Four of the summer projects were put in a category called Fundamentals because they involved fundamental ideas not clearly associated with any of the other project groups. This does not imply that other projects were any less fundamental. The project on LES in complex boundaries, by Verzicco, Mohd-Yusof, Orlandi, and Haworth, was designed to test the immersed boundary method for representing fixed and moving boundaries on a stationary Cartesian mesh as applied to flow in a motored axisymmetric piston-cylinder system. Calculations were made assuming axisymmetric flow (2D mesh) for the purposes of method development, followed by DNS and LES with a full 3D concentric structured mesh initialized by a perturbation on the axisymmetric initial field. The method was shown to be extremely effective and relatively inexpensive compared to calculations on a deforming unstructured mesh. The DNS study of trailing vortices by Orlandi, Carnevale, Lele, and Shariff was an exploration of some new ideas for accelerating the breakup of aircraft trailing vortices. The group first studied a basic short-wavelength instability associated with interaction of the two vortices and then turned their attention to an exploration of how density variation along the axis of the vortices (perhaps produced by modulated engine exhaust entrainment) might be used to accelerate the breakup. The work showed that these density variations could indeed accelerate the rapid cross-diffusion of vorticity between the primary vortices when they are close to one another and thus opened the door to a possible new way of aircraft trailing vortex control. A method for predicting the statistics of turbulence using a Rayleigh-Ritz variational formulation was explored by Eyink and Wray. This was an attempt to bring ideas from non-linear dynamics to bear on study of turbulence. The theory provides a procedure for calculating the evolution of the two-time velocity cospectra from the evolution of k and epsilon as found from a k-epsilon model, using a modeled Langevin equation for the Fourier coefficients of the velocity fluctuations. The goal of the project was to test this model and, if possible, to improve it. The k-epsilon-RR model appeared to work well for short time separations. A simple convection correction seemed to improve things for longer time separations, suggesting to the authors that a RANS-RR model could give much better long-time predictability. Oberlack has been applying Lie Group Analysis to a variety of turbulent flow problems, most recently flow in a channel being rotated about a streamwise axis. This is a model flow for studying the effects of frame rotation in axial flow turbomachinery. The group analysis predicts the scaling that one should find in this flow, and the objective of the paper by Oberlack, Cabot, and Rogers was to test this using DNS. The work confirms the basic linear mean streamwise and spanwise velocity variations predicted by the group analysis. The DNS was limited by the size of the computational domain, but it was sufficient to show that this is a very interesting canonical test case. Common two-equation models do not account for rotation effects, so this flow is both a challenge to turbulence modeling and a possible source for inspiration and calibration of new turbulence models.