On the Structure and Dynamics of Sheared and Rotating Turbulence: Direct Numerical Simulations and Wavelet Based Coherent Vortex Extraction

The influence of rotation on the structure and dynamics of sheared turbulence is investigated using a series of direct numerical simulations. Five cases are considered: turbulent shear flow without rotation, with moderate rotation, and with strong rotation, where the rotation configuration is either parallel or antiparallel. For moderate rotation rates an antiparallel configuration increases the growth of the turbulent kinetic energy, while the parallel case reduces the growth as compared to the nonrotating case. For strong rotation rates decay of the energy is observed, linear effects dominate the flow, and the vorticity probability density functions tend to become Gaussian. Visualizations of vorticity show that the inclination angle of the vortical structures depends on the rotation rate and orientation. Coherent vortex extraction, based on the orthogonal wavelet decomposition of vorticity, is applied to split the flow into coherent and incoherent parts. It was found that the coherent part preserves the vortical structures using only a few percent of the degrees of freedom. The incoherent part was found to be structureless and of mainly dissipative nature. With increasing rotation rates, the number of wavelet modes representing the coherent vortices decreases, indicating an increased coherency of the flow. Restarting the direct numerical simulation with the filtered fields confirms that the coherent component preserves the temporal dynamics of the total flow, while the incoherent component is of dissipative nature

Tensor Approximation for Multidimensional and Multivariate Data

Tensor decomposition methods and multilinear algebra are powerful tools to cope with challenges around multidimensional and multivariate data in computer graphics, image processing and data visualization, in particular with respect to compact representation and processing of increasingly large-scale data sets. Initially proposed as an extension of the concept of matrix rank for 3 and more dimensions, tensor decomposition methods have found applications in a remarkably wide range of disciplines. We briefly review the main concepts of tensor decompositions and their application to multidimensional visual data. Furthermore, we will include a first outlook on porting these techniques to multivariate data such as vector and tensor fields

Visual analytics methods for shape analysis of biomedical images exemplified on rodent skull morphology

In morphometrics and its application fields like medicine and biology experts are interested in causal relations of variation in organismic shape to phylogenetic, ecological, geographical, epidemiological or disease factors - or put more succinctly by Fred L. Bookstein, morphometrics is "the study of covariances of biological form". In order to reveal causes for shape variability, targeted statistical analysis correlating shape features against external and internal factors is necessary but due to the complexity of the problem often not feasible in an automated way. Therefore, a visual analytics approach is proposed in this thesis that couples interactive visualizations with automated statistical analyses in order to stimulate generation and qualitative assessment of hypotheses on relevant shape features and their potentially affecting factors. To this end long established morphometric techniques are combined with recent shape modeling approaches from geometry processing and medical imaging, leading to novel visual analytics methods for shape analysis. When used in concert these methods facilitate targeted analysis of characteristic shape differences between groups, co-variation between different structures on the same anatomy and correlation of shape to extrinsic attributes. Here a special focus is put on accurate modeling and interactive rendering of image deformations at high spatial resolution, because that allows for faithful representation and communication of diminutive shape features, large shape differences and volumetric structures. The utility of the presented methods is demonstrated in case studies conducted together with a collaborating morphometrics expert. As exemplary model structure serves the rodent skull and its mandible that are assessed via computed tomography scans

The Vortex Dynamics of Laminar Separation Bubbles

Laminar separation bubbles (LSBs) are common features in low Reynolds number flows, and can have considerable performance impacts in applications such as hydrofoils, small-to-medium scale wind turbines, micro and unmanned aerial vehicles, glider planes, and aircrafts operating at low speed or high altitude. In particular, the very presence of an LSB can cause loss in lift, increase in drag, and/or unwanted noise emissions, while also leaving the flow in an unstable configuration, as only slight changes in the environment or operating conditions can lead to further detrimental effects, such as the sudden onset of stall. All of these performance impacts are rooted in the laminar--turbulent transition process of an LSB, where disturbance growth in the unstable shear layer leads to its roll-up and the formation of coherent shear layer vortices that govern the reattachment process and are the source of unsteady loads and noise emissions. Therefore, a comprehensive understanding of LSB transition and vortex dynamics is a prerequisite to the development of effective control strategies. The work completed as part of this thesis is at the forefront of this effort, as flow development in laminar separation bubbles is studied and a new forcing technique is developed and tested. The supporting data is experimental and is collected primarily by means of particle image velocimetry. First, flow development in a nominally two-dimensional LSB formed over an airfoil is studied. Forcing at the LSB fundamental frequency and the first subharmonic of this frequency are found to inhibit and promote the prevalence of vortex merging in the LSB, respectively. When left to develop naturally, the flow development is characterized by the periodic roll-up of the separated shear layer upstream of the mean maximum height location. The vortices are strongly two-dimensional at formation, but quickly develop spanwise deformations with downstream convection, leading to their breakdown to smaller scales near the mean reattachment point. The deformations take the form of spanwise undulations in the vortex filaments, which tend to develop at wavelengths ranging between one and seven times the streamwise wavelength of the structures. These undulations continually intensify, ultimately leading to the breakdown of the vortices, while re-orienting vorticity from the spanwise direction into the streamwise and wall-normal directions, creating hairpin-like structures. An instability mechanism is hypothesized to be responsible for the development of these spanwise undulations, and a new forcing technique is developed to target it. The technique is capable of producing deterministic, three-dimensional disturbances modulated to a desired spanwise wavelength, while holding all other parameters (amplitude, frequency, and streamwise wavelength) constant. This is achieved using two alternating current, dielectric barrier discharge (AC-DBD) plasma actuators arranged in streamwise succession, which are operated simultaneously. The upstream actuator produces a spanwise uniform disturbance, which is then spanwise modulated by the output of the downstream actuator, with a relative phase delay introduced in order to spatially superimpose the two outputs. The technique is verified to produce the desired disturbance characteristics through a detailed experimental characterization that considers both quiescent and in-flow conditions. The effects of this forcing technique and the subsequent growth in spanwise modes is studied in an LSB formed over a flat plate subject to an adverse pressure gradient. Disturbance growth is tracked throughout the LSB, identifying small amplitude disturbances of a frequency matching the primary Kelvin-Helmholtz instability that undergo convective amplification downstream of the mean separation point. In comparing results from forcing the flow with two and three-dimensional disturbances, with the latter modulated to a spanwise-to-streamwise wavelength ratio of 2:1, disturbance amplitudes in this region are higher for the three-dimensional case, indicating a preferential amplification of spanwise modes in the upstream boundary layer. While this growth may result from the underlying stability of the upstream boundary layer, it could also stem from a low frequency modulation of the base flow, as significant spanwise non-uniformities of the same wavelength are found in the unforced natural flow. Nevertheless, stability predictions in the LSB find that, regardless of the forcing scenario, the normal (two-dimensional) modes are subject to the highest amplification rates throughout the length of the LSB, while disturbance modes of an oblique wave angle of less than 30 deg. experience comparable, yet reduced, growth rates. Thus, disturbance growth in the LSB is confirmed to be spanwise wavelength dependent. The effectiveness of the spanwise modulated forcing, in terms of effecting change in disturbance and flow development, is justified, as its wavelength ratio (2:1) corresponds to a wave angle of 26.5 deg., while the other three-dimensional forcing configurations considered are less effective on account of their larger wave angles (33.7 and 45 deg.). The effect of unstable spanwise modal growth on the development of the LSB shear layer vortices and the ensuing vortex dynamics is assessed. The small amplitude perturbations tracked through the fore portion of the LSB manifest in the shear layer vortices, imparting a spanwise wavelength, if present, in the vortex filaments. Thus, in the case of two-dimensional forcing, the shear layer vortices remain largely two-dimensional until their breakdown, while for the three-dimensional forcing case, significant spanwise undulations develop at the 2:1 ratio prescribed by the forcing. The filaments surge forward in the streamwise direction downstream of the three-dimensional actuator's active regions, while lagging behind at spanwise locations downstream of the actuator gaps. A continual intensification of vortex stretching ensues, leading to rapid filament deformations. Through supporting observations from a simplified vortex filament model, the undulatory shape of the vortex filament is shown to self-induce a net rotational motion, causing the streamwise forward and rearward sections of the filament to tilt away and toward the wall, respectively. This, coupled with the wall-normal velocity gradient, causes the continual stretching of the filament. These vortex motions are observed consistently for all LSBs studied throughout this thesis, and apply more broadly to all LSBs, since regardless of how a spanwise undulations is initially produced, if present, a vortex filament will tend to develop in the way shown in any near-wall shear flow. Thus, these dynamics are found to be intrinsic to the breakup process of shear layer vortices in laminar separation bubbles

Visuelle Analyse großer Partikeldaten

Partikelsimulationen sind eine bewährte und weit verbreitete numerische Methode in der Forschung und Technik. Beispielsweise werden Partikelsimulationen zur Erforschung der Kraftstoffzerstäubung in Flugzeugturbinen eingesetzt. Auch die Entstehung des Universums wird durch die Simulation von dunkler Materiepartikeln untersucht. Die hierbei produzierten Datenmengen sind immens. So enthalten aktuelle Simulationen Billionen von Partikeln, die sich über die Zeit bewegen und miteinander interagieren. Die Visualisierung bietet ein großes Potenzial zur Exploration, Validation und Analyse wissenschaftlicher Datensätze sowie der zugrundeliegenden Modelle. Allerdings liegt der Fokus meist auf strukturierten Daten mit einer regulären Topologie. Im Gegensatz hierzu bewegen sich Partikel frei durch Raum und Zeit. Diese Betrachtungsweise ist aus der Physik als das lagrange Bezugssystem bekannt. Zwar können Partikel aus dem lagrangen in ein reguläres eulersches Bezugssystem, wie beispielsweise in ein uniformes Gitter, konvertiert werden. Dies ist bei einer großen Menge an Partikeln jedoch mit einem erheblichen Aufwand verbunden. Darüber hinaus führt diese Konversion meist zu einem Verlust der Präzision bei gleichzeitig erhöhtem Speicherverbrauch. Im Rahmen dieser Dissertation werde ich neue Visualisierungstechniken erforschen, welche speziell auf der lagrangen Sichtweise basieren. Diese ermöglichen eine effiziente und effektive visuelle Analyse großer Partikeldaten

Anisotropy Across Fields and Scales

This open access book focuses on processing, modeling, and visualization of anisotropy information, which are often addressed by employing sophisticated mathematical constructs such as tensors and other higher-order descriptors. It also discusses adaptations of such constructs to problems encountered in seemingly dissimilar areas of medical imaging, physical sciences, and engineering. Featuring original research contributions as well as insightful reviews for scientists interested in handling anisotropy information, it covers topics such as pertinent geometric and algebraic properties of tensors and tensor fields, challenges faced in processing and visualizing different types of data, statistical techniques for data processing, and specific applications like mapping white-matter fiber tracts in the brain. The book helps readers grasp the current challenges in the field and provides information on the techniques devised to address them. Further, it facilitates the transfer of knowledge between different disciplines in order to advance the research frontiers in these areas. This multidisciplinary book presents, in part, the outcomes of the seventh in a series of Dagstuhl seminars devoted to visualization and processing of tensor fields and higher-order descriptors, which was held in Dagstuhl, Germany, on October 28–November 2, 2018

Anisotropy Across Fields and Scales

This open access book focuses on processing, modeling, and visualization of anisotropy information, which are often addressed by employing sophisticated mathematical constructs such as tensors and other higher-order descriptors. It also discusses adaptations of such constructs to problems encountered in seemingly dissimilar areas of medical imaging, physical sciences, and engineering. Featuring original research contributions as well as insightful reviews for scientists interested in handling anisotropy information, it covers topics such as pertinent geometric and algebraic properties of tensors and tensor fields, challenges faced in processing and visualizing different types of data, statistical techniques for data processing, and specific applications like mapping white-matter fiber tracts in the brain. The book helps readers grasp the current challenges in the field and provides information on the techniques devised to address them. Further, it facilitates the transfer of knowledge between different disciplines in order to advance the research frontiers in these areas. This multidisciplinary book presents, in part, the outcomes of the seventh in a series of Dagstuhl seminars devoted to visualization and processing of tensor fields and higher-order descriptors, which was held in Dagstuhl, Germany, on October 28–November 2, 2018

Annual Research Briefs, 1990

The 1990 annual progress reports of the Research Fellows and students of the Center for Turbulent Research (CTR) are included. It is intended primarily as a contractor report to NASA, Ames Research Center. In addition, numerous CTR Manuscript Reports were published last year. The purpose of the CTR Manuscript Series is to expedite the dissemination of research results by the CTR staff. The CTR is devoted to the fundamental study of turbulent flow; its objectives are to produce advances in physical understanding of turbulence, in turbulence modeling and simulation, and in turbulence control

Analysis of stationary and non-stationary phenomena in turbulent subcritical flow behind two parallel cylinders

This study presents the analysis of the bistable phenomenon for turbulent flows around two cylinders side-by-side using two methods for data analysis and chaos theory for dynamic analysis. The experimental data were acquired for various Reynolds numbers and pitch-todiameter ratio p/D of 1.16, 1.26, and 1.60, cylinders diameter was 25.1 mm. The experimental technique consists of measuring the velocity fluctuations in an aerodynamic channel using hot-wire anemometry. The study presents the application of the Hilbert-Huang transform (HHT) as a tool of analysis for non-stationary and non-linear signals. The method was first validated using single cylinders and then extended for two cylinders side-by-side. Results show that the HHT method may provide information about particular events in timefrequency space and about the physics of flow scales. The statistical analysis of the experimental data is performed to identify statistical patterns that can be used to characterize the bistable flow. The signals are scanned by a moving window for the statistical analysis, creating blocks of probability density functions (PDFs). The four first statistical moments of each PDF are calculated, and a tendency of behavior based on their variations is established. The dynamics of the bistable flow system are studied applying chaos theory tools, like the largest Lyapunov exponent. The strange attractors of the velocity-time series are reconstructed, and their topology is useful to understand the physics of the bistable system. Each flow wake mode is analyzed separately. A general model of the bistable flow is reconstructed using probability functions. The application of a set of tools in the analysis of the turbulent wake behind cylinders is useful for the comprehension of turbulent phenomena, producing meaningful results and allowing the identification of turbulent structures and flow scales, and a better understanding of the system dynamics.Este estudo apresenta a análise do fenômeno da biestabilidade no escoamento em torno de dois cilindros lado a lado usando dois métodos para análise de sinais, e teoria do caos para a análise da dinâmica. Os dados experimentais foram adquiridos para vários números de Reynolds e várias razões de aspecto p/D de 1,16, 1,26 e 1,60, o diâmetro dos cilindros é de 25,1 mm. A técnica experimental utilizada consiste em medir as flutuações de velocidade em um canal aerodinâmico utilizando anemometria de fio quente. O estudo apresenta a aplicação da transformada de Hilbert-Huang (HHT) como ferramenta de análise para sinais não estacionários e não lineares. O método é primeiramente validado utilizando sinais experimentais para um cilindro sobre escoamento turbulento e após aplicado ao escoamento sobre dois cilindros lado a lado. Resultados mostram que o método de HHT fornece não só uma definição mais precisa de eventos específicos no espaço tempo-frequência, mas também permite uma interpretação física mais significativa dos processos dinâmicos das escalas do escoamento. A análise estatística dos dados experimentais é feita com o objetivo de identificar padrões estatísticos que possam ser utilizados para caracterização do escoamento biestável. Para a análise estatística os dados são varridos por uma janela móvel, criando blocos de funções densidade de probabilidade (PDFs). Os quatro primeiros momentos estatísticos são calculados e é possível estabelecer uma tendência de comportamento baseada em suas variações. A dinâmica do sistema biestável é estudada aplicando ferramentas da teoria do caos, como o maior expoente de Lyapunov. O atrator estranho da série temporal da velocidade é reconstruído e sua topologia é utilizada para melhor compreensão do comportamento físico do fenômeno da biestabilidade. Cada esteira do escoamento biestável é analisada separadamente. Um modelo geral do escoamento biestável é reconstruído utilizando funções de probabilidade. A aplicação de um conjunto de ferramentas para a análise da turbulência das esteiras dos cilindros é útil para a melhor compreensão de fenômenos turbulentos, produzindo resultados significativos e permitindo a identificação de estruturas turbulentas e escalas do escoamento e um entendimento sobre a dinâmica do sistema