This research will investigate the structure of eddies in moderate Reynolds number, canonical wall turbulence for the purpose of developing a unified physical-mathematical description including all scales ranging from the near- wall to the very large-scale motions. It is now clear that large- and very-large-scale motions (LSM and VLSM) occur in all wall flows and account for more than one-half of the turbulent kinetic energy and Reynolds shear stress in the outer layer. But, very little is known about their form, and even less about their origins. Aside from some evidence that they are correlated with the small, near-wall eddies, there is no understanding of how eddies in the buffer layer, the logarithmic layer, and the wake are related to the LSM and the VLSM. The other weakness in our ability to describe the three-dimensional structure is that a unified mathematical methodology has yet to be applied to the full range of scale and the full set of canonical flows. The specific goals are therefore to adapt three-dimensional proper orthogonal decomposition (POD) to this purpose and apply it to three flows: pipe, channel and boundary-layer using data from existing direct numerical simulations. The structure of quasi-streamwise vortices in the near-wall and their dynamics are becoming reasonably well understood. This work would put our understanding of the structure of the logarithmic layer and large/very-large scale on a comparable footing, and establish a basis for addressing the dynamics of these motions. Incorporating the LSM/VLSM eddies into a unified picture will answer a long-standing question concerning autonomy of the near-wall layer and the physical processes that determine the statistical behavior. Deeper understanding of POD modes and their relation to coherent structures on multiple scales will materially advance our methodology for extracting information from the richness of Direct Navier Stokes simulation databases. It would also impact the formulation of large eddy simulations and Reynolds Averaged Navier Stokes computational methods, and scaling laws for engineering systems and the formulation of techniques to reduce drag and otherwise manage turbulent flow over surfaces. Very broadly, such improvements have value to society in the areas of energy, transportation, weather prediction and other geophysical processes.
