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 Montréal. 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.

Titles in this series are co-published with the Centre de Recherches Mathématiques.

Readership

Graduate students and research mathematicians interested in fluid mechanics, numerical analysis, turbulences, and Navier-Stokes equations; physicists and engineers.

Table of Contents

• E. S. C. Ching -- Probabilities and conditional averages in turbulence
• H. S. Greenside -- Spatiotemporal chaos in large systems: The scaling of complexity with size
• M. Kirby and R. Miranda -- Empirical dynamical system reduction I: Global nonlinear transformations
• D. R. Hundley, M. Kirby, and R. Miranda -- Empirical dynamical system reduction II: Neural charts
• C. Lee and P. S. Marcus -- Asymmetries in eastward and westward jets in a model planetary atmosphere
• C. Meneveau and T. S. Lund -- Lagrangian averaging for dynamic Eddy-viscosity subgrid models for filtered Navier-Stokes equation
• J. B. Weiss -- Punctuated Hamiltonian models of structured turbulence