The lectures collected for this volume were given during a workshop entitled, 'Semi-analytic Methods for the Navier Stokes Equations' held at the CRM in Montreal. The title reflects the current reality in fluid dynamics: Navier-Stokes equations (NSE) describe the behavior of fluid in a wide range of physical situations, the solutions of these equations are sufficiently complicated, so that another level of analysis is clearly needed. The fundamental problem is not just to solve the NSE, but also to understand what the solutions mean. One of the goals of the workshop was to bring together people who, while working in different fields, share a common perspective on the nature of the problem to be solved. The lectures present a diverse set of techniques for modelling, computing, and understanding phenomena such as instabilities, turbulence and spatiotemporal chaos in fluids.
Probabilities and conditional averages in turbulence by E. S. C. Ching Spatiotemporal chaos in large systems: The scaling of complexity with size by H. S. Greenside Empirical dynamical system reduction I: Global nonlinear transformations by M. Kirby and R. Miranda Empirical dynamical system reduction II: Neural charts by D. R. Hundley, M. Kirby, and R. Miranda Asymmetries in eastward and westward jets in a model planetary atmosphere by C. Lee and P. S. Marcus Lagrangian averaging for dynamic Eddy-viscosity subgrid models for filtered Navier-Stokes equation by C. Meneveau and T. S. Lund Punctuated Hamiltonian models of structured turbulence by J. B. Weiss.