adopted to identify coherent structures in katabatic flows over steep slopes. Coherent motions are responsible for the maintenance of turbulence in the ABL, hence their characterization is of fundamental importance toward a better understanding of boundary-layer dynamics. Packets of hairpins are found to connect in the streamwise direction to form large-scale motions (LSMs). For the lower sloping angles that are considered, it is then shown how LSMs further align to form very-large-scale motions (VLSMs). LSMs and VLSMs are found to be dominant contributors to streamwise momentum variance and turbulent momentum transfer in the above-jet regions. Next, drag properties of fractal-like sea ice surface morphologies are examined within the large-eddy simulation framework. The effects of large-scale surface features on wind flow are accounted for by an immersed boundary method. Conversely, the drag forces caused by subgrid-scale features are modeled through a novel dynamic roughness approach, in which the hydrodynamic roughness length parameter is determined using the first-principles based constraint that the total momentum flux (drag) must be independent of the grid-filter scale. This approach leads to accurate flow predictions, and provides an estimate of the otherwise unknown roughness parameter for sea ice surfaces, of use in climate, weather prediction and scalar transport models to evaluate the hydrodynamic roughness length.

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For the modelling of the transport and diffusion of atmospheric pollutants during accidental releases, sophisticated emergency response systems are used. These modelling systems usually consist of three main parts. The atmospheric flow conditions can be simulated with a numerical weather prediction (NWP) model. The evolution of the pollutant cloud is described with a dispersion model of variable complexity. The NWP and the dispersion models have to be coupled with a so-called meteorological pre-processor. This means that all the necessary – in most cases turbulence related – variables which are not available from the standard output of the NWP model have to be diagnosed. The main difficulty of the turbulence coupling is that these subgrid scale variables of NWP models are not routinely verified and thus little is known concerning their quality and impact on dispersion processes. The general aim of the present work is to better understand and improve this coupling mechanism. For this purpose all the three main components of the emergency response system of MeteoSwiss are carefully evaluated and possible improvement strategies are suggested. In the first part, the NWP component of the system, namely the COSMO model, is investigated focusing on the model performance in the Planetary Boundary Layer (PBL). Three case studies, representing both unstable and stable situations, are analyzed and the COSMO simulations are validated with turbulence measurements and Large Eddy Simulation (LES) data. It is shown that the COSMO model is able to reproduce the main evolution of the boundary layer in dry convective situations with the operational parameter setting. However, it is found that the COSMO model tends to simulate a too moist and too cold PBL with shallower PBL heights than observed. During stable conditions the operational parameter setting has to be significantly modified (e.g., the minimum diffusion coefficient) to obtain a good model performance. The turbulence scheme of COSMO, which carries a prognostic equation for Turbulent Kinetic Energy (TKE), is studied in detail to understand the shortcomings of the simulations. The turbulent transport term (third order moment) in the TKE equation is found to be significantly underestimated by the COSMO model during unstable situations. This results in inaccurate TKE profiles and hence missing entrainment fluxes at the top of the PBL. A solution to increase the TKE transport in the PBL is proposed in the present work and evaluated during a three-month continuous period. While improving the TKE profile substantially, the modification is demonstrated to not impair other model output characteristics. The second component of the emergency response system, namely the meteorological pre-processor, is also validated on case studies and a continuous period. The main objective of this analysis is to compare the currently operational coupling approach, which is based on the direct usage of the prognostic TKE from the COSMO model, to a classical approach based on similarity theory considerations, thereby using turbulence measurements on the one hand and LES data on the other hand. To be able to use similarity theory approaches for the determination of turbulence characteristics, the PBL height has first to be diagnosed from the NWP model. In the present study, several approaches for the determination of PBL height have been implemented and validated with radio sounding measurements. Based on the verification results and the operational convenience, the method based on the bulk Richardson number method has been chosen for the diagnosis of the PBL height. Validation results of post-diagnosed turbulence characteristics show that during convective situations, the similarity approach tends to overestimate the turbulence intensity, while the approach based on the direct usage of TKE yields more accurate results. For stable conditions the different approaches are closer to each other and both give reasonable predictions. It is found that the main drawback of the direct approach is the isotropic assumption in the horizontal direction. A new hybrid method is proposed which uses similarity considerations for the partitioning of horizontal TKE between along-wind and cross-wind directions. In the last part, pollutant dispersion in complex terrain is studied using a new scaling approach for TKE that is suited for steep and narrow Alpine valleys. This scaling approach is introduced in the interface between COSMO and a Lagrangian particle dispersion model (LPDM), and its results are compared to those of a classical similarity theory approach and to the operational coupling type, which uses the TKE from the COSMO model directly. For the validation of the modelling system, the TRANSALP-89 tracer experiment is used, which was conducted in highly complex terrain in southern Switzerland. The ability of the COSMO model to simulate the valley-wind system is assessed with several meteorological surface stations. The dispersion simulation is evaluated with the measurements from 25 surface samplers. The sensitivity of the modelling system towards the soil moisture, horizontal grid resolution, and boundary layer height determination is investigated. It is shown that if the flow field is correctly reproduced, the new scaling approach improves the tracer concentration simulation compared to the classical coupling methods.

Large-eddy simulation (LES) is a very promising technique for the numerical computation of unsteady turbulent flows, and seems to be the perfect tool to simulate the compressible air flow around a high-speed train in a tunnel, providing unsteady results for aerodynamic and aeroacoustic analysis. To look into this possible future application of LES, two major lines of investigation are pursued in this thesis: first, the study of the effective ability of shock-capturing schemes to predict fundamental turbulent phenomena; second, the analysis of the aerodynamic phenomena induced by a high-speed train in a tunnel. The numerical simulation of compressible flows requires the use of shock-capturing schemes. These schemes can be relatively dissipative and mask the subgrid-scale contribution introduced in a large-eddy simulation to account for the unresolved turbulence scales. To estimate their effective dissipation and their ability to resolve turbulence phenomena, shock-capturing schemes widely used for aeronautical applications, from second- to fifth-order space accuracy, are employed here for simulating well-known fundamental flows in subsonic and supersonic regimes. Direct and large-eddy numerical simulations are undertaken for the inviscid and viscous Taylor-Green vortex decay problem, the freely decaying homogeneous and isotropic turbulence, and the fully developed channel flow. For all the turbulent flows investigated, several turbulence statistics are computed and the numerical dissipation of the schemes tested is interpreted in terms of subgrid-scale dissipation in a LES context, yielding an equivalent Smagorinsky or dynamic coefficient. This coefficient is for all schemes of the same order of magnitude as the commonly accepted values in LES for the subgrid-scale term. On the grounds of this analysis and of the comparisons of the turbulence statistics with accurate data obtained in the literature, the addition of explicit subgrid-scale models to the shock-capturing schemes tested is not recommended. It is thus concluded that the use of the LES technique for compressible turbulent flows is not yet suitable for industrial applications. The aerodynamic phenomena generated by a high-speed train travelling in a tunnel are also discussed, their importance on the design of high-speed lies is pointed out, and the analysis tools commonly employed for their study are reviewed. To study numerically the three-dimensional, compressible and turbulent air flow around a high-speed train accelerating in a tunnel, by accounting for the unsteady effects at inlet and outlet boundaries due to the propagation of pressure waves generated at the train departure, new coupling conditions between one-dimensional and three-dimensional domains are developed. These conditions are applied successfully to the numerical simulation of the unsteady wake developing behind two- and three-dimensional vehicles, where the averaged Navier-Stokes equations are solved with the turbulence modelling approach. The influence on the wake of the length of the vehicle tail is also discussed and results of multi-dimensional simulations are compared with one-dimensional data.

Water vapor plays an important role in weather, global climate processes and atmospheric chemistry. It is the most significant greenhouse gas and affects the planet's radiative and non-radiative energy balance. The distribution of water vapor in the atmosphere is quite variable both horizontally and vertically and has a significant influence on the atmospheric circulation and temperature structure. Accurate data about water vapor and temperature is needed for weather forecasting, weather and climate research, boundary layer and cloud process studies, and atmospheric chemistry. Despite the need for these data, obtaining accurate water vapor and temperature measurements with high temporal and spatial resolution has remained an only partially solved problem. The Raman lidar technique for water vapor and temperature measurements is a straightforward method and is based on well-known physical principles. It can supply accurate data with high spatial and temporal resolution for weather, climate, atmospheric boundary layer (ABL) studies and other atmospheric research. One of the two goals of this thesis is to develop and construct a Raman lidar instrument with high spatial (1.5 m) and temporal (1 s) resolution and an operational range of 15 – 500 m for systematic observations of water vapor profiles. The measured profiles together with a new generation of Large Eddy Simulations (LES) will be used to attain an improved understanding of the complex linkages between the land surface and the overlying atmospheric boundary layer. The second goal is to develop and test a new method for the determination of the atmospheric transmission correction factor for non solar-blind water vapor Raman lidars based exclusively on the use of Raman lidar signals without needing a priori information about the aerosol optical properties.