This thesis explores two topics: spline trajectory planning and rigidity-based formation control. The analyses presented in this thesis for each topic are self-contained and so this thesis is presented in two parts. The first chapter focuses on spline trajectory planning. We revisit a popular methodology from the quadrotor trajectory planning literature and address two roadblocks encountered in its practical implementation. Specifically, we consider the computational complexity of prototypical algorithms from the literature as well as their scalability. From this analysis, we propose two new algorithms: (i) Algorithm 1, which generates spline trajectories with linear computational complexity and (ii) Algorithm 2, an iterative algorithm that generates time-optimal spline trajectories with linear computational complexity in each iteration. Both methods are faster and plan larger trajectories than the state-of-the-art. We apply our methods to demonstrate their efficacy by conducting an experimental quadrotor flight and by proposing a novel rapidly-exploring random tree (RRT*) algorithm. The second chapter considers the use of rigidity theory for the formation control problem. We analyse a non-Euclidean norm and present a rigidity theory for frameworks under the 1-norm. We then use this rigidity theory to derive a distributed control law that, under a reasonable condition, comes with an exponentially stability result. The qualities of our new control law are investigated, particularly in comparison with other, related rigidity-based approaches.

The thesis concerns linear feedback control of vortex shedding behind a two-dimensional cylinder at low Reynolds numbers, with a particular focus on the linear modelling of flow dynamics and the placement of sensors and actuators. To accommodate high-dimensionality, we first propose an efficient modelling approach in which the linearised Navier-Stokes equations are recast into an input-output form (i.e. resolvent operator) from which frequency responses can be computed. Low-order models can thus be identified from frequency responses for optimal feedback control design using H-infinity loop shaping. We investigate two distinct single-input-single-output setups: i) a pair of body forces near the cylinder surface is in feedback with a velocity sensor located in the wake; ii) a collocated actuator-sensor pair that oscillates the cylinder according to the lift measurement. We demonstrate the effect of different control setups and sensor placements on control performance and robustness as well as physical mechanisms behind them. Reduced-order modelling generally leads to a local optimum and prevents the further disclosure of physical mechanisms that affect control performance. Therefore, we present a resolvent-based algorithm that designs (full-dimensional) H2-optimal feedback controllers without any model-order reduction, in which an iterative procedure is used to achieve the global optimum. We consider the optimal placements of a single sensor and a single actuator for linear feedback control. Two independent problems are considered: i) optimal estimation (OE) where we measure the state at one position to estimate the whole flow; ii) full-state information control (FIC) where we measure the entire flow but actuate it at only a single location. By varying the stability of the flow system, optimal placements that were found separately for the OE, FIC problems are compared to those found for the optimal feedback control problems, which reveals key factors and conflicting trade-offs that limit feedback control performance. We also compare optimal placements to those predicted in previous studies (e.g. using modal analyses) and discuss implications for effective feedback control. The last part of the thesis investigates discrepancies between saturated nonlinear vortex shedding and its quasi-linear model (i.e. resolvent modes) from an energy-transfer perspective. We demonstrate across-frequency energy-transfer pathways and the contribution of nonlinear interactions in the true flow and compare them to those predicted from resolvent analysis. In this way, we gain insight into the extent to which resolvent analysis can correctly model nonlinear energy transfer, which is essential for improving the modelling and simulation of nonlinear fluid flows.

Aqueous electrolytes confined in nanoporous materials are involved in many biological and technological systems. Both atomistic simulation and experiments have revealed that the non-classical solvation state, ion spatial location, or in-pore density of electrolyte can emerge in nanoconfinement. The ability to develop quantitative models to describe the microscopic structure of nanoconfined electrolytes is crucial to allow the new nanoscience to be readily harvested for future engineering design. Although atomistic simulations can predict a detailed microscopic structure for nanoconfined aqueous electrolytes, the limited model size and time scale of atomistic simulations make it difficult to scale up the results for experimental design. By contrast, conventional continuum modelling is computationally efficient to describe and predict the behaviour or performance of a macroscale system. However, it is generally challenging to have atomic structure considered in continuum modelling, which will affect the accuracy of the resultant models. Continuum models that can describe the microscopic structure of aqueous electrolytes are so far very rare due to limited understanding of the crowdedly interplayed physical interactions in nanoconfinement and the lack of approaches for quantitatively measuring or parameterizing the interplayed physical interactions. Using water-filled graphene nanoslits and a range of selected aqueous electrolytes as a model system, this PhD work aims to examine the critical role of nanoconfined water structure on the electrolyte ion structure and develop nanoscience-based continuum models to describe quantitatively the microscopic electrolyte structure that are parameterized with MD simulations. Such an approach enables the proposed continuum models to have the essential components necessary to reproduce the microscopic electrolyte structure observed in MD simulations, meanwhile, to maintain its capability to predict and design nanoconfined aqueous-electrolyte-based applications on a large scale. Specifically, the spatial density of aqueous electrolytes including NaBF4, LiBF4, and CsBF4 in non-electrified graphene nanoslits was first studied. By incorporating the non-electrostatic interaction energy between ions and graphene wall from the MD simulations, the modified Poisson-Boltzmann model can capture the oscillated layering of ion density profiles. The accuracy of the resultant continuum model can be further improved after the water distribution effect was considered through a new lattice-gas model. The conventional Poisson-Boltzmann model was then modified to improve the prediction of electric potential values in the electrified interface system. After the orientation of interfacial water molecules was considered, the modified continuum model can remedy the oversimplified surface potential values predicted by the Poisson-Boltzmann model and the artificial layer equipped by an implicit dielectric constant in the Poisson-Boltzmann-Stern model. The continuum models developed were then combined with the nuclear magnetic resonance spectra of the aqueous electrolytes absorbed between graphene layers obtained by experimental collaborators to study the ion absorption density inside multilayered graphene membranes. The high simulation efficiency of the continuum modelling enabled the investigation of the membrane thickness effect on ion absorption density inside nanochannels. The prediction of the continuum model was in good agreement with experimental results when the slit sizes were relatively large (> 1.2nm). It also revealed that the electrical polarization of the graphene membrane contributed to the electroneutrality breakdown in nanochannels. In addition, the results show that not only the ion-graphene interaction strength but also the ion layered distribution structure played dominant roles in the ion accessibility inside nanochannels.

Turbulent jets and plumes form when a fluid of one density is injected into another quiescent fluid of same density or a different density, respectively. From violent volcanic eruptions to the smoke rising from a cigarette, these flows are omnipresent in nature and engineering environments at a wide range of scales. In this dissertation, experimental measurements of simultaneous, time-resolved velocity and density using particle image velocimetry (PIV) and planar laser induced florescence (PLIF) are carried out to analyse such flows in a laboratory setting. Unlike non-buoyant flows like turbulent jets, plumes pose a challenge in using standard optical measurement techniques PIV and PLIF, because of the local changes in refractive index, when two fluids mix. This has led to most of the previous research being focussed on global measurements of entrainment, whereas the local measurements, which are required for a clearer understanding of the entrainment phenomenon, are practically non-existent. One of the ways to circumvent this problem is to match the refractive index of two solutions while maintaining the density difference, by adding certain chemicals to them. These chemicals suggested in the literature are compared, and one of the combinations of KH2PO4 and glycerine is found to be most suitable to be used in laboratory environments. The combination, although having several advantages over the commonly used solution, is rarely employed by researchers because the attenuation coefficients are not characterised. Here we characterise these solutions for simultaneous PIV/PLIF measurements by evaluating the attenuation of light passing through it. Apart from the obvious advantages such as being safer to use, allowing higher density differences and easy to store, it also causes lower attenuation than only other characterised combination of chemicals, ethanol and NaCl. Velocity and density measurements with and without refractive index matching are carried out. Not matching the refractive index results in over-prediction of turbulence fluctuations in the flow. The error induced is directly related to the refractive index mismatch between the measurement location and the ambient. A correction procedure is developed to correct for the distortions caused by refractive index mismatch. The method is observed to work by correcting the distorted flow-fields by using a known correctly measured refractive index (RI) field as well was a modelled RI field based on the probability density fields of RI. A new second-order integral model for the prediction of volume, momentum and buoyancy fluxes is developed. The several existing integral entrainment models in the literature are compared for prediction based on the data obtained by the present experiments as well as data taken from literature. The new model fares well in comparison. The model also quantifies the contributions to entrainment coefficient from the physical processes in the flow like turbulence, pressure and the varying shape of the profiles of velocity and density. The turbulence contribution to the entrainment in jets is slightly lower than its contribution in plumes. This suggests that the higher entrainment in plumes is related more to the mean buoyancy than buoyancy induced turbulence. The local entrainment process at the smallest scales is examined. This is accomplished by identifying and tracking the turbulent/non-turbulent interface and directly calculating the local entrainment velocity on it. This is made possible by the implementation of high temporal and spatial resolution velocity and density measurements. The characteristic of local entrainment velocity for jets agrees well with the literature confirming the accuracy of the methodology to measure local entrainment velocity. The procedure is extended to application in plumes. Buoyancy on global level results in an increase of entrainment in the plume when compared to jet. However, on the local level buoyancy does not directly affect the properties of local entrainment velocity, rather the entrainment velocity scales directly with the smallest velocity scales in the flow, the Kolmogorov velocity scales. As such, from a local point of view, a larger Kolmogorov velocity scales in plumes result in larger entrainment in plumes compared to jets. The instantaneous interface exhibits fractal behaviour, and the fractal scaling obtained agrees well with the literature. Finally, we confirm that in plumes, the mass-flux across the TNTI is observed to be independent of the scale of measurement.

Rotating flows and induced convection by centrifugal forces are prevalent in nature and also encountered in several engineering applications. This study is inspired by an engineering problem with relevance to the modern gas-turbine engine. In an internal air system of a high-pressure compressor, cavities form between the co-rotating compressor disks. The fluid flow due to the rotation of these cavities and the induced heat transfer rate from the disks directly affects the operational efficiency and safety of a gas turbine engine. The fluid flow inside these cavities exhibits complex phenomena as it involves a multitude of control parameters such as Rayleigh number, which defines the strength of the buoyancy-induced force to viscous force, the Rossby number, which characterizes the significance of the Coriolis forces induced due to the rotation and the flow Mach number. Direct numerical simulations for a closed cavity configu- ration are conducted with a systematic variation of parameters to scrutinize their effects on the flow quantities and the heat transfer rate. An interplay between these parameters is further investigated by conducting the linear-stability analy- ses to find the critical values of these parameters at the onset of convection. The investigations show that compressibility effects lead to a reduction of the growth rate of the dominant mode, and it modifies the overall formation of convection cells in the cavity. A stability criterion is proposed that showed that both Rossby and Mach number affect the stability of flow in the rotating cavities. A para- metric study of Rossby number suggests that a small change in the magnitude of Coriolis forces directly influences the behaviour of convection plumes and induced heat transfer rate. The near-wall temperature profiles in the plume-ejection region exhibit the logarithmic behaviour analogous to turbulent shear flows and recon- cile the transition to the ultimate regime of convection with an increased power exponent of N u–Ra scaling law. Further, first-ever high-fidelity simulations are carried out for a cavity with an axial-through flow, which closely represents the internal air cooling system of a gas turbine engine, to shed light into the flow structure that previously was poorly understood. The results show a flow structure dominated by a toroidal vortex in the inner region of the cavity. In the remaining outer region of the cavity, radial flares emerge from the toroidal vortex which forms cyclonic and anti-cyclonic vortices and are found to be responsible for thermal mixing and heat transfer from the side disks. In the outer region, the flow is observed to move radially outwards by Ekman layers formed on the side disks. The near shroud region is mostly dominated by the centrifugal buoyancy-induced flow and the Nusselt number values, which measure the effectiveness of convection heat transfer inside the cavity, highlights the inefficacy of axial-through flow to enhance the overall heat transfer rate.

Wall-bounded turbulent flows are pervasive in nature and are also encountered in many engineering applications; common examples include the flow over an airplane wing, or the atmospheric boundary layer over the Earth's surface, etc. A dominant feature present within these flows is the appearance of recurring eddies or so-called coherent structures that are highly three-dimensional (3-D) in geometry and are statistically significant over a wide range of scales. This has led to the proposal of various coherent structure-based models in the literature, with the attached eddy model (AEM) of wall-turbulence being the most popular amongst them. Their predictive capabilities, however, are still lacking due to the dearth of 3-D information on the coherent motions which they model. The present thesis reports a new and unique set of multi-point hotwire measurements conducted in a frictional Reynolds number, $Re_{\tau}$ $\sim$ $\mathcal{O}$(10$^4$) canonical turbulent boundary layer (TBL) to reconstruct the 3-D statistical picture of these energy-containing motions. The measurements are complemented by performing a similar reconstruction using published direct numerical simulation datasets at $Re_{\tau}$ $\sim$ $\mathcal{O}$(10$^3$), thereby facilitating an examination of the scaling of these structures, in flows spanning over a decade of $Re_{\tau}$. Results of these investigations provide direct empirical support towards the AEM, with the prospect of further enhancing its efficiency by defining the representative eddy geometry based on data-driven estimates. The first part of the thesis focuses on investigating characteristics of the inertially dominated wall-coherent structures (i.e. the ones extending down to the wall), which are responsible for the increased skin-friction in high-$Re_{\tau}$ TBLs. Their geometric characteristics are investigated in the wall-parallel plane by estimating, for the first time, the 2-D cross-spectrum of the streamwise velocity using the synchronous velocity fluctuations measured at a log-region ($z_{o}$) and near-wall ($z_{r}$) location. Constant energy contours of this spectrum, which are representative of the energy distribution across the range of streamwise (${\lambda}_{x}$) and spanwise (${\lambda}_{y}$) wavelengths, are found to follow the ${{\lambda}_{x}}/{z_{o}}$ $\approx$ 7(${{\lambda}_{y}}/{z_{o}}$) relationship in the large-scale range, indicative of geometric self-similarity. This suggests that a self-similar structure conforming to Townsend's attached eddy hypothesis (Townsend 1976) is ingrained in the flow, and can be conceptually modelled using the AEM framework given by Perry \& Chong (1982). The very-large-scale wall-coherent structures (i.e. the superstructures), on the other hand, do not conform to Townsend's attached eddies and are found to have a similar spanwise width as the largest motions in the self-similar hierarchy. This result, which is found via a scale-specific coherence analysis of the velocity fluctuations, also reveals the periodic organization of the superstructures along the spanwise direction. Finally, an analysis of the scale-specific phase of the coherence reveals the streamwise inclination angle of the large wall-coherent motions, which is found to be nominally 45$^{\circ}$. This fulfills the minimum geometric information required to statistically model these energetic wall-coherent motions based on the AEM. The second part of the thesis focuses on investigating the range of energy-containing structures coexisting in the log-region, which contribute significantly to the bulk turbulence production in high-$Re_{\tau}$ wall-bounded flows. Townsend (1961) hypothesized that these structures can be segregated into active and inactive motions, where the active motions are solely responsible for producing the Reynolds shear stress, the key momentum transport term in these flows. While the wall-normal component of velocity is associated exclusively with the active motions, the wall-parallel components of velocity are associated with both active and inactive motions. To test this hypothesis, the present study proposes a methodology to segregate the active and inactive components of the 2-D energy spectrum (${\Phi}_{ii}$, where $i$ denotes the velocity-component) at $z_{o}$, thereby permitting to test the self-similarity characteristics of the former which are central to theoretical models for wall-turbulence. The methodology utilizes the multi-point dataset, in conjunction with a spectral linear stochastic estimation-based procedure, to linearly decompose the total energy at $z_{o}$ (${\Phi}_{ii}$) into contributions predominantly from the active (${\Phi}^{a}_{ii}$) and inactive (${\Phi}^{ia}_{ii}$) motions. This is confirmed by ${\Phi}^{a}_{ii}$ exhibiting wall-scaling for both ${\lambda}_x$ and ${\lambda}_y$. The Reynolds shear stress cospectra, estimated solely from the active contributions, is also found to closely match the one obtained conventionally from the dataset, thereby providing direct empirical support for the concept of active and inactive motions. Both ${\Phi}^{a}_{ii}$ and ${\Phi}^{ia}_{ii}$ contours are found to depict geometric self-similarity in the log-region, suggesting that this entire region can be conceptually modelled using the AEM framework. Inactive contributions from the attached eddies also bring out the pure $k^{-1}$-scaling for the associated 1-D spectra (where $k$ is the streamwise/spanwise wavenumber), lending further empirical support to the AEM.

A major area of interest in engineering is the skin-friction drag and convective heat transfer of surfaces in turbulent flow, such as turbine blades, marine vehicles, and airplanes. While these surfaces may appear smooth, they almost always have some form of roughness, for example, pitting on the surface of a turbine blade, barnacles on the hull of a marine vehicle, or rivets on the wings of an airplane. For a given roughness and flow speed, the Moody diagram can be used to find the frictional drag or pressure drop. A similar diagram can be constructed to find heat transfer. Although widely used, the biggest limitation of the Moody diagram is that the Nikuradse equivalent sand grain roughness has to be known for the rough surface in question. Another limitation of the Moody diagram is in predicting skin friction for transitionally rough surfaces, owing to the unrepresentative Colebrook fit. Also, while the effects of varying key roughness topographical parameters on momentum transfer have been studied extensively, relatively little is known on heat transfer. Over the years, researchers have used computational and experimental methods to investigate the flows over a number of roughness types. This thesis expands on the computational works on sinusoidal roughness by systematically investigating the effect of varying roughness solidity on both momentum and heat transfer in turbulent air flow, and the underlying flow physics that give rise to the observed behaviour. Rough-wall flows transfer more momentum and heat when compared to smooth-wall flows, and it is found that an increase in solidity for a matched equivalent sand-grain roughness height causes a greater increase in heat transfer than the increase in momentum transfer due to increased wetted area and increased recirculation region that facilitates mixing.

Gravity currents are horizontal flows of fluid of a higher density into an ambient fluid of slightly lower density. They occur frequently in the atmosphere as sea-breeze fronts, thunderstorm outflows, katabatic flows etc., and are also encountered in industrial applications. The initial density difference between the two fluids can either be due to the presence of a salt or a temperature difference. While a majority of the studies employ a salinity based stratification, this work focuses on the flow dynamics of a gravity current generated as a result of an initial temperature difference. In the laboratory environment, a gravity current can be produced using a lock-exchange experiment in which the two fluids, initially at rest, are separated by a vertical barrier (or lock gate). At time $t$ = 0, a rapid removal of the lock gate results in the formation of a gravity current. The present gravity currents were produced in a Perspex tank of 2.0 m x 0.2 m x 0.2 m where the lock was located mid-way. The present flows were first visualized by mixing a dye in the heavier (cold) side to evaluate the bulk properties of the flow e.g. Froude number, $Fr$. Subsequently, simultaneous measurements of streamwise velocity and temperature field were conducted using the single-component molecular tagging velocimetry (1c-MTV) and molecular tagging thermometry (MTT) respectively. These experiments were focused at the interface between the hot and cold fluid to estimate the resultant mixing across the interface. The measurements were acquired using a 1024 x 1024 pixel Princeton Instruments PI: MAX4 camera and were shown to resolve the Kolmogorov (velocity) and Batchelor (scalar) length scales. To the author's knowledge, to date no previous experimental study has documented lock-exchange mixing at this level of resolution. The obtained density (temperature) distribution allows an estimation of the background potential energy of the flow which was used to quantify the diapycnal mixing. Specifically, mixing is attributed to the irreversible changes in fluid properties associated with fluid motions [1] and therefore differentiated from buoyancy induced reversible stirring. These measurements yield a mixing efficiency of 0.13 for the Reynolds number range considered ($Re \leq \mathcal{O}(10^4)$). Flow analysis revealed that the locally high values of mixing efficiency occur \textit{after} the occurrence of certain dissipative stirring events in the flow. These events, largely associated with vortical overturns, are commonly observed at the interface between the two fluids and are shown to lead the locally efficient mixing.

Flames diluted by combustion products can reduce emissions such as Carbon Monoxide (CO) and Oxides of Nitrogen (NOx) in industrial applications. In applications such as gas turbines, these flames are confined in a combustor and can interact with relatively cold walls. This interaction can quench the flame, producing incomplete combustion products. In this study, Flame-Wall Interaction (FWI) for methane/air flames diluted by hot combustion products was investigated using Direct Numerical Simulation (DNS). One-Dimensional (1D) Head-On Quenching (HOQ) was first simulated to examine operating parameter effects on CO emissions from transient quenching processes. Average CO within the quenching region was used to evaluate these effects, and the species transport budget was used to investigate the dominant terms. At higher dilution levels, the peak average near-wall CO decreases, and the rate of near-wall CO reduction also decreases. At higher wall temperatures, the peak average near-wall CO and its reduction rate increases. The near-wall CO may be modelled under some conditions using only the integrated diffusion term. Then, a two-Dimensional (2D) laminar V-flame was simulated in both steady and forced conditions. The changes in peak near-wall CO due to varying dilution level and wall temperature show similar trends to the 1D results. The exhaust CO is linked directly to the oxidation residence time, which is determined by the flame length. Due to the role of the flame length, the contribution of near-wall CO to the exhaust CO increases as dilution level or the wall temperature is reduced. Premixed flames can extinguish inside the cold-wall thermal boundary layer, which can leave high near-wall CO. This results in disproportionate levels of CO mass flux in the near-wall regions. The near-wall CO features large variations when the local Damkohler number is greater than 0.1. Analysis of the CO transport budget shows that unlike 1D simulation, both convection and diffusion dominate the CO transport in the near-wall region, except for the case with autoignition at the wall. Finally, a three-Dimensional (3D) turbulent V-flame in a channel was simulated with hot and cold walls. A main reaction zone in the central region supported by periodic bulk ignition events changes the position of volumetric reaction zones where CO is formed. Consistent with the 2D results, a lower wall temperature leads to a longer flame, thereby having more contribution to the exhaust CO. Near-wall turbulence-flame interaction creates wrinkled and streaky flame surfaces, and localizes the near-wall CO distribution. The high mean of CO mass fraction locates in the free-stream where the free-stream autoignition happens, while the high RMS of CO mass fraction is present closer to the wall. 1D flame solutions might be sufficient for modelling CO in the free-stream region and some parts of the near-wall region but not closer to be adjacent to the wall. Turbulent mixing and diffusion contribute to this deviation. These results set a benchmark for future near-wall CO modelling.

The behaviour of turbulent boundary layers over surfaces composed of spanwise-alternating smooth and rough strips is investigated experimentally. The width of the strips S vary such that 0.32 < S/\delta < 6.81, where \delta is the boundary-layer thickness averaged over one spanwise wavelength of the heterogeneity. The experiments are configured to examine the influence of spanwise variation in wall shear stress over a large S/\delta range. Hot-wire anemometry (HWA) and particle image velocimetry (PIV) reveal that the half-wavelength S/\delta governs the diameter and strength of the resulting mean secondary flows. Three possible cases are observed: limiting cases where S/\delta << 1 or S/\delta >> 1 and the secondary flows are either confined near the wall or near the roughness change, respectively, and intermediate cases (S/\delta \approx 1), where the secondary flows fill the entire boundary layer and the outer layer similarity is destroyed. The size and strength of the time-averaged secondary flows are approximately capped by either the boundary-layer thickness \delta or the roughness patch width S. Instantaneously, however, these secondary flows appear very similar to naturally occurring large-scale structures that are spanwise-locked by the roughness transition with a residual meandering tendency about these locations. The efficacy of the roughness to lock the secondary flows in place and the meandering of the secondary flows are a function of S/\delta, most prominent when S/\delta \approx 1. Further analysis of the energy spectrograms and fluctuating flow fields obtained from PIV show that both secondary flows and the naturally occurring large-scale structures formed in turbulence over smooth walls meander in a similar manner and both coexist in the limits where S/\delta << 1 and S/\delta >> 1.

Flow passing over the surface of vehicles creates significant skin-friction drag. The reduction of that drag through flow-control techniques, driven by environmental and financial incentives, has already received substantial attention by fluid mechanicians and will continue to be one of the prominent topics in the field. In this dissertation, we study turbulent flow over riblets, i.e. over tiny streamwise-aligned surface grooves that have the potential to reduce skin-friction drag compared to a smooth wall. Small riblets with spacings of typically less than 20 viscous units (a few tens of micrometres on an aircraft fuselage in cruise conditions) are known to reduce skin-friction drag compared to a smooth wall, but larger riblets allow inertial-flow mechanisms to appear and cause drag reduction to break down. One of these mechanisms is a Kelvin-Helmholtz instability that Garcia-Mayoral & Jimenez (J. Fluid Mech., vol. 678, 2011, pp. 317-347) identified in turbulent flow over blade riblets. In order to evaluate its dependence on riblet shape and thus gain a broader understanding of the underlying physics, we employ the minimal-span channel concept for cost-efficient Direct Numerical Simulations of rough-wall flows (MacDonald et al., J. Fluid Mech., vol. 816, 2017, pp. 5-42). This allows us to investigate seven different riblet shapes and various viscous-scaled sizes between those of maximum drag reduction and significant drag increase for a total of 29 configurations. We verify that the small numerical domains capture all relevant physics by varying the domain size and by comparing to reference data from full-span channel flow. Specifically, we find that, in the previously identified spectral region occupied by drag-increasing Kelvin-Helmholtz rollers, the energy-difference relative to smooth-wall flow is not affected by the narrow domain, even though these structures have large spanwise extents. This allows us to evaluate the influence of the Kelvin-Helmholtz instability by comparing the flow fields over riblets to that over a smooth wall. We find that in this data set only large sharp-triangular and blade riblets have a drag penalty associated with the Kelvin-Helmholtz instability and that the mechanism appears to be absent for blunt-triangular and trapezoidal riblets of any size. We therefore investigate two indicators for the occurrence of Kelvin-Helmholtz rollers in turbulent flow over riblets. First, we confirm for the different riblet shapes that the groove cross-sectional area in viscous units serves as a proxy for the wall-normal permeability that is necessary for the development of Kelvin-Helmholtz rollers. Additionally, we find that the occurrence of the instability correlates with a high momentum absorption at the riblet tips. The momentum absorption can be qualitatively predicted using Stokes flow. We further investigate the drag characteristics of multi-scale riblets, i.e. trapezoidal grooves with a half-height riblet in the centre. Garcia-Mayoral & Jimenez (J. Fluid Mech., vol. 678, 2011, pp. 317-347) proposed to measure the riblet size by the square root of their cross-sectional area $\ell_g^+$, which scales the size of minimum drag for different fully open single-scale grooves. We find that $\ell_g^+$ is not the optimal description of the riblet size for multi-scale geometries. Upon investigating effects of the secondary riblet on the flow field and overall drag of the surface, we propose a generalised measure of the riblet size for multi-scale surfaces.

Studies pertaining to turbulent plumes in confined spaces are of utmost interest due to its relevance in practical flows that are associated with, but not restricted to, the propagation of smoke and hot gases generated by fires in buildings, road and railway tunnels, etc. In this dissertation, direct numerical simulations (DNS) of the governing equations are carried out to analyze such flows with the focus on (i) free turbulent line plumes, and (ii) wall attached turbulent line plumes, in confined spaces. In all cases, the computation domain is rectangular with no-slip and adiabatic boundary conditions at the top, bottom, and lateral side walls. In free turbulent line plume simulations, the plume originates from a line heat source of length, L, located at the centre of the bottom wall and rises until it impinges on the top wall and eventually spreading out laterally thereby producing a buoyant fluid layer at the top wall. Since the region is confined, the continuous heat source forces the top layer to move downwards, until it reaches the bottom wall, when the flow is said to be at the asymptotic state (Baines and Turner 1969). DNS data at three Reynolds numbers (ReH), 1800, 3600 and 7200, based on box height H and the buoyant velocity scale, F_1/3 0 , where F_0 is buoyancy flux per unit length, are presented for plume lengths, L/H = 1, 2 and 4 and box aspect ratio, R/H = 1. Here, R is the box half-width. Following the initial transient dynamics, a flapping motion of the plume is observed, where the plume oscillates around the centre plane of the box. The DNS results reveal that the long-term behavior of the flow consists of a meandering, flapping plume with a counter-rotating vortex pair on either side of the plume. Additionally, the plume volume, momentum, and buoyancy fluxes obtained from the simulations are compared to the theoretical models proposed by Baines and Turner (1969) and Barnett (1991). Further, simulations of turbulent line plumes are carried out at increased box aspect ratios R/H = 1, 2, 4, 8 and 16, to study the horizontal outflow of the buoyant fluid layer after the plume impinges on the top wall. Following the axisymmetric plume model of Kaye and Hunt (2007), a theoretical model to compute the horizontal outflow properties is developed for turbulent line plumes. In the case of wall attached thermal plumes, the plume originates from a local line heat source placed at the bottom left corner of the box. The plume develops along the vertical side wall while remaining attached to it before spreading across the top wall forming a buoyant fluid layer and eventually moving downwards and filling the whole box. The simulations are carried out at ReH = 14530 and L/H = 0.5, and a parametric study is conducted for boxes of aspect ratios R/H = 1 and 2. Furthermore, the original filling box model of Baines and Turner Baines and Turner (1969) is modified to incorporate the wall shear stress and are compared against the results obtained from the DNS. A reasonable agreement is observed for the volume and momentum fluxes in the quiescent uniform environment and for the time-dependent buoyancy profiles calculated further away from the plume. Finally, the entrainment processes in both free and wall attached line plumes are assessed, using the DNS data. Both cases show similar contributions to entrainment due to net buoyancy. However, a deficit in the entrainment coefficient is observed for wall plumes due to the effect of the wall, which in turn suppressed the turbulent kinetic energy production.