Extreme-scale motions in turbulent plane Couette flows

We study the size of large-scale motions in turbulent plane Couette flows at moderate Reynolds number up to $Re_\tau$ = 500. Direct numerical simulation domains were as large as $100\pi\delta\times2\delta\times5\pi\delta$, where $\delta$ is half the distance between the walls. The results indicate that there are structures with streamwise extent, as measured by the wavelength, as long as 78$\delta$ and at least 310$\delta$ at $Re_\tau$ = 220 and 500, respectively. The presence of these very long structures is apparent in the spectra of all three velocity components and the Reynolds stress. In DNS using a smaller domain, the large structures are constrained, eliminating the streamwise variations present in the larger domain. Effects of a smaller domain are also present in the mean velocity and the streamwise velocity variance in the outer flow.Comment: Accepted manuscript in the Journal of Fluid Mechanic

The Parallel C++ Statistical Library for Bayesian Inference: QUESO

The Parallel C++ Statistical Library for the Quantification of Uncertainty for Estimation, Simulation and Optimization, Queso, is a collection of statistical algorithms and programming constructs supporting research into the quantification of uncertainty of models and their predictions. Queso is primarily focused on solving statistical inverse problems using Bayes's theorem, which expresses a distribution of possible values for a set of uncertain parameters (the posterior distribution) in terms of the existing knowledge of the system (the prior) and noisy observations of a physical process, represented by a likelihood distribution. The posterior distribution is not often known analytically, and so requires computational methods. It is typical to compute probabilities and moments from the posterior distribution, but this is often a high-dimensional object and standard Reimann-type methods for quadrature become prohibitively expensive. The approach Queso takes in this regard is to rely on Markov chain Monte Carlo (MCMC) methods which are well suited to evaluating quantities such as probabilities and moments of high-dimensional probability distributions. Queso's intended use is as tool to assist and facilitate coupling uncertainty quantification to a specific application called a forward problem. While many libraries presently exist that solve Bayesian inference problems, Queso is a specialized piece of software primarily designed to solve such problems by utilizing parallel environments demanded by large-scale forward problems. Queso is written in C++, uses MPI, and utilizes libraries already available to the scientific community

Coherent structures in a simulated turbulent mixing layer

A direct numerical simulation of a plane turbulent mixing layer has been performed. The simulation was initialized using two turbulent velocity fields obtained from direct numerical simulation of a turbulent boundary layer at momentum thickness Reynolds number 300 (Spalart, 1988). The mixing layer is allowed to evolve long enough for self-similar linear growth to occur, with the visual thickness Reynolds number reaching 14,000. The simulated flow is examined for evidence of the coherent structures expected in a mixing layer (rollers and rib vortices). Before the onset of self-similar growth, such structures are present with properties similar to the corresponding laminar or transitional structures. In the self-similar growth regime, however, only the rollers are present with no indication of rib vortices and no indication of conventional pairing. This results in a reduction of mixing and layer growth

THE "ENHANCING RURAL ECONOMIES" PROJECT: CONTEXT AND PURPOSE, TECHNIQUES AND PROCEDURES, AND EXPERIENCE TO DATE

This paper is a part of a series of reports of the activities conducted under a grant from the Fund for Rural America, U.S. Department of Agriculture. Funds for the three year grant entitled "Enhancing Rural Economies Through Comprehensive Extension, Research & Partnering Approaches Using Multi-County Clusters in Michigan With Application to National Rural Settings" were received by Michigan State University's Department of Agricultural Economics in March, 1998. The major goal of the grant is to increase economic development activity in four clusters of rural counties in Michigan through the utilization of the resources of the Michigan State University Extension Service, Michigan Agricultural Experiment Station, and other resources of Michigan State University. Various local, state, and federal public partners as well as the private sector are to co-sponsor projects. This paper represents an overview of some of the project activities undertaken by December, 1999.Community/Rural/Urban Development,

RURAL RETIREES IN MICHIGAN: ISSUES AND OPPORTUNITIES - FINDINGS FROM FOCUS GROUP MEETINGS

This paper is a part of a series of reports of the activities conducted under a grant from the Fund for Rural America, U.S. Department of Agriculture. Funds for the three year grant entitled "Enhancing Rural Economies Through Comprehensive Extension, Research & Partnering Approaches Using Multi-County Clusters in Michigan With Application to National Rural Settings" were received by Michigan State University's Department of Agricultural Economics in March, 1998. The major goal of the grant is to increase economic development activity in four clusters of rural counties in Michigan through the utilization of the resources of the Michigan State University Extension Service, Michigan Agricultural Experiment Station, and other resources of Michigan State University. Various local, state, and federal public partners as well as the private sector are to co-sponsor projects. This paper represents the first stages of a continuing project to explore the utilization of retirement community human resources in rural Michigan and to develop Extension programs to meet their needs. Future activities include focus groups, labor supply analysis, a conference, and perhaps a rural academy to be developed by Michigan State University and its partners.Community/Rural/Urban Development,

Representing model inadequacy: A stochastic operator approach

Mathematical models of physical systems are subject to many uncertainties such as measurement errors and uncertain initial and boundary conditions. After accounting for these uncertainties, it is often revealed that discrepancies between the model output and the observations remain; if so, the model is said to be inadequate. In practice, the inadequate model may be the best that is available or tractable, and so despite its inadequacy the model may be used to make predictions of unobserved quantities. In this case, a representation of the inadequacy is necessary, so the impact of the observed discrepancy can be determined. We investigate this problem in the context of chemical kinetics and propose a new technique to account for model inadequacy that is both probabilistic and physically meaningful. A stochastic inadequacy operator $\mathcal{S}$ is introduced which is embedded in the ODEs describing the evolution of chemical species concentrations and which respects certain physical constraints such as conservation laws. The parameters of $\mathcal{S}$ are governed by probability distributions, which in turn are characterized by a set of hyperparameters. The model parameters and hyperparameters are calibrated using high-dimensional hierarchical Bayesian inference. We apply the method to a typical problem in chemical kinetics---the reaction mechanism of hydrogen combustion

Direct numerical simulation of turbulent channel flow up to Reτ≈5200Re_\tau \approx 5200

A direct numerical simulation of incompressible channel flow at $Re_\tau$ = 5186 has been performed, and the flow exhibits a number of the characteristics of high Reynolds number wall-bounded turbulent flows. For example, a region where the mean velocity has a logarithmic variation is observed, with von Karman constant $\kappa = 0.384 \pm 0.004$. There is also a logarithmic dependence of the variance of the spanwise velocity component, though not the streamwise component. A distinct separation of scales exists between the large outer-layer structures and small inner-layer structures. At intermediate distances from the wall, the one-dimensional spectrum of the streamwise velocity fluctuation in both the streamwise and spanwise directions exhibits $k^{-1}$ dependence over a short range in $k$. Further, consistent with previous experimental observations, when these spectra are multiplied by $k$ (premultiplied spectra), they have a bi-modal structure with local peaks located at wavenumbers on either side of the $k^{-1}$ range.Comment: Under consideration for publication in J. Fluid Mec

Sampling inhomogeneous turbulent fields

The reconstruction of an inhomogeneous random process from a finite number of discrete samples can be performed in terms of the Karhunen-Loeve (KL) expansion for that process. The n(th) eigenfunction has n - 1 zero crossings which are the sampling points for the inhomogeneous process. The rapid variation of the KL eigenfunctions makes it unnecessary to have a high density of sampling (or grid points) near the wall. However, this result should not be construed to indicate that with spectral simulations significantly fewer grid points are required with the KL expansion as compared to other orthogonal expansions. Moin and Moser (1989) have shown that the advantage of the KL expansion over Chebychev expansion rapidly diminishes when high percentage (say 90 percent) energy recovery is demanded