Many real-world engineering problems require large amounts of data in order to accurately model and predict outcomes. However, this data is often noisy, sampled and discontinuous, making the data difficult to process and giving rise to incorrect models. In order to address this issue, different interpolation techniques are commonly used to make the data continuous. This can then followed by a filtering process in order to reduce noise and further reduce discontinuities. In this report, our approach to filtering is the use of convolution kernels, which smooths out the data. By doing so, a better visual representation of the limited data available can be obtained. For instance, in the specific case of studying streamlines and vortices, filtering techniques have been used to produce more realistic plots. While the use of filters can be beneficial, it is important to note that the choice of filter and its parameters can greatly impact the results obtained. In particular, we found that, for the filters we studied, applying these to analytical functions can actually increase the error. On the other hand, when filters are applied to discontinuous functions, they can improve the accuracy of the data. Overall, when analyzing stream functions with filters, significant improvements can be seen in the quality of the data. This underscores the importance of careful selection and application of filtering techniques in engineering problems that involve large amounts of noisy and discontinuous data.

京都大学 / 新制・課程博士 / 博士(工学) / 甲第24211号 / 工博第5039号 / 新制||工||1787(附属図書館) / 京都大学大学院工学研究科社会基盤工学専攻 / (主査)教授 中北 英一, 准教授 山口 弘誠, 教授 田中 賢治 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

The contributions of vortex stretching, dilatation, baroclinic torque, and viscous diffusion to vorticity transport are experimentally investigated in a high-Reynolds number cavity combustor using high-speed particle image velocimetry and broadband chemiluminescence. An adaptive wall geometry forming converging, diverging, and nominal configurations is implemented to study the effects of pressure gradient on local flow physics and vorticity dynamics. The spatial profiles of the local turbulence terms are conditioned on the mean flame front to characterize the influence of the pressure gradient field and exothermic heat release on vortex dynamics in the cavity. In addition to isolate the influence of combustion on the flow, a nonreacting analysis is performed and a correlation is made between combustor geometry and the turbulence transport processes. Vorticity transport through dilatation was found to be significant relative to the other transport terms across all the configurations studied. These results contrast with direct numerical simulations of high Reynolds number flows in homogeneous isentropic turbulence. In addition, a scaling is proposed to quantify the significance of the flow induced vorticity and pressure fields on dilatation and baroclinic torque vorticity production. Experimental studies of similar confined combustors show a similar trend to the numerical studies with baroclinic torque dominating the transport mechanisms, motivating this study to understand the dependence of vorticity transport on the underlying flow physics.

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One of the key open problems in the field of theoretical fluid mechanics concerns the possibility of the singularity formation in solutions of the 3D Navier-Stokes system in finite time. This phenomenon is associated with the behaviour of the enstrophy, which is an L2 norm of the vorticity and must become unbounded if such a singularity occurs. Although there is no blow-up in the 2D Navier-Stokes equation, we would like to investigate how much enstrophy can a planar incompressible flow in a bounded domain produce given certain initial enstrophy. We address this issue by formulating an optimization problem in which the time derivative of the enstrophy serves as the objective functional and solve it using tools of the optimization theory and calculus of variations. We propose an efficient computational approach which is based on the iterative steepest-ascent procedure. In addition, we introduce an easy-to-implement method of computing the gradient of the objective functional. Finally, we present computational results addressing the key question of this project and provide numerical evidence that the maximum enstrophy growth exhibits the scaling dE/dt ~ C*E*E for C>0 and very small E. All computations are performed using the Chebyshev spectral method. / Thesis / Master of Science (MSc) / For many decades, scientists have been investigating fundamental aspects of the Navier-Stokes equation, a central mathematical model arising in fluid mechanics. Although the equation is widely used by engineers to describe numerous flow phenomena, it is still an open question whether the Navier-Stokes system always admits physically meaningful solutions. To address this issue, we want to explore its mathematical aspects deeper by analyzing the behaviour of the enstrophy, which is a quantity associated with the vorticity of the flow and a convenient measure of the regularity of the solution. In this study, we consider a planar and incompressible flow bounded by solid walls. Using basic tools of mathematical analysis and optimization theory, we propose a computational method enabling us to find out how much enstrophy can such a flow produce instantaneously. We present numerical evidence that this instantaneous growth of enstrophy has a well-defined asymptotic behavior, which is consistent with physical assumptions.

Bubbly turbulent flows occur in a variety of industrial, naval and geophysical problems. In these flows, the bubbles in the flow interact with turbulence and/or vortical structures present in the continuous phase, resulting in bubble motion and deformation, and at the same time modifying the turbulence and/or vortical structures. Despite the fact that this has been a subject of interest for some time, mechanisms of bubble break-up due to turbulence and turbulence modulation due to bubbles are not well understood. To help understand this two-way coupled problem, we study in this thesis, the interaction of single and multiple bubbles with vortical structures; the thesis being broadly divided in to three parts. In the first part, we study the interaction of a single bubble with a single vortical structure, namely a vortex ring, formed in the continuous phase (water). This may be thought of as a simplified case of the interaction of bubbles with vortical structures in any turbulent flow. We then increase the complexity and study the interaction of a single bubble with naturally occurring vortical structures present in a fully developed turbulent channel flow, and then finally to the case of a large number of bubbles injected in to a fully developed turbulent channel. The bubble motions and deformations in all three cases are directly imaged using high speed visualizations, while the flow field information is obtained using time-resolved Particle-Image Velocimetry (PIV) in the first two cases, and from pressure drop measurements within the channel in the latter case. The interaction of a single vortex ring with a bubble has been studied for a large range of vortex ring strengths, represented in terms of a Weber number (We). We find that in all cases, the bubble is first captured by the low pressure within the core of the ring, then stretched azimuthally within the core, and gradually broken up in to a number of smaller bubbles. Along with these bubble deformations, the vorticity within the core of the ring is also modified significantly due to bubble capture. In particular, at low We, we find that the core of the ring fragments as a result of the interaction resulting in a large reduction in the enstrophy of the ring and its convection speed. In the second part of the thesis, interaction of a single bubble with naturally occurring vortical structures present in a fully developed turbulent channel is studied. In this case, single bubbles of different sizes are injected either from bottom or top wall into a channel at Reynolds number of about 60,000. We study the trajectories of the single bubble, and also investigate the effect that such bubbles have on the naturally occurring vortical structures present in these flows. The injected bubble is found to have three broadly different types of bubble paths when injected from the bottom wall, which are sliding along the wall, bouncing motions and vertical escape from the vicinity of the wall. Even at the same bubble diameter Db and channel flow Re, we find that different realizations show considerable variations, with all three bubble paths being possible. PIV measurements of a bubble captured by a naturally occurring vortical structure in the flow, shows a more rapid decrease in enstrophy compared to naturally occurring structures in the absence of bubbles, as seen in the interaction of a bubble with a vortex ring. We also find that the bubble can interact with multiple vortical structures, depending on their strength and spatial distribution in the flow, resulting in a complex bouncing bubble motion. In the third part of the study, a large number of bubbles are injected in to the channel through porous plates fixed at the top and bottom channel walls. The main parameters here are the channel Re, bubble void fraction (α) and the orientation of injection. In this case, in addition to bubble visualizations, the pressure drop through the channel is measured at different vertical locations. These measurements show large vertical variations in the measured pressure drop due to the presence of bubbles. The overall drag reduction in these cases is obtained from an integral of the pressure drop variation along the vertical direction. The visualizations show a number of bubble dynamics regimes depending on the parameters, with possibilities of both increased and decreased drag compared to the reference no bubble case. From simultaneous measurements, we relate the variations in drag reduction to the different bubble dynamics regimes. We find that at the same void fraction (α), the drag reduction obtained can be very different due to changes in bubble dynamics regimes caused by changes in other parameters. Top wall injection is observed to give good drag reductions over a wide range of flow Re and α, but is seen to saturate beyond a threshold α. In contrast, the bottom wall injection case shows that drag reduction continuously increases with αat high Re. The present study shows a maximum of about 60% increase and a similar 60% reduction in wall drag over the entire range of conditions investigated.

This thesis examines previously unresolved issues regarding the fluid dynamics of the spread of buoyant water into a rotating environment. We focus in particular on the role that finite potential vorticity and background turbulence play in determining the flow properties. When water of an anomalous density enters into an oceanic basin, gravity-driven surface flows can be established as a result of the density difference. These flows are often of a sufficiently large scale that the dynamics are affected by the Coriolis force arising from the rotation of the earth. This causes the formation of a large outflow gyre near to the source which feeds into a propagating gravity current that is confined to the coast. Previous experimental work in this field has sought to simplify the problem through the use of a point source and a quiescent ambient. We extend this work to provide a better representation of the real-world flow by introducing a source of finite depth and background turbulence to the rotating ambient. This study seeks to answer three key questions that are critical to the understanding of the flow behaviour in this scenario. First, what is the effect of the finite potential vorticity of the outflow on the properties of the outflow vortex and the boundary current? Second, what role does the presence of the the outflow vortex play in determining the behaviour of the current? Third, what is the effect of background turbulence on the flow properties? To carry out the investigation, experiments were conducted in the laboratory and compared with a theoretical description of the flow. The currents are generated inside a rotating tank filled with saltwater by the continuous release of buoyant freshwater from a source structure located at the fluid surface. A horizontal source of finite depth is used to introduce finite potential vorticity into the outflow. The impact of background turbulence is examined by introducing an oscillating grid into the rotating tank. We find that the finite potential vorticity of the outflow plays an important role in determining the flow properties for sufficiently low Rossby and Froude number. As the value of these parameters is increased a zero potential vorticity model is able to capture the key elements of the flow behaviour. The outflow vortex is found to act as a time-varying source to the boundary current, with the current velocity fixed by the vortex velocity field. The vortex vorticity is seen to decrease with time, while the vortex radius continues to increase at late times despite the vortex having reached a limiting depth, which enables potential vorticity to be conserved and the current to be supplied with a non-zero velocity. Finally, the structure of the background turbulence is found to be key in determining the effect that it has on the flow properties, with different behaviours observed for three-dimensional and quasi- two-dimensional turbulence.

Les tourbillons sont des structures importantes pour une large gamme d'écoulements de fluides, notamment les sillages, l'interaction fluide-structure, les décollements de couche limite et la turbulence. Cependant, les méthodes numériques classiques n'arrivent généralement pas à donner une représentation précise des tourbillons. Ceci est principalement lié à la dissipation numérique des schémas qui, si elle n'est pas spécifiquement calibrée pour le calcul des écoulements tourbillonnaires, conduit à une diffusion artificielle très rapide des tourbillons dans les calculs. Parmi d'autres approches, la méthode "Vorticity Confinement" (VC) de J. Steinhoff permet de compenser la dissipation des schémas au sein des tourbillons en introduisant une anti-dissipation non-linéaire, mais elle n’est précise qu’au premier ordre. D’autre part, des progrès significatifs ont récemment été accomplis dans le développement de méthodes numériques d’ordre élevé. Celles-ci permettent de réduire ce problème de dissipation excessive, mais la diffusion des tourbillons reste importante pour de nombreuses applications. La présente étude vise à développer des extensions d’ordre élevé de la méthode VC pour réduire cette dissipation excessive des tourbillons, tout en préservant la précision d'ordre élevé des schémas. Tout d'abord, les schémas de confinement sont analysés dans le cas de l'équation de transport linéaire, à partir de discrétisations couplées et découplées en espace et en temps. Une analyse spectrale de ces schémas est effectuée analytiquement et numériquement en raison de leur caractère non linéaire. Elle montre des propriétés dispersives et dissipatives améliorées par rapport aux schémas linéaires de base à tous les ordres de précision. Dans un second temps, des schémas VC précis au troisième et cinquième ordre sont développés pour les équations de Navier-Stokes compressibles. Les termes correctifs restent conservatifs, invariants par rotation et indépendants du schéma de base, comme la formulation originale VC2. Les tests numériques valident l'ordre de précision et la capacité des extensions VC d’ordre élevé à réduire la dissipation dans les tourbillons. Enfin, les schémas avec VC sont appliqués au calcul des écoulements turbulents, dans une approche de simulation de grandes échelles implicite (ILES). Les schémas numériques avec VC présentent une résolvabilité améliorée par rapport à leur version linéaire de base, et montrent leur capacité à décrire de façon cohérente ces écoulements tourbillonnaires complexes. / Vortices are flow structures of primary interest in a wide range of fluid dynamics applications including wakes, fluid-structure interaction, flow separation and turbulence. Albeit their importance, standard Computational Fluid Dynamics (CFD) methods very often fail to provide an accurate representation of vortices. This is primarily related to the schemes’ numerical dissipation which, if inadequately tuned for the calculation of vortical flows, results in the artificial spreading and diffusion of vortices in numerical simulations. Among other approaches, the Vorticity Confinement (VC) method of J. Steinhoff allows balancing the baseline dissipation within vortices by introducing non-linear anti-dissipation in the discretization of the flow equations, but remains at most first-order accurate. At the same time, remarkable progress has recently been made on the development of high-order numerical methods. These allow reducing the problem of excess dissipation, but the diffusion of vortices remains important for many applications. The present study aims at developing high-order extensions of the VC method to reduce the excess dissipation of vortices, while preserving the accuracy of high-order methods. First, the schemes are analyzed in the case of the linear transport equation, based on time-space coupled and uncoupled formulations. A spectral analysis of nonlinear schemes with VC is performed analytically and numerically, due to their nonlinear character. These schemes exhibit improved dispersive and dissipative properties compared to their linear counterparts at all orders of accuracy. In a second step, third- and fifth-order accurate VC schemes are developed for the compressible Navier-Stokes equations. These remain conservative, rotationally invariant and independent of the baseline scheme, as the original VC2 formulation. Numerical tests validate the increased order of accuracy and the capability of high-order VC extensions to balance dissipation within vortices. Finally, schemes with VC are applied to the calculation of turbulent flows, in an implicit Large Eddy Simulation (ILES) approach. In these applications, numerical schemes with VC exhibit improved resolvability compared to their baseline linear version, while they are capable of producing consistent results even in complex vortical flows.

Swirling flows abound in nature and numerous engineering applications. Under conditions which are not completely understood, the swirling cores could undergo a sudden enlargement of their vortex core, leading to a ’vortex breakdown’. The physics of vortex breakdown and strategies to control it have been active areas of research for nearly half a century. There are many competing theories of vortex breakdown in the literature; broadly, these are surmised on similarities to flow separation, hydrodynamic instability or transition from a supercritical to a subcritical state. However, a rational criterion for vortex breakdown continues to be elusive. One of the most well known criteria in the literature is the one due to Brown and Lopez (1990) based on an inviscid vortex dynamics model which suggests that the helix angle of the velocity vector should enclose the helix angle of the vorticity vector. However it appears that this only suggests that the stream surface would diverge and not necessarily constitute a condition for breakdown. In this work, we propose a new criterion based on helicity (scalar product of velocity and vorticity vectors) for characterizing breakdown since it has fundamental topological interpretations relating to change in linkages of vortex lines. In particular, it is suggested that the breakdown location corresponds to the location where helicity becomes zero. We study the problem of vortex breakdown in a cylindrical container with a rotating top lid in order to clarify and elucidate our hypothesis. We present results from Direct Numerical Simulation of this problem for three different Reynolds numbers and evaluate the utility of our proposed helicity criterion. Our studies indicate that helicity is indeed a better choice for characterizing vortex breakdown.

abstract: Chiral symmetry and its anomalous and spontaneous breaking play an important role in particle physics, where it explains the origin of pion and hadron mass hierarchy among other things. Despite its microscopic origin chirality may also lead to observable effects in macroscopic physical systems -- relativistic plasmas made of chiral (spin-$\frac{1}{2}$) particles. Such plasmas are called \textit{chiral}. The effects include non-dissipative currents in external fields that could be present even in quasi-equilibrium, such as the chiral magnetic (CME) and separation (CSE) effects, as well as a number of inherently chiral collective modes called the chiral magnetic (CMW) and vortical (CVW) waves. Applications of chiral plasmas are truly interdisciplinary, ranging from hot plasma filling the early Universe, to dense matter in neutron stars, to electronic band structures in Dirac and Weyl semimetals, to quark-gluon plasma produced in heavy-ion collisions. The main focus of this dissertation is a search for traces of chiral physics in the spectrum of collective modes in chiral plasmas. I start from relativistic chiral kinetic theory and derive first- and second-order chiral hydrodynamics. Then I establish key features of an equilibrium state that describes many physical chiral systems and use it to find the full spectrum of collective modes in high-temperature and high-density cases. Finally, I consider in detail the fate of the two inherently chiral waves, namely the CMW and the CVW, and determine their detection prospects. The main results of this dissertation are the formulation of a fully covariant dissipative chiral hydrodynamics and the calculation of the spectrum of collective modes in chiral plasmas. It is found that the dissipative effects and dynamical electromagnetism play an important role in most cases. In particular, it is found that both the CMW and the CVW are heavily damped by the usual Ohmic dissipation in charged plasmas and the diffusion effects in neutral plasmas. These findings prompt a search for new physical observables in heavy-ion collisions, as well as a revision of potential applications of chiral theories in cosmology and solid-state physics. / Dissertation/Thesis / Doctoral Dissertation Physics 2019