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Traditional weather models struggle to resolve the details of complex terrain and the strongly stable stratification often observed in near surface temperature inversions. Conversely, traditional engineering computational fluid dynamics codes often use high resolution grid meshes, but do not include forcing from synoptic scale weather. As computational power grows, a new class of models is emerging. These are nested large-eddy simulations (LES), which are both highly resolved and include large scale weather forcing. In this case, high resolution implies grid meshes that are fine enough to resolve the most energetic eddies in the atmospheric boundary layer. These high resolution domains are nested, i.e. forced at the lateral boundaries, by coarser mesoscale models. The role of nested large-eddy simulation in the study of atmospheric boundary layer is twofold. First, trusted LES data allow the study of important dynamics with all the relevant forcing of real flow, but without dense observation networks. Though observations are still critical to the validation of these models, in some cases, as in fire weather, sufficiently detailed observations are very difficult to carry out due to practical concerns. In other cases, simulation is simply a less expensive means to achieve higher resolution data than even the densest sensor network can provide. In this sense, LES is a valuable tool for the research community. For the forecasting community, however, LES cannot be used in place of coarser models given current computational power. As prediction is an ultimate goal of weather modeling, we turn to the second role of LES, the generation of subgrid parameterizations for use in coarse models that can be run for real-time forecasting. The dual purpose of LES, the direct study of atmospheric boundary layer dynamics and the development of parameterizations for mesoscale models, motivate three investigations into the dynamics of the atmospheric boundary layer presented here. Each study conducts LES with the Weather Research and Forecasting (WRF) model, an advanced numerical weather prediction (NWP) code. Unlike traditional NWP or engineering codes, these simulations include both complex terrain as well as realistic weather forcing to advance our understanding of atmospheric boundary layer dynamics and the LES technique itself. The first project is conducted as part of the Mountain Terrain Atmospheric Modeling and Observations (MATERHORN) program. During the field campaign of the MATERHORN, large temperature fluctuations were observed on the slope of Granite Peak, Utah, which partially encloses a cold-air pool in the east basin. These flow features are able to be resolved using LES within the WRF model with ∆x = 100 m, allowing accurate representation of lee vortices with horizontal length scale of O(1 km). At this resolution, terrain slopes become quite steep, and some model warm biases remain in the east basin due to limits on terrain-following coordinates that prevent the model from fully resolving drainage flows with this steep terrain. A new timestep limit for the WRF model related to these steep slopes is proposed. In addition, the initialization of soil moisture is adjusted by drying the shallowest layer to assist the formation of a cold pool in the LES. These real case simulations compare well to observations and also to previously published simulations using idealized configurations to study similar phenomena. For instance, the values of non-dimensional mountain height, which characterize flow regimes in idealized studies, are similar in the real case. With their predictive capabilities established, these non-dimensional numbers are likely to provide the future basis for parameterization of the lee vortices which cannot be resolved by NWP models.The second study addresses a challenge to simulating turbulent flow in multiscale atmospheric applications, the efficient generation of resolved turbulence motions over an area of interest. One approach is to apply small perturbations to flow variables near the inflow planes of turbulence-resolving simulation domains nested within larger mesoscale domains. While this approach has been examined in numerous idealized and simple terrain cases, its efficacy in complex terrain environments has not yet been fully explored. Here, we examine the benefits of the stochastic cell perturbation method (CPM) over real complex terrain using data from the 2017 Perdigão field campaign, conducted in an approximately 2-km wide valley situated between two nearly parallel ridges. Following a typical configuration for multiscale simulation using nested domains within the WRF model to downscale from a mesoscale to an LES, we apply the CPM on a domain with a relatively coarse LES mesh spacing of 150 m. LES at this resolution often generates spurious coherent structures under unstable atmospheric conditions with moderate mean wind speeds. We examine the impacts of the CPM on the representation of turbulence within the nested LES domain under moderate mean flow conditions in three different stability regimes: weakly convective, strongly convective, and weakly stable. In addition, two different resolutions of the underlying terrain are used to explore the role of the complex topography itself in generating turbulent structures. We demonstrate that the CPM improves the representation of turbulence within the LES domains, relative to the use of high-resolution complex terrain alone. During the convective conditions, the CPM improves the rate at which smaller-scales of turbulence form, while also accelerating the attenuation of the spurious numerically-generated roll structures near the inflow boundary. During stable conditions, the coarse mesh spacing of the LES used herein was insufficient to maintain resolved turbulence using CPM as the flow develops downstream, highlighting the need for yet higher resolution under even weakly stable conditions. The CPM was particularly efficient during the evening transition period. A final study investigates fundamental controls on drainage flow dynamics. Historically called katabatic flow, drainage flow is buoyancy driven and directed downslope in response to surface cooling typical of the nocturnal period. Analogous upslope flow due to surface heating during the day is often called anabatic flow. A fundamental question is at what time during the evening transition does the slope wind system switch from anabatic to drainage flow. A natural benchmark for this transition is sunset, but the presence of terrain results in shadows cast onto east-facing slopes which can complicate this analysis. To guide this analysis, functional forms for the time of the shadow front propagation are presented for an idealized terrain shape used for an LES in WRF. Even with idealized topography, the present LES are significantly more advanced than previous models used to investigate idealized drainage flow, which prescribed surface cooling rather than prognosticating the cooling in response to the diurnal cycle of insolation and the characteristics of the surface and soil types, as done here. This complexity allows for potentially counterintuitive results, such as the onset of drainage flow occurring on the shadow-cast eastern slopes later than on the sunnier western slopes due to convective structures which persist after sunset. Despite these complications during the development of drainage flow in the evening, there are periods during the night when analytical solutions compare well to the LES solution of drainage flow profiles. A novel analytical solution also explains a dependence on the angle of the slope found in observation data but missing in the original (Prandtl 1942) solution by replacing the traditional Dirichlet with a Neumann boundary condition. The favorable comparison between analytical solutions and results from the high resolution numerical model are a first step towards the ultimate parameterization of drainage flow in coarser NWP models.

In 1831, Michael Faraday observed the formation of standing waves on the surface of a vibrating fluid body. Subsequent experiments have revealed the existence of a rich tapestry of patterned states that can be accessed by varying the frequency and amplitude of the vibration and have spurred vast research in hydrodynamics and pattern formation. These include linear analyses to determine the conditions for the onset of the patterns, weakly nonlinear studies to understand pattern selection, and dynamical systems approaches to study mode competition and chaos. Recently, there has been some work towards numerical simulations in various three-dimensional geometries. These methods however possess low orders of accuracy, making them unsuitable for nonlinear regimes.We present a new technique for fast and accurate simulations of nonlinear Faraday waves in a cylinder. Beginning from a viscous potential flow model, we generalize the Transformed Field Expansion to this geometry for finding the highly non-local Dirichlet-to-Neumann operator (DNO) for the Laplace equation. A spectral method relying on Zernike polynomials is developed to rapidly compute the bulk potential. We prove the effectiveness of representing functions on the unit disc in terms of these polynomials and also show that the DNO algorithm possesses spectral accuracy, unlike a method based on Bessel functions. The free surface evolution equations are solved in time using Picard iterations carried out by left-Radau quadrature. The results are in perfect agreement with the instability thresholds and surface patterns predicted for the linearized problem. The nonlinear simulations reproduce several qualitative features observed experimentally. In addition, by enabling one to switch between various nonlinear regimes, the technique allows a precise determination of the mechanisms triggering various experimental observations.

The pathology of many cardiovascular diseases is believed to be heavily tied to local hemodynamics. A positive feedback loop of remodeling and unhealthy flow conditions can lead to blood vessel abnormalities, such as aneurysms, stenoses, and plaques. Doctors use medical imaging techniques to visualize vascular disease within patients. However, while treatments based on these images for some diseases have been well-established, there is room for improvement. Many treatment decisions are based on simplified criteria and incomplete data and our understanding behind the pathophysiology of many of these diseases remains woefully incomplete. A stronger grasp of the relationship between disease and hemodynamics can help clinicians plan better treatment outcomes or help prevent some complications from occurring.4D-Magnetic Resonance (MR) Imaging can be a powerful tool for quantifying the flow field within the cardiovasculature, but remains difficult to integrate for clinical use due to the involving process required to convert noisy magnetic resonance image data from a set of symbols to an easily digestible image. Treatment decisions are based on standardized practices, but no standardization for the processing and interpretation of 4D-MR images exist. Computational Fluid Dynamics (CFD) can simulate patient hemodynamics with much finer temporal and spatial resolution than 4D-MR. However, computational methods must still use boundary conditions obtained from imaging data, which means CFD results can only be as accurate as the images they are based upon. Additionally, the logistics of performing CFD, which require extensive training and time, is a strong barrier against its adoption in a clinical setting.This thesis presents a model for using in vivo (live) and simulated flow data as complementary methods to explore potential mechanisms of pathophysiology and aid the treatment of cardiovascular diseases. We developed pipelines for processing 4D-MR images and for building patient-specific CFD simulations. We first attempted to measure the experimental error in 4D-Flow MRI within a cerebral aneurysm phantom and explored how that error might propagate into CFD results based on those MR measurements. We used those results to predict how this sensitivity would affect the treatment of aneurysms based on their hemodynamics. We then used both 4D-MR and CFD methods to characterize a rarely explored vascular territory, the cerebral venous outflow tract (CVOT). 4D-Flow MR was used to categorize geometries and flows in the CVOT. CFD was used to investigate a potential association between flow and symptoms in a subcategory of internal jugular vein geometries.