Magnetohydrodynamics (MHD) studies the interaction between the flow of an electrically conducting fluid and magnetic fields. It involves such diverse topics as the evolution and dynamics of astrophysical objects, thermonuclear fusion, metallurgy and semiconductor crystal growth, etc. Although the first ideas in magnetohydrodynamics appeared at the beginning of the last century, the explosion in theoretical and experimental studies occurred in the 1950s-60s. This state-of-the-art book aims at revising the evolution of ideas in various branches of magnetohydrodynamics (astrophysics, earth and solar dynamos, plasmas, MHD turbulence and liquid metals) and reviews current trends and challenges.

One of the priority areas of ICSU (The International Council for Science) is "Natural and Human-Induced Environmental Hazards and Disasters." The School held at the Institute for Mathematical Sciences, Singapore from 20 April to 2 May 2009 on which this volume is based on was sponsored by ICSU and by its members from IUTAM (the International Union of Theoretical and Applied Mechanics) and IUGG (the International Union of Geodesy and Geophysics).

The book provides an indepth graduate-level introduction to the fluid dynamics and geophysics of hazards such as tropical cyclones, flooding, atmospheric pollution and tsunamis. It also includes discussion of the possible effects of climate change on these phenomena. Indeed, the current importance of this area is of great public concern.

The Institute for Mathematical Sciences at the National University of Singapore hosted a Spring School on Fluid Dynamics and Geophysics of Environmental Hazards from 19 April to 2 May 2009. This volume contains the content of the nine short lecture courses given at this School, with a focus mainly on tropical cyclones, tsunamis, monsoon flooding and atmospheric pollution, all within the context of climate variability and change.The book provides an introduction to these topics from both mathematical and geophysical points of view, and will be invaluable for graduate students in applied mathematics, geophysics and engineering with an interest in this broad field of study, as well as for seasoned researchers in adjacent fields.

Turbulence is widely recognized as one of the outstanding problems of the physical sciences, but it still remains only partially understood despite having attracted the sustained efforts of many leading scientists for well over a century. In A Voyage Through Turbulence we are transported through a crucial period of the history of the subject via biographies of twelve of its great personalities, starting with Osborne Reynolds and his pioneering work of the 1880s. This book will provide absorbing reading for every scientist, mathematician and engineer interested in the history and culture of turbulence, as background to the intense challenges that this universal phenomenon still presents.

Exploring the origins and evolution of magnetic fields in planets, stars and galaxies, this book gives a basic introduction to magnetohydrodynamics and surveys the observational data, with particular focus on geomagnetism and solar magnetism. Pioneering laboratory experiments that seek to replicate particular aspects of fluid dynamo action are also described. The authors provide a complete treatment of laminar dynamo theory, and of the mean-field electrodynamics that incorporates the effects of random waves and turbulence. Both dynamo theory and its counterpart, the theory of magnetic relaxation, are covered. Topological constraints associated with conservation of magnetic helicity are thoroughly explored and major challenges are addressed in areas such as fast-dynamo theory, accretion-disc dynamo theory and the theory of magnetostrophic turbulence. The book is aimed at graduate-level students in mathematics, physics, Earth sciences and astrophysics, and will be a valuable resource for researchers at all levels.

Turbulence is widely recognized as one of the outstanding problems of the physical sciences, but it still remains only partially understood despite having attracted the sustained efforts of many leading scientists for well over a century. In A Voyage Through Turbulence we are transported through a crucial period of the history of the subject via biographies of twelve of its great personalities, starting with Osborne Reynolds and his pioneering work of the 1880s. This book will provide absorbing reading for every scientist, mathematician and engineer interested in the history and culture of turbulence, as background to the intense challenges that this universal phenomenon still presents.

Magnetohydrodynamics (MHD) studies the interaction between the flow of an electrically conducting fluid and magnetic fields. It involves such diverse topics as the evolution and dynamics of astrophysical objects, thermonuclear fusion, metallurgy and semiconductor crystal growth, etc. Although the first ideas in magnetohydrodynamics appeared at the beginning of the last century, the "explosion" in theoretical and experimental studies occurred in the 1950s-60s.

This state-of-the-art book aims at revising the evolution of ideas in various branches of magnetohydrodynamics (astrophysics, earth and solar dynamos, plasmas, MHD turbulence and liquid metals) and reviews current trends and challenges.

Helmholtz's seminal paper on vortex motion (1858) marks the beginning of what is now called topological fluid mechanics.After 150 years of work, the field has grown considerably. In the last several decades unexpected developments have given topological fluid mechanics new impetus, benefiting from the impressive progress in knot theory and geometric topology on the one hand, and in mathematical and computational fluid dynamics on the other.

This volume contains a wide-ranging collection of up-to-date, valuable research papers written by some of the most eminent experts in the field. Topics range from fundamental aspects of mathematical fluid mechanics, including topological vortex dynamics and magnetohydrodynamics, integrability issues, Hamiltonian structures and singularity formation, to DNA tangles and knotted DNAs in sedimentation. A substantial introductory chapter on knots and links, covering elements of modern braid theory and knot polynomials, as well as more advanced topics in knot classification, provides an invaluable addition to this material.

Exploring the origins and evolution of magnetic fields in planets, stars and galaxies, this book gives a basic introduction to magnetohydrodynamics and surveys the observational data, with particular focus on geomagnetism and solar magnetism. Pioneering laboratory experiments that seek to replicate particular aspects of fluid dynamo action are also described. The authors provide a complete treatment of laminar dynamo theory, and of the mean-field electrodynamics that incorporates the effects of random waves and turbulence. Both dynamo theory and its counterpart, the theory of magnetic relaxation, are covered. Topological constraints associated with conservation of magnetic helicity are thoroughly explored and major challenges are addressed in areas such as fast-dynamo theory, accretion-disc dynamo theory and the theory of magnetostrophic turbulence. The book is aimed at graduate-level students in mathematics, physics, Earth sciences and astrophysics, and will be a valuable resource for researchers at all levels.