This book is a formal presentation of lectures given at the 1987 Summer School on Turbulence, held at the National Center for Atmospheric Research under the auspices of the Geophysical Turbulence Program. The lectures present in detail certain of the more challenging and interesting current turbulence research problems in engineering, meteorology, plasma physics, and mathematics. The lecturers-Uriel Frisch (Mathematics), Douglas Lilly (Meteorology), David Montgomery (Plasma Physics), and Hendrik Tennekes (Engineering) ? are distinguished for both their research contributions and their abilities to communicate these to students with enthusiasm. This book is distinguished by its simultaneous focus on the fundamentals of turbulent flows (in neutral and ionized fluids) and on a presentation of current research tools and topics in these fields.

This book is based on the lectures delivered at the 19th Canberra International Physics Summer School held at the Australian National University in Canberra (Australia) in January 2006.The problem of turbulence and coherent structures is of key importance in many fields of science and engineering. It is an area which is vigorously researched across a diverse range of disciplines such as theoretical physics, oceanography, atmospheric science, magnetically confined plasma, nonlinear optics, etc. Modern studies in turbulence and coherent structures are based on a variety of theoretical concepts, numerical simulation techniques and experimental methods, which cannot be reviewed effectively by a single expert.The main goal of these lecture notes is to introduce state-of-the-art turbulence research in a variety of approaches (theoretical, numerical simulations and experiments) and applications (fluids, plasmas, geophysics, nonlinear optical media) by several experts. A smooth introduction is presented to readers who are not familiar with the field, while reviewing the most recent advances in the area. This collection of lectures will provide a useful review for both postgraduate students and researchers new to the advancements in this field, as well as specialists seeking to expand their knowledge across different areas of turbulence research.

Wave Turbulence refers to the statistical theory of weakly nonlinear dispersive waves. There is a wide and growing spectrum of physical applications, ranging from sea waves, to plasma waves, to superfluid turbulence, to nonlinear optics and Bose-Einstein condensates. Beyond the fundamentals the book thus also covers new developments such as the interaction of random waves with coherent structures (vortices, solitons, wave breaks), inverse cascades leading to condensation and the transitions between weak and strong turbulence, turbulence intermittency as well as finite system size effects, such as “frozen” turbulence, discrete wave resonances and avalanche-type energy cascades. This book is an outgrow of several lectures courses held by the author and, as a result, written and structured rather as a graduate text than a monograph, with many exercises and solutions offered along the way. The present compact description primarily addresses students and non-specialist researchers wishing to enter and work in this field.

This self-contained volume introduces modern methods of statistical mechanics in turbulence, with three harmonised lecture courses by world class experts.

In January 1937, Nobel laureate in Physics Subrahmanyan Chandrasekhar was recruited to the University of Chicago. He was to remain there for his entire career, becoming Morton D. Hull Distinguished Service Professor of Theoretical Astrophysics in 1952 and attaining emeritus status in 1985. This is where his then student Ed Spiegel met him during the summer of 1954, attended his lectures on turbulence and jotted down the notes in hand. His lectures had a twofold purpose: they not only provided a very elementary introduction to some aspects of the subject for novices, they also allowed Chandra to organize his thoughts in preparation to formulating his attack on the statistical problem of homogeneous turbulence. After each lecture Ed Spiegel transcribed the notes and filled in the details of the derivations that Chandrasekhar had not included, trying to preserve the spirit of his presentation and even adding some of his side remarks. The lectures were rather impromptu and the notes as presented here are as they were set down originally in 1954. Now they are being made generally available for Chandrasekhar’s centennial.

These lecture notes are woven around the subject of Burgers' turbulence/KPZ model of interface growth, a study of the nonlinear parabolic equation with random initial data. The analysis is conducted mostly in the space-time domain, with less attention paid to the frequency-domain picture. However, the bibliography contains a more complete information about other directions in the field which over the last decade enjoyed a vigorous expansion. The notes are addressed to a diverse audience, including mathematicians, statisticians, physicists, fluid dynamicists and engineers, and contain both rigorous and heuristic arguments. Because of the multidisciplinary audience, the notes also include a concise exposition of some classical topics in probability theory, such as Brownian motion, Wiener polynomial chaos, etc.