Multidimensional turbulence spectra - Statistical analysis of turbulent vortices

Strong nonlinear or very fast phenomena such as mixing, coalescence and breakup in chemical engineering processes, are not correctly described using average turbulence properties. Since these phenomena are modeled by the interaction of fluid particles with single or paired vortices, distribution of the properties of individual turbulent vortices should be studied and understood. In this paper, statistical analysis of turbulent vortices was performed using a novel vortex tracking algorithm. The vortices were identified using the normalized Q-criterion with extended volumes calculated using the Biot Savart law in order to capture most of the coherent structure related to each vortex. This new and fast algorithm makes it possible to estimate the volume of all resolved vortices. Turbulence was modeled using large-eddy simulation with the dynamic Smagorinsky-Lilly subgrid scale model for different Reynolds numbers. Number density of turbulent vortices were quantified and compared with different models. It is concluded that the calculated number densities for vortices in the inertial subrange and also for the larger scales are in very good agreement with the models proposed by Batchelor and Martinez-Bazan. Moreover, the associated enstrophy within the same size of coherent structures is quantified and its distribution is compared to models for distribution of turbulent kinetic energy. The associated enstrophy within the same size of coherent structures has a wide distribution that is normal distributed in the logarithmic scale

Global burden of 288 causes of death and life expectancy decomposition in 204 countries and territories and 811 subnational locations, 1990–2021: a systematic analysis for the Global Burden of Disease Study 2021

BACKGROUND Regular, detailed reporting on population health by underlying cause of death is fundamental for public health decision making. Cause-specific estimates of mortality and the subsequent effects on life expectancy worldwide are valuable metrics to gauge progress in reducing mortality rates. These estimates are particularly important following large-scale mortality spikes, such as the COVID-19 pandemic. When systematically analysed, mortality rates and life expectancy allow comparisons of the consequences of causes of death globally and over time, providing a nuanced understanding of the effect of these causes on global populations. METHODS The Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2021 cause-of-death analysis estimated mortality and years of life lost (YLLs) from 288 causes of death by age-sex-location-year in 204 countries and territories and 811 subnational locations for each year from 1990 until 2021. The analysis used 56 604 data sources, including data from vital registration and verbal autopsy as well as surveys, censuses, surveillance systems, and cancer registries, among others. As with previous GBD rounds, cause-specific death rates for most causes were estimated using the Cause of Death Ensemble model-a modelling tool developed for GBD to assess the out-of-sample predictive validity of different statistical models and covariate permutations and combine those results to produce cause-specific mortality estimates-with alternative strategies adapted to model causes with insufficient data, substantial changes in reporting over the study period, or unusual epidemiology. YLLs were computed as the product of the number of deaths for each cause-age-sex-location-year and the standard life expectancy at each age. As part of the modelling process, uncertainty intervals (UIs) were generated using the 2·5th and 97·5th percentiles from a 1000-draw distribution for each metric. We decomposed life expectancy by cause of death, location, and year to show cause-specific effects on life expectancy from 1990 to 2021. We also used the coefficient of variation and the fraction of population affected by 90% of deaths to highlight concentrations of mortality. Findings are reported in counts and age-standardised rates. Methodological improvements for cause-of-death estimates in GBD 2021 include the expansion of under-5-years age group to include four new age groups, enhanced methods to account for stochastic variation of sparse data, and the inclusion of COVID-19 and other pandemic-related mortality-which includes excess mortality associated with the pandemic, excluding COVID-19, lower respiratory infections, measles, malaria, and pertussis. For this analysis, 199 new country-years of vital registration cause-of-death data, 5 country-years of surveillance data, 21 country-years of verbal autopsy data, and 94 country-years of other data types were added to those used in previous GBD rounds. FINDINGS The leading causes of age-standardised deaths globally were the same in 2019 as they were in 1990; in descending order, these were, ischaemic heart disease, stroke, chronic obstructive pulmonary disease, and lower respiratory infections. In 2021, however, COVID-19 replaced stroke as the second-leading age-standardised cause of death, with 94·0 deaths (95% UI 89·2-100·0) per 100 000 population. The COVID-19 pandemic shifted the rankings of the leading five causes, lowering stroke to the third-leading and chronic obstructive pulmonary disease to the fourth-leading position. In 2021, the highest age-standardised death rates from COVID-19 occurred in sub-Saharan Africa (271·0 deaths [250·1-290·7] per 100 000 population) and Latin America and the Caribbean (195·4 deaths [182·1-211·4] per 100 000 population). The lowest age-standardised death rates from COVID-19 were in the high-income super-region (48·1 deaths [47·4-48·8] per 100 000 population) and southeast Asia, east Asia, and Oceania (23·2 deaths [16·3-37·2] per 100 000 population). Globally, life expectancy steadily improved between 1990 and 2019 for 18 of the 22 investigated causes. Decomposition of global and regional life expectancy showed the positive effect that reductions in deaths from enteric infections, lower respiratory infections, stroke, and neonatal deaths, among others have contributed to improved survival over the study period. However, a net reduction of 1·6 years occurred in global life expectancy between 2019 and 2021, primarily due to increased death rates from COVID-19 and other pandemic-related mortality. Life expectancy was highly variable between super-regions over the study period, with southeast Asia, east Asia, and Oceania gaining 8·3 years (6·7-9·9) overall, while having the smallest reduction in life expectancy due to COVID-19 (0·4 years). The largest reduction in life expectancy due to COVID-19 occurred in Latin America and the Caribbean (3·6 years). Additionally, 53 of the 288 causes of death were highly concentrated in locations with less than 50% of the global population as of 2021, and these causes of death became progressively more concentrated since 1990, when only 44 causes showed this pattern. The concentration phenomenon is discussed heuristically with respect to enteric and lower respiratory infections, malaria, HIV/AIDS, neonatal disorders, tuberculosis, and measles. INTERPRETATION Long-standing gains in life expectancy and reductions in many of the leading causes of death have been disrupted by the COVID-19 pandemic, the adverse effects of which were spread unevenly among populations. Despite the pandemic, there has been continued progress in combatting several notable causes of death, leading to improved global life expectancy over the study period. Each of the seven GBD super-regions showed an overall improvement from 1990 and 2021, obscuring the negative effect in the years of the pandemic. Additionally, our findings regarding regional variation in causes of death driving increases in life expectancy hold clear policy utility. Analyses of shifting mortality trends reveal that several causes, once widespread globally, are now increasingly concentrated geographically. These changes in mortality concentration, alongside further investigation of changing risks, interventions, and relevant policy, present an important opportunity to deepen our understanding of mortality-reduction strategies. Examining patterns in mortality concentration might reveal areas where successful public health interventions have been implemented. Translating these successes to locations where certain causes of death remain entrenched can inform policies that work to improve life expectancy for people everywhere. FUNDING Bill & Melinda Gates Foundation

Structures, Properties and Dynamics of Turbulent Vortices

The development of models for several phenomena that occur in turbulent single- and multi-phase flows requires improved descriptions and quantifications of turbulent vortices. In many engineering applications, the time scale of these phenomena is equal to or smaller than the lifetime of turbulent vortices; consequently, they are not adequately described by using average turbulence properties. The above mentioned phenomena are better described by the properties of single turbulent vortices, e.g. number density, size, enstrophy, energy, lifetime and vortex dynamics. In this thesis, a vortex-tracking algorithm that meets the thesis objectives was successfully developed. Using the Biot-Savart law and morphological methods, the vortex-tracking algorithm captures most of the coherent turbulent structure in individual vortices with clear separated boundaries. The novel vortex-tracking algorithm increases the total energy captured within individual vortices from 27% to 82%. The vortex-tracking algorithm works efficiently and fast. It allows for the identification of thousands of vortices individually, while different properties attributed to them can be quantified. Additionally, a new model for the number density of turbulent vortices in the entire energy spectrum was developed. This model significantly improves the prediction of the turbulent vortices number density. Moreover, it was observed that the number densities of turbulent vortices, modeled and quantified, vary at different radial locations, e.g. where the highest number density is found in the near-wall region and the lowest number density is found in the bulk of the flow. In addition to this, the average size distributions of turbulent vortices show that the sizes of vortices increase from the near-wall region to the bulk of the flow. It was concluded that the associated enstrophy and energy within turbulent vortices of the same size was log-normal distributed. The research in this thesis also examines the lifetimes of vortices. It was found that the lifetime of turbulent vortices depends on vortex size, energy and position. Also, it was concluded that the lifetime of turbulent vortices can be reasonably estimated base on their sizes and positions. Moreover, the birth frequencies of turbulent vortices were also studied

Analysis of Turbulent Flows-From Chaos to Structure

The development of models for several phenomena occurring in turbulent single and multi-phase flows requires improved description and quantification of turbulent structures. Phenomena such as, for example, mixing, coalescence and break-up, are often fast and nonlinear. In many engineering applications, the time scale is equal to or smaller than the lifetime of turbulent vortices; thus, these phenomena are not adequately described by using average turbulence properties. The interaction is better described by the properties of single turbulent vortices. For this reason, turbulence has been modeled using LES and with the help of the dynamic Smagorinsky-Lilly SGS model for different Reynolds numbers. As a result, an efficient vortex-tracking algorithm to identify and quantify thousands of vortices and their turbulent properties has been developed.This thesis presents the results of the analyses of a number of turbulent vortices. The results of these analyses of turbulent kinetic energy in turbulent structures, using the normalized Q criterion, showed that peak turbulent kinetic energy is located near the edge of the region identified as coherent, making the analysis challenging and model development difficult. Using the Biot-Savart law, it is possible to extend the region identified as coherent to capture the required amount of turbulent kinetic energy with the help of vortices. A detailed analysis of a small number of coherent vortices of turbulent pipe flow from LES revealed new information about the growth of these vortices (i.e. entrainment of the surrounding liquid), enstrophy and energy mechanisms over time.Furthermore, this thesis investigates the statistical properties of turbulent vortices including the number density and distribution of associated enstrophy within the same size of coherent structures. The statistical analysis of thousands of vortices was performed at different Reynolds numbers. The number densities of turbulent vortices were described as a function of spatial positions. The number density computed was highly compatible with the models suggested by Batchelor and Martinez for vortices located in the inertial subrange and those that were larger. Moreover, it was discovered that the associated enstrophy within the same size of coherent structures had a similarly wide distribution function as turbulent kinetic energy

Structures, Properties and Dynamics of Turbulent Vortices

The development of models for several phenomena that occur in turbulent single- and multi-phase flows requires improved descriptions and quantifications of turbulent vortices. In many engineering applications, the time scale of these phenomena is equal to or smaller than the lifetime of turbulent vortices; consequently, they are not adequately described by using average turbulence properties. The above mentioned phenomena are better described by the properties of single turbulent vortices, e.g. number density, size, enstrophy, energy, lifetime and vortex dynamics. In this thesis, a vortex-tracking algorithm that meets the thesis objectives was successfully developed. Using the Biot-Savart law and morphological methods, the vortex-tracking algorithm captures most of the coherent turbulent structure in individual vortices with clear separated boundaries. The novel vortex-tracking algorithm increases the total energy captured within individual vortices from 27% to 82%. The vortex-tracking algorithm works efficiently and fast. It allows for the identification of thousands of vortices individually, while different properties attributed to them can be quantified. Additionally, a new model for the number density of turbulent vortices in the entire energy spectrum was developed. This model significantly improves the prediction of the turbulent vortices number density. Moreover, it was observed that the number densities of turbulent vortices, modeled and quantified, vary at different radial locations, e.g. where the highest number density is found in the near-wall region and the lowest number density is found in the bulk of the flow. In addition to this, the average size distributions of turbulent vortices show that the sizes of vortices increase from the near-wall region to the bulk of the flow. It was concluded that the associated enstrophy and energy within turbulent vortices of the same size was log-normal distributed. The research in this thesis also examines the lifetimes of vortices. It was found that the lifetime of turbulent vortices depends on vortex size, energy and position. Also, it was concluded that the lifetime of turbulent vortices can be reasonably estimated base on their sizes and positions. Moreover, the birth frequencies of turbulent vortices were also studied

Analysis of Turbulent Flows-From Chaos to Structure

The development of models for several phenomena occurring in turbulent single and multi-phase flows requires improved description and quantification of turbulent structures. Phenomena such as, for example, mixing, coalescence and break-up, are often fast and nonlinear. In many engineering applications, the time scale is equal to or smaller than the lifetime of turbulent vortices; thus, these phenomena are not adequately described by using average turbulence properties. The interaction is better described by the properties of single turbulent vortices. For this reason, turbulence has been modeled using LES and with the help of the dynamic Smagorinsky-Lilly SGS model for different Reynolds numbers. As a result, an efficient vortex-tracking algorithm to identify and quantify thousands of vortices and their turbulent properties has been developed.This thesis presents the results of the analyses of a number of turbulent vortices. The results of these analyses of turbulent kinetic energy in turbulent structures, using the normalized Q criterion, showed that peak turbulent kinetic energy is located near the edge of the region identified as coherent, making the analysis challenging and model development difficult. Using the Biot-Savart law, it is possible to extend the region identified as coherent to capture the required amount of turbulent kinetic energy with the help of vortices. A detailed analysis of a small number of coherent vortices of turbulent pipe flow from LES revealed new information about the growth of these vortices (i.e. entrainment of the surrounding liquid), enstrophy and energy mechanisms over time.Furthermore, this thesis investigates the statistical properties of turbulent vortices including the number density and distribution of associated enstrophy within the same size of coherent structures. The statistical analysis of thousands of vortices was performed at different Reynolds numbers. The number densities of turbulent vortices were described as a function of spatial positions. The number density computed was highly compatible with the models suggested by Batchelor and Martinez for vortices located in the inertial subrange and those that were larger. Moreover, it was discovered that the associated enstrophy within the same size of coherent structures had a similarly wide distribution function as turbulent kinetic energy

Multidimensional Turbulence Spectra- Properties of Turbulent Vortices

Detailed description of turbulence is necessary to predict chemical engineering processes and develop new models. Strong nonlinear or very fast phenomena, e.g. mixing, coalescence and break up, are not correctly described using average turbulence properties. This is due to the fact that they interact with single turbulent vortices. Results from development of a vortex tracking method and analysis of a number of turbulent vortices including turbulent kinetic energy, lifetime, and growth rate are presented in this paper. One striking observation was that the lifetimes of turbulent vortices close to the walls were much larger than expected from RANS modeling

Identification and characterization of three-dimensional turbulent flow structures

Many phenomena in chemical processes for example fast mixing, coalescence and break-up of bubbles and drops are not correctly described using average turbulence properties as the outcome is governed by the interaction with individual vortices. In this study, an efficient vortex-tracking algorithm has been developed to identify thousands of vortices and quantify properties of the individual vortices. The traditional algorithms identifying vortex-cores only capture a fraction of the total turbulent kinetic energy, which is often not sufficient for modeling of coalescence and break-up phenomena. In the present algorithm, turbulent vortex-cores are identified using normalized Q-criterion, and allowed to grow using morphological methods. The growth is constrained by estimating the influence from all neighboring vortices using the Biot-Sawart law. This new algorithm allows 82% of the total turbulent kinetic to be captured, at the same time the individual vortices can be tracked in time. (c) 2015 American Institute of Chemical Engineers AIChE J, 62: 1265-1277, 201

Multidimensional Turbulence Spectra- Properties of Turbulent Vortices

Detailed description of turbulence is necessary to predict chemical engineering processes and develop new models. Strong nonlinear or very fast phenomena, e.g. mixing, coalescence and break up, are not correctly described using average turbulence properties. This is due to the fact that they interact with single turbulent vortices. Results from development of a vortex tracking method and analysis of a number of turbulent vortices including turbulent kinetic energy, lifetime, and growth rate are presented in this paper. One striking observation was that the lifetimes of turbulent vortices close to the walls were much larger than expected from RANS modeling