This work brings together previously unpublished notes contributed by participants of the IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence (Moscow, 25-30 August 2006). The study of vortex motion is of great interest to fluid and gas dynamics: since all real flows are vortical in nature, applications of the vortex theory are extremely diverse, many of them (e.g. aircraft dynamics, atmospheric and ocean phenomena) being especially important.

Elementary vortices – those tubular swirling vortical structures with concentrated vorticity commonly observed in various kinds of turbulent flows – play key roles in turbulence dynamics (e.g. enhancement of mixing, diffusion and resistance) and characterize turbulence statistics (e.g. intermittency). Because of their dynamical importance, manipulation of elementary vortices is expected to be effective and useful in turbulence control as well as in construction of turbulence modeling. The most advanced research works on elementary vortices and related problems were presented and discussed at the IUTAM Symposium in Kyoto, Japan, 26-28 October 2004. This book contains 40 contributions presented there, the subjects of which cover vortex dynamics, coherent structures, chaotic advection and mixing, statistical properties of turbulence, rotating and stratified turbulence, instability and transition, dynamics of thin vortices, finite-time singularity, and superfluid turbulence. The book should be useful for readers of graduate and advanced levels in the field of fluid turbulence.

This volume contains the proceedings of the IUTAM Symposium on Computational Physics and New Perspectives in Turbulence, held at Nagoya University, Nagoya, Japan, in September 2006. With special emphasis given to fundamental aspects of the physics of turbulence, coverage includes experimental approaches to fundamental problems in turbulence, turbulence modeling and numerical methods, and geophysical and astrophysical turbulence.

The Symposium brought together many of the world’s experts in fluid mechanics, microfabrication and control theory to discover the synergy that can lead to real advances and perhaps find ways in which collaborative projects may proceed. The high profile meeting was attended by keynote speakers who are leaders in their fields. A key driver was the improvement in flow efficiency to reduce drag, and thereby emissions arising from transport. About 65 papers were presented.

This book illustrates the broad range of Jerry Marsden’s mathematical legacy in areas of geometry, mechanics, and dynamics, from very pure mathematics to very applied, but always with a geometric perspective. Each contribution develops its material from the viewpoint of geometric mechanics beginning at the very foundations, introducing readers to modern issues via illustrations in a wide range of topics. The twenty refereed papers contained in this volume are based on lectures and research performed during the month of July 2012 at the Fields Institute for Research in Mathematical Sciences, in a program in honor of Marsden's legacy. The unified treatment of the wide breadth of topics treated in this book will be of interest to both experts and novices in geometric mechanics. Experts will recognize applications of their own familiar concepts and methods in a wide variety of fields, some of which they may never have approached from a geometric viewpoint. Novices may choose topics that interest them among the various fields and learn about geometric approaches and perspectives toward those topics that will be new for them as well.

The book serves as a core text for graduate courses in advanced fluid mechanics and applied science. It consists of two parts. The first provides an introduction and general theory of fully developed turbulence, where treatment of turbulence is based on the linear functional equation derived by E. Hopf governing the characteristic functional that determines the statistical properties of a turbulent flow. In this section, Professor Kollmann explains how the theory is built on divergence free Schauder bases for the phase space of the turbulent flow and the space of argument vector fields for the characteristic functional. Subsequent chapters are devoted to mapping methods, homogeneous turbulence based upon the hypotheses of Kolmogorov and Onsager, intermittency, structural features of turbulent shear flows and their recognition.

Rotating Thermal Flows in Natural and Industrial Processes provides the reader with a systematic description of the different types of thermal convection and flow instabilities in rotating systems, as present in materials, crystal growth, thermal engineering, meteorology, oceanography, geophysics and astrophysics. It expressly shows how the isomorphism between small and large scale phenomena becomes beneficial to the definition and ensuing development of an integrated comprehensive framework. This allows the reader to understand and assimilate the underlying, quintessential mechanisms without requiring familiarity with specific literature on the subject. Topics treated in the first part of the book include: Thermogravitational convection in rotating fluids (from laminar to turbulent states); Stably stratified and unstratified shear flows; Barotropic and baroclinic instabilities; Rossby waves and Centrifugally-driven convection; Potential Vorticity, Quasi-Geostrophic Theory and related theorems; The dynamics of interacting vortices, interacting waves and mixed (hybrid) vortex-wave states; Geostrophic Turbulence and planetary patterns. The second part is entirely devoted to phenomena of practical interest, i.e. subjects relevant to the realms of industry and technology, among them: Surface-tension-driven convection in rotating fluids; Differential-rotation-driven (forced) flows; Crystal Growth from the melt of oxide or semiconductor materials; Directional solidification; Rotating Machinery; Flow control by Rotating magnetic fields; Angular Vibrations and Rocking motions; Covering a truly prodigious range of scales, from atmospheric and oceanic processes and fluid motion in "other solar-system bodies", to convection in its myriad manifestations in a variety of applications of technological relevance, this unifying text is an ideal reference for physicists and engineers, as well as an important resource for advanced students taking courses on the physics of fluids, fluid mechanics, thermal, mechanical and materials engineering, environmental phenomena, meteorology and geophysics.