In this thesis, we introduced a model based on momentum entrainment to investigate the interaction of fluid flow with canopies of solid elements. We have used this model for different canopy types and flow situations to control the wakes and optimize the design factors and energy efficiency for a variety of applications.

In the first section, the model is used to introduce a new design for cost reduction of CO2 direct air capture systems. Although Direct Air Capture of CO2 has the potential to be a large source of negative carbon emissions, the design still needs to be much more cost effective and energy efficient to be economically viable. The land required for DAC systems is considerably less than other carbon renewal methods like biomass and reforestation; and currently the high cost is the most limiting factor for wide usage of DAC. Fair amount of work has been done to explore and optimize the internal system and chemical reactions, whereas the fluid mechanics and external design have been neglected. We developed a model to explore flow and carbon mass field for optimal design and cost reduction of DAC systems. Using this model, we have explored a new design based on thinner absorbers spread in a larger land area which can be effectively operated by wind flow if placed in regions with sufficient wind potential.

In the second section, a more generalized form of the model is developed to estimate the flow power loss through flexible vegetation canopies. Performing accurate estimates of bottom friction in tidal channels is essential to obtain precise assessments of the fluid power available for extraction by arrays of turbines. The presence of vegetation canopies can increase the bottom drag coefficient and change the velocity profile considerably. In order to improve available estimations of drag coefficients, we developed a model that is applicable to rigid and flexible canopies in both fully developed and developing flow regions. The results were validated by performing new experiments and setting up comparisons with past theories and experimental data. We found that the total drag force is highly affected by the flexibility of the vegetation. The pattern and length of the canopy can also increase the drag force by changing the length of developing flow through the canopy. Based on our results, the drag force is highly underestimated in the regions where vegetation canopies tend to grow.

Lastly, the third section addresses the characterization and control of vortical flows, which are primarily responsible for momentum entrainment into the canopies. We apply the Koopman mode representation (through an SVD-enhanced DMD algorithm) to co-rotating, patch-like vortices in inviscid and viscous flows. We recover the linear stability eigenvalues and eigenmodes. We show that Koopman mode analysis can detect qualitatively distinct stages of vortex merger. By applying Koopman mode decomposition to symmetric and asymmetric vortices, we quantitatively characterize the dynamics of each instability, and propose a criterion for symmetry-breaking. These results suggest a path forward towards using KMD for data-driven modeling of vortex flows.

Turbulence contains vortices with a broad range of spatial and temporal scales, which dominate the safety and performance of systems like turbomachinery and aerospace vehicles. The expensive efforts needed to resolve all vortices in these flows have led to the development of hybrid algorithms, where vortical regions are treated differently. In this study, we first illustrate the physical meaning of the dominant structures extracted through proper orthogonal decomposition (POD) and Koopman mode decomposition (KMD). We then verify that KMD recovers linear stability eigenvalues and eigenmodes associated with the inviscid merger of two co-rotating vortices. Thereafter, Koopman analysis results are provided to quantitatively and qualitatively assess the viscous interactions of co-rotating vortices. The onset of symmetry-breaking is found weakly sensitive to Reynolds number, but highly sensitive to small details in initial conditions. We build on our results to seek a data-driven model that balances efficiency and accuracy. We record total circulation, enstrophy, and angular impulse and solve their theoretical evolution equations to automate the selection of the model parameter values. We provide a test of algorithmic performance in simulating vortex merging. We first test the robustness of selecting each of the above three flow quantities to enforce accuracy. We then verify that KMD eigenvalues recover the correct time scales of the flow systems. Finally, we analyze the model performance by simulating the merger of uniform, patch-like co-rotating vortex pairs under different Reynolds numbers. This approach has the potential to be beneficial for simulating flows comprising fine vortical features in large domains.

In this study, we also delve into the topic of superhydrophobic drag reduction at high Reynolds numbers, utilizing adaptive octree discretizations in distributed environments to conduct simulations that are both accurate and computationally feasible. This work builds upon the parallel level-set schemes developed by Mirzadeh et al., employing {\tt p4est} and extending the research presented in Egan et al.. Superhydrophobic surfaces (SHS) have shown high drag reductions in turbulent flows. However, simulating the high gas fractions and high Reynolds numbers typical of naval applications poses a challenge due to the sharp gradients that arise near the transitions between no-slip regions and gas-liquid interfaces. To address this, we leverage high-performance multicore systems and scalable linear solvers to simulate SHS structures, enabling a relatively rapid exploration of the parameter space up to gas fractions of 93.75\%. We introduce momentum flow lines to map the pathways taken by the streamwise momentum as it is transported from the channel interior towards the walls, aiding in the understanding of the flow dynamics. This study reveals how flow properties, including Reynolds stresses and vortical structures, are influenced by gas fraction and Reynolds number. These insights can contribute to the development of refined models that are valid across different flow regimes.

Several novel wind energy systems produce wakes with annular cross-sections, which are qualitatively different from the wakes with circular cross-sections commonly generated by conventional horizontal-axis wind turbines and by compact obstacles. Since wind farms use arrays of hundreds of turbines, good analytical wake models are essential for efficient wind farm planning. Several models already exist for circular wakes; however, none have yet been proposed for annular wakes, making it impossible to estimate their array performance. We use the entrainment hypothesis to develop a reduced-order model for the shape and flow velocity of an annular wake from a generic annular obstacle. Our model consists of a set of three ordinary differential equations, which we solve numerically. In addition, by assuming that the annular wake does not drift radially, we further reduce the problem to a model comprising only two differential equations, which we solve analytically. Both of our models are in good agreement with previously published large eddy simulation results.

This dissertation presents an experimental investigation of turbulent boundary layer flows arising over arrays of identical, two-dimensional bluff obstacles, motivated by contemporary engineering and geophysical flow applications. At sufficiently high Reynolds numbers, rough-surface boundary layers are primarily parameterized by the geometry of the individual obstacles, as well as by their spacing s, normalized by the obstacle height k. When the roughness enhances the turbulent fluxes between the near wall region and the outer flow, the log-law profile of the mean velocity is shifted closer to the wall. This shift is empirically determined, and is traditionally encoded by the equivalent sand grain roughness k_s, such that larger values of k_s/k represent surfaces that induce greater fluxes, for a given obstacle height.

Although square bar geometries and their effects on the flow have been studied extensively, arrays consisting of thin, plate-like obstacles have been understudied. For square bars, it has been demonstrated that, as the spacing decreases below s/k~7, the flow enters a different regime with drastically reduced turbulent fluxes, and with values of k_s/k that are over one order of magnitude smaller. However, it is not known whether plate-like obstacles may delay this transition to smaller spacings, or whether they may experience a less significant drop in k_s/k. This would be highly valuable in applications, as it would allow obstacles to be more densely packed without sacrificing fluxes between the obstacles and overlying flow.

The first part of this dissertation presents a review of the underlying physics for smooth and rough surfaces before discussing investigations of various roughness geometries, ultimately arguing that plate roughness is understudied. The experimental and processing methods are then described. Particle-Image Velocimetry in a water channel is used to obtain time-resolved velocity fields over bar and plate obstacles for 1< s/k < 10. It is found that plate obstacles can be packed closer together while still yielding a k_s/k that is one order of magnitude higher than for square bar geometries.

Surfactants —molecules with a tendency to adsorb to interfaces between fluids— have been known to critically affect the behavior of multiphase flows for decades. They slow the rise of air bubbles in water, increase the thickness of liquid coating films, and trigger the motion of the so-called “tears” in a glass of wine, to name a few examples. In recent years, it has been shown that these substances also play a central role in the performance of superhydrophobic surfaces (SHS), textures designed to reduce friction by retaining a layer of air while immersed in water. Indeed, the presence of even small traces of surfactants, unavoidable not only in the environment but also in nominally clean conditions, inevitably leads to adverse Marangoni forces that substantially inhibit drag reduction. Quantifying and predicting these effects would have far-reaching technological implications in energy efficiency, yet it is extremely challenging due to the underlying mathematical complexity and the difficulty in the detection and control of surfactants in experiments.

The first part of this dissertation introduces two numerical methods: one is designed for the surfactant transport problem in deforming geometries, while the other solves the incompressible Navier-Stokes equations for the fluid flow in parallel multi-processor environments. The computational framework is based on a level-set representation of moving interfaces and the utilization of adaptive Cartesian grids, providing a unique tool to efficiently tackle the full problem in relatively general scenarios. We then describe the first theoretical model for laminar flows over superhydrophobic surfaces inclusive of surfactant, based on simplifying physical assumptions that apply in the specific case of two-dimensional SHS gratings. In practice, however, flows over realistic SHS textures have key three-dimensional features. To overcome this limitation, a new model for three-dimensional gratings is presented, allowing for the first time to compare theoretical predictions with experimental measurements, which we perform using confocal microscopy in microfluidic devices. Additionally, this thesis presents (i) a striking experimental demonstration of maze-solving by surfactants in the context of free-surface flows, and (ii) a concise theoretical study on the sunlight inactivation of the SARS-CoV-2 virus, with potential applications in UV disinfection technology.