Optimal Nonlinear Eddy Viscosity in Galerkin Models of Turbulent Flows

We propose a variational approach to identification of an optimal nonlinear eddy viscosity as a subscale turbulence representation for POD models. The ansatz for the eddy viscosity is given in terms of an arbitrary function of the resolved fluctuation energy. This function is found as a minimizer of a cost functional measuring the difference between the target data coming from a resolved direct or large-eddy simulation of the flow and its reconstruction based on the POD model. The optimization is performed with a data-assimilation approach generalizing the 4D-VAR method. POD models with optimal eddy viscosities are presented for a 2D incompressible mixing layer at $Re=500$ (based on the initial vorticity thickness and the velocity of the high-speed stream) and a 3D Ahmed body wake at $Re=300,000$ (based on the body height and the free-stream velocity). The variational optimization formulation elucidates a number of interesting physical insights concerning the eddy-viscosity ansatz used. The 20-dimensional model of the mixing-layer reveals a negative eddy-viscosity regime at low fluctuation levels which improves the transient times towards the attractor. The 100-dimensional wake model yields more accurate energy distributions as compared to the nonlinear modal eddy-viscosity benchmark {proposed recently} by \"Osth et al. (2014). Our methodology can be applied to construct quite arbitrary closure relations and, more generally, constitutive relations optimizing statistical properties of a broad class of reduced-order models.Comment: 41 pages, 16 figures; accepted for publication in Journal of Fluid Mechanic

How Important is Access to Jobs? Old Question - Improved Answer

We study the impact of job proximity on individual employment and earnings. The analysis exploits a Swedish refugee dispersal policy to get exogenous variation in individual locations. Using very detailed data on the exact location of all residences and workplaces in Sweden, we find that having been placed in a location with poor job access in 1990-91 adversely affected employment in 1999. Doubling the number of jobs in the initial location in 1990-91 is associ­ated with 2.9 percentage points higher employment probability in 1999. The analysis suggests that residential sorting leads to underestimation of the impact of job access.Spatial Mismatch; Endogenous Location; Natural Experiment

How important is access to jobs? Old question - improved answer

We study the impact of job proximity on individual employment and earnings. The analysis exploits a Swedish refugee dispersal policy to get exogenous variation in individual locations. Using very detailed data on the exact location of all residences and workplaces in Sweden, we find that having been placed in a location with poor job access in 1990–91 adversely affected employment in 1999. Doubling the number of jobs in the initial location in 1990–91 is associated with 2.9 percentage points higher employment probability in 1999. The analysis suggests that residential sorting leads to underestimation of the impact of job access.Spatial mismatch; endogenous location; natural experiment

The geographies of recruiting a partner from abroad. An exploration of Swedish data

International marriages are both a result and a driver of higher levels of global mobility and interconnectivity. Increasing ease of air travel for work and leisure, rising numbers of individuals studying, working and travelling abroad, and the emergence of international partnering websites have expanded traditionally local marriage fields – the geographical areas where people meet the partner – to global proportions. This expansion has increased the chance of meeting a potential partner from abroad resulting in an increase in international marriage migration. Recruiting a partner from abroad is surrounded by prejudice and stigma. ‘Knowledge’ about the characteristics of the individual ‘importing’ a partner from abroad is often based on anecdotic evidence and myths. In this paper we explore the factors that determine the probability that a native Swede recruits a partner from abroad. Along with various demographic and socioeconomic characteristics of the Swede we will pay specific attention to the geographies of marriage migration: the opportunity structure. This study uses longitudinal population data for the whole of Sweden, containing information on all individuals who lived in Sweden between 1994 and 2004. The results from multinomial logistic regression models shed a unique light on gendered and geographic patterns of partner recruitment.Migration; International marriage; Marriage migartion; Demographic characteristics; Socioeconomic characteristics; Globalisation; Sweden

The flow around a simplified tractor-trailer model studied by large eddy simulation

Large-eddy simulation (LES) is used to study the flow around a simplified tractor-trailer model. The model consists of two boxes placed in tandem. The front box represents the cab of a tractor-trailer road vehicle and the rear box represents the trailer. The LES was made at the Reynolds number of 0.51×106 based on the height of the rear box and the inlet air velocity. Two variants of the model were studied, one where the leading edges on the front box are sharp and one where the edges are rounded. One small and one large gap width between the two boxes were studied for both variants. Two computational grids were used in the LES simulations and a comparison was made with available experimental force measurements. The results of the LES simulations were used to analyze the flow field around the cab and in the gap between the two boxes of the tractor-trailer model. Large vortical structures around the front box and in the gap were identified. The flow field analysis showed how these large vortical structures are responsible for the difference in the drag force for the model that arises when the leading edges on the front box are rounded and the gap width is varied

Simulations of flow around a simplified train model with a drag reducing device

Partially Averaged Navier Stokes is used to simulate the flow around a simple train model. The train model has previously been studied in wind tunnel experiments and has a length to height/width ratio of 7:1. The Reynolds number based on the height of the train model is 0.37 x 10^6. For this Reynolds number, the flow separates from the curved leading edges on the front then attaches again on the roof and sides forming a boundary layer there before separating in the wake. The first case is of the natural flow around the train model where direct comparison to experimental data of drag coefficient and pressure coefficient are made. In the second case an open cavity is placed on the base of the train model with the aim of reducing the overall drag on the model. The results show that the drag for model with the cavity is reduced by some 10% compared to the drag of the natural case. The agreement to experimental data for the natural case is not perfect but the general features in the flow field are simulated correctly

On the need for a nonlinear subscale turbulence term in POD models as exemplified for a high Reynolds number flow over an Ahmed body

We investigate a hierarchy of eddy-viscosity terms in POD Galerkin models to account for a large fraction of unresolved fluctuation energy. These Galerkin methods are applied to Large Eddy Simulation data for a flow around the vehicle-like bluff body call Ahmed body. This flow has three challenges for any reduced-order model: a high Reynolds number, coherent structures with broadband frequency dynamics, and meta-stable asymmetric base flow states. The Galerkin models are found to be most accurate with modal eddy viscosities as proposed by Rempfer & Fasel (1994). Robustness of the model solution with respect to initial conditions, eddy viscosity values and model order is only achieved for state-dependent eddy viscosities as proposed by Noack, Morzynski & Tadmor (2011). Only the POD system with state-dependent modal eddy viscosities can address all challenges of the flow characteristics. All parameters are analytically derived from the Navier-Stokes based balance equations with the available data. We arrive at simple general guidelines for robust and accurate POD models which can be expected to hold for a large class of turbulent flows.Comment: Submitted to the Journal of Fluid Mechanic

Cluster-based reduced-order modelling of a mixing layer

We propose a novel cluster-based reduced-order modelling (CROM) strategy of unsteady flows. CROM combines the cluster analysis pioneered in Gunzburger's group (Burkardt et al. 2006) and and transition matrix models introduced in fluid dynamics in Eckhardt's group (Schneider et al. 2007). CROM constitutes a potential alternative to POD models and generalises the Ulam-Galerkin method classically used in dynamical systems to determine a finite-rank approximation of the Perron-Frobenius operator. The proposed strategy processes a time-resolved sequence of flow snapshots in two steps. First, the snapshot data are clustered into a small number of representative states, called centroids, in the state space. These centroids partition the state space in complementary non-overlapping regions (centroidal Voronoi cells). Departing from the standard algorithm, the probabilities of the clusters are determined, and the states are sorted by analysis of the transition matrix. Secondly, the transitions between the states are dynamically modelled using a Markov process. Physical mechanisms are then distilled by a refined analysis of the Markov process, e.g. using finite-time Lyapunov exponent and entropic methods. This CROM framework is applied to the Lorenz attractor (as illustrative example), to velocity fields of the spatially evolving incompressible mixing layer and the three-dimensional turbulent wake of a bluff body. For these examples, CROM is shown to identify non-trivial quasi-attractors and transition processes in an unsupervised manner. CROM has numerous potential applications for the systematic identification of physical mechanisms of complex dynamics, for comparison of flow evolution models, for the identification of precursors to desirable and undesirable events, and for flow control applications exploiting nonlinear actuation dynamics.Comment: 48 pages, 30 figures. Revised version with additional material. Accepted for publication in Journal of Fluid Mechanic

Розвиток музичної освіти у період середньовіччя та відродження

У статті обґрунтовано ставлення і розвиток музичної освіти у період Середньовіччя та Відродження, застосування музики як засобу естетичного виховання молоді.It has been grounded the development of musical education at the period of middle ages and the Renaissance, the usage of music as the means of aesthetical upbringing of the youth. The leading place is devoted to the choral, instrumental and vocal genres, musical-enlightming activity off the composers and the singers. The teachers of high educational institutions of different types which had influenced cultural-national Renaissance and awakening of the peoples consciousness. Besides the author has proposed the methods and the ways of mastering the peculiarities of the musical art by the pupils of mass secondary educational institutions and the methods of forming of musical culture of different social strata