This book springs from the programme Quantized Vortex Dynamics and Sup- ?uid Turbulence held at the Isaac Newton Institute for Mathematical Sciences (University of Cambridge) in August 2000. What motivated the programme was the recognition that two recent developments have moved the study of qu- tized vorticity, traditionally carried out within the low-temperature physics and condensed-matter physics communities, into a new era. The ?rst development is the increasing contact with classical ?uid dynamics and its ideas and methods. For example, some current experiments with - lium II now deal with very classical issues, such as the measurement of velocity spectra and turbulence decay rates. The evidence from these experiments and many others is that super?uid turbulence and classical turbulence share many features. The challenge is now to explain these similarities and explore the time scales and length scales over which they hold true. The observed classical aspects have also attracted attention to the role played by the ?ow of the normal ?uid, which was somewhat neglected in the past because of the lack of direct ?ow visualization. Increased computing power is also making it possible to study the coupled motion of super?uid vortices and normal ?uids. Another contact with classical physics arises through the interest in the study of super?uid vortex - connections. Reconnections have been studied for some time in the contexts of classical ?uid dynamics and magneto-hydrodynamics (MHD), and it is useful to learn from the experience acquired in other ?elds.

A comprehensive overview of the basic principles of vortex dynamics in superfluids, this book addresses the problems of vortex dynamics in all three superfluids available in laboratories (4He, 3He, and BEC of cold atoms) alongside discussions of the elasticity of vortices, forces on vortices, and vortex mass. Beginning with a summary of classical hydrodynamics, the book guides the reader through examinations of vortex dynamics from large scales to the microscopic scale. Topics such as vortex arrays in rotating superfluids, bound states in vortex cores and interaction of vortices with quasiparticles are discussed. The final chapter of the book considers implications of vortex dynamics to superfluid turbulence using simple scaling and symmetry arguments. Written from a unified point of view that avoids complicated mathematical approaches, this text is ideal for students and researchers working with vortex dynamics in superfluids, superconductors, magnetically ordered materials, neutron stars and cosmological models.

This book discusses the properties of quantized vortex lines in superfluid helium-4 in the light of research on vortices in modern fluid mechanics, and gives the first comprehensive treatment of the problem. The author's comprehensive approach will make this book invaluable for students taking advanced undergraduate or graduate courses, and for all those involved in research on classical and quantum vortices.

This book springs from the programme Quantized Vortex Dynamics and Sup- ?uid Turbulence held at the Isaac Newton Institute for Mathematical Sciences (University of Cambridge) in August 2000. What motivated the programme was the recognition that two recent developments have moved the study of qu- tized vorticity, traditionally carried out within the low-temperature physics and condensed-matter physics communities, into a new era. The ?rst development is the increasing contact with classical ?uid dynamics and its ideas and methods. For example, some current experiments with - lium II now deal with very classical issues, such as the measurement of velocity spectra and turbulence decay rates. The evidence from these experiments and many others is that super?uid turbulence and classical turbulence share many features. The challenge is now to explain these similarities and explore the time scales and length scales over which they hold true. The observed classical aspects have also attracted attention to the role played by the ?ow of the normal ?uid, which was somewhat neglected in the past because of the lack of direct ?ow visualization. Increased computing power is also making it possible to study the coupled motion of super?uid vortices and normal ?uids. Another contact with classical physics arises through the interest in the study of super?uid vortex - connections. Reconnections have been studied for some time in the contexts of classical ?uid dynamics and magneto-hydrodynamics (MHD), and it is useful to learn from the experience acquired in other ?elds.

Leading experts summarize our current understanding of the fundamental nature of turbulence, covering a wide range of topics.

Recent investigations have highlighted the similarities between turbulence in cryogenic fluids at temperatures close to absolute zero, in particular superfluid helium, and turbulence in ordinary fluids. This book contains lectures on various theoretical and experimental aspects of the problem given by experts at the advanced school “Vortices and Turbulence at Low Temperatures” held at CISM, Udine, in the summer of 2007. The lectures provide an introduction into this rapidly expanding area of research. The book is suitable to PhD students and young researchers starting their career as well as established researchers in either low temperature physics or fluid mechanics who are interested in this problem.