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

Characteristic eddy decomposition of turbulence in a channel

The proper orthogonal decomposition technique (Lumley's decomposition) is applied to the turbulent flow in a channel to extract coherent structures by decomposing the velocity field into characteristic eddies with random coefficients. In the homogeneous spatial directions, a generaliztion of the shot-noise expansion is used to determine the characteristic eddies. In this expansion, the Fourier coefficients of the characteristic eddy cannot be obtained from the second-order statistics. Three different techniques are used to determine the phases of these coefficients. They are based on: (1) the bispectrum, (2) a spatial compactness requirement, and (3) a functional continuity argument. Results from these three techniques are found to be similar in most respects. The implications of these techniques and the shot-noise expansion are discussed. The dominant eddy is found to contribute as much as 76 percent to the turbulent kinetic energy. In both 2D and 3D, the characteristic eddies consist of an ejection region straddled by streamwise vortices that leave the wall in the very short streamwise distance of about 100 wall units

Direct numerical simulation of curved turbulent channel flow

Low Reynolds number, mildly curved, turbulent channel flow has been simulated numerically without subgrid scale models. A new spectral numerical method developed for this problem was used, and the computations were performed with 2 million degrees of freedom. A variety of statistical and structural information has been extracted from the computed flow fields. These include mean velocity, turbulence stresses, velocity skewness, and flatness factors, space time correlations and spectra, all the terms in the Reynolds stress balance equations, and contour and vector plots of instantaneous velocity fields. The effects of curvature on this flow were determined by comparing the concave and convex sides of the channel. The observed effects are consistent with experimental observations for mild curvature. The most significant difference in the turbulence statistics between the concave and convex sides was in the Reynolds shear stress. This was accompanied by significant differences in the terms of the Reynolds shear stress balance equations. In addition, it was found that stationary Taylor-Gortler vortices were present and that they had a significant effect on the flow by contributing to the mean Reynolds shear stress, and by affecting the underlying turbulence

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,

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