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This thesis represents the first large-scale, systematic study to use the double trace moment (DTM) technique in order to characterize the universal multifractal nature of aircraft-based measurements of wind velocity and several passive scalar concentrations under a variety of ambient conditions. Power-law scaling behaviour was demonstrated for the examined fields, from the smallest accessible measurement scales up to at least 250 km, right through the "mesoscale gap" postulated by the standard model of atmospheric dynamics. DTM results indicate remarkable stability in the estimates of the multifractality index, $ alpha$, and the codimension of mean singularity, $C sb1$, for wind velocity measured under different conditions of surface type, time of year, and measurement height within the surface boundary layer. Estimates for $ rm CO sb2, H sb2O, and O sb3$ were largely dominated by the wind velocity statistics as expected, but slightly sensitive to measurement height and moderately sensitive to significant changes in the underlying surface. Results showed that all of the fields examined may be classified as "unconditionally hard" multifractals, which is consistent with previously-published results for ground-based wind velocity measurements. It was demonstrated using probability distribution and multifractal analyses that ensemble statistical moments above approximately second-order can be expected to diverge for all examined fields due to the extremely singular nature of the fields at sub-resolution scales, and that the currently-employed quasi-local aircraft based sampling strategy is capable of reliably characterizing the statistical behaviour of the examined fields up to this physically-imposed limit. (Abstract shortened by UMI.)

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The accurate modelling of the wind speed profile at altitudes relevant to wind energy (i.e. up to 200m) is important for preliminary wind resource assessments, forecasting of the wind resource, and estimating shear loads on turbine blades. Modelling of the wind profile at these altitudes is particularly challenging in stable stratification due to weak turbulence and the influence of a broad range of additional processes. Models used to simulate the wind profile range from equilibrium-based 1D analytic extrapolation models to time-evolving 3D atmospheric models. Extrapolation models are advantageous due to their low computational requirements but provide a very limited account of atmospheric physics. Conversely, 3D models are more physically comprehensive but have considerably higher computational cost and data requirements. The middle ground between these two approaches has been largely unexplored. The intent of this research is to compare the ability of a range of models of varying complexity to model the wind speed profile up to 200m under stable stratification. I focus in particular on models that are more physically robust than conventional extrapolation models but less computationally expensive than a 3D model. Observational data taken from the 213-m Cabauw meteorological tower in the Netherlands provide a basis for much of this analysis. I begin with a detailed demonstration of the limitations and breakdown in stable stratification of Monin-Obukhov similarity theory (MOST), the theoretical basis for the logarithmic wind speed profile model. I show that MOST (and its various modifications) are reasonably accurate up to 200m for stratification no stronger than weakly stable. At higher stratifications, the underlying assumptions of MOST break down and large errors in the modelled wind profiles are found. I then consider the performance of a two-layer MOST-Ekman layer model, which provides a more physically-comprehensive description of turbulence compared to MOST-based models and accounts for the Coriolis force and large-scale wind forcing (i.e. geostrophic wind). I demonstrate considerable improvements in wind profile accuracy up to 200m compared to MOST-based approaches. Next, I contrast the performance of a two-layer model with a more physically-comprehensive equilibrium-based single-column model (SCM) approach. I demonstrate several limitations of the equilibrium SCM approach - including frequent model breakdown - that limit its usefulness. I also demonstrate no clear association between the accuracy of the wind profile and the order of turbulence closure used in the SCM. Furthermore, baroclinic influences due to the land-sea temperature gradient are shown to have only modest influence on the SCM wind speed profile in stable conditions. Overall, the equilibrium SCM (when it does not break down) is found to generally outperform the two-layer model. Finally, I contrast the performance of the equilibrium SCM with a time-evolving SCM and a time-evolving 3D mesoscale model using a composite set of low-level jet (LLJ) case studies as well as a 10-year dataset at Cabauw. For the LLJ case studies, the time-evolving SCM and 3D model are found to accurately simulate the evolving stratification, the inertial oscillation, and the LLJ. The equilibrium SCM is shown to have comparatively less skill. Over the full 10-year data set, the sensitivity of the time-evolving SCM to horizontally-driven temperature changes in the ABL is found to be a considerable limitation. Despite its various limitations and simplified physics, the time-evolving SCM is generally found to be equally as accurate as the mesoscale model while using a fraction of the computational cost and requiring only a minimal amount of easily attainable local observations. Overall, the time-evolving SCM model is found to perform the best (considering both accuracy and robustness) compared to a range of equilibrium approaches as well as a time-evolving 3D model, while offering the best balance of observational data requirements, physical applicability, and computational requirements. This thesis presents a compelling case for the use of SCMs in the field of wind energy meteorology. / Graduate

This thesis investigates several aspects of stratified flow over isolated topography in ocean, lake, and atmospheric settings. Three major sub-topics are addressed: steady, inviscid internal waves trapped over topography in a pycnocline stratification, topographically generated internal waves and their interaction with the viscous bottom boundary layer, and flow over large-scale crater topography in the atmosphere. The first topic examines the conditions that lead to very large internal waves trapped over topography in a fluid with a pycnocline stratification. This type of stratification is connected to ocean or lake settings. The steady-state Euler equations of motion are used to derive a single partial differential equation for the isopycnal displacement in supercritical flows under two conditions: a vertically varying background current under the Boussinesq approximation and a constant background current under non-Boussinesq conditions. A numerical method is developed to solve these equations for an efficient exploration of parameter space. Very large waves are found over depression topography when the background flow speed is close to a limiting value. Variations in the background current are examined, as well as comparisons between Boussinesq and non-Boussinesq results. The second topic aims to extend the above subject by considering unsteady, viscous flows. Once again, supercritical flow over topography in a pycnocline stratification generates internal waves. These internal waves interact with the viscous bottom boundary layer to produce bottom boundary instabilities. The three-dimensional aspects of these instabilities are studied under changes in viscosity. The boundary layer instabilities have important implications for sediment transport in the coastal oceans or lakes. Lastly, the final topic is motivated by the connection between dust streaks on the Martian surface and crater topography. Flow over a large 100-km diameter crater is examined with numerical simulations conducted using the Weather Research and Forecasting model. Modifications to the stratification and topography are applied. It is found that a large hydraulic structure of amplitude comparable to the crater depth forms in many cases. This structure may have important implications for dust transport in the atmosphere. In addition, Martian atmospheric parameters are used to study the flow properties under Mars-like conditions.

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