This book offers a guide to understanding models of vortex rings, starting from classical ones (circular vortex filament, Hill and Norbury-Fraenkel inviscid models) to very recent models incorporating viscous effects and realistic shapes of the vortex core. Unconfined and confined viscous vortex rings are described by closed formulae for vorticity, stream function, translational velocity, energy, impulse and circulation. Models are applied to predict the formation number of optimal vortex rings and to describe two-phase vortex ring-like structures generated in internal combustion engines. The book provides a detailed presentation of analytical developments of models, backed up by illustrations and systematic comparisons with results of direct numerical simulations. The book is useful for graduate students in applied mathematics, engineering and physical sciences. It is a useful reference for researchers and practising engineers interested in modelling flows with vortex rings.

Vortex flow is one of the fundamental types of fluid and gas motion. These flows are the most spectacular in the form of concentrated vortices, characterized by the localization of vorticity (curl of velocity) in bounded regions of a space, beyond which the vorticity is either absent or rapidly falls down to zero. Concentrated vortices are often observed in nature, exemplified by atmospheric cyclones, whirlwinds and tornados, oceanic vortices, whirlpools on a water s- face, and ring vortices caused by explosive outburst of volcanoes. In technical - vices concentrated vortices form when flow separates from sharp edges of flying vehicles and ships. Among these are vortices flowing off the ends of airplane wings, and intentionally generated vortices for intensification of burning in c- bustion chambers, vortices in cyclonic devices used for mixing or separation of impurities in fluids and gases. One such remarkable and frequent type of conc- trated vortices is a vortex ring which constitutes a vortex tube closed into a t- oidal ring moving in a surrounding fluid like an isolated body out of contact with solid boundaries of the flow region if such boundaries exist. Formation and motion of vortex rings are important part of the dynamics of a continuum medium and have been studied for more than a century.

Fluid Vortices is a comprehensive, up-to-date, research-level overview covering all salient flows in which fluid vortices play a significant role. The various chapters have been written by specialists from North America, Europe and Asia, making for unsurpassed depth and breadth of coverage. Topics addressed include fundamental vortex flows (mixing layer vortices, vortex rings, wake vortices, vortex stability, etc.), industrial and environmental vortex flows (aero-propulsion system vortices, vortex-structure interaction, atmospheric vortices, computational methods with vortices, etc.), and multiphase vortex flows (free-surface effects, vortex cavitation, and bubble and particle interactions with vortices). The book can also be recommended as an advanced graduate-level supplementary textbook. The first nine chapters of the book are suitable for a one-term course; chapters 10--19 form the basis for a second one-term course.

This book offers a guide to understanding models of vortex rings, starting from classical ones (circular vortex filament, Hill and Norbury-Fraenkel inviscid models) to very recent models incorporating viscous effects and realistic shapes of the vortex core. Unconfined and confined viscous vortex rings are described by closed formulae for vorticity, stream function, translational velocity, energy, impulse and circulation. Models are applied to predict the formation number of optimal vortex rings and to describe two-phase vortex ring-like structures generated in internal combustion engines. The book provides a detailed presentation of analytical developments of models, backed up by illustrations and systematic comparisons with results of direct numerical simulations. The book is useful for graduate students in applied mathematics, engineering and physical sciences. It is a useful reference for researchers and practising engineers interested in modelling flows with vortex rings. .

Vortex dynamics is a natural paradigm for the field of chaotic motion and modern dynamical system theory. However, this volume focuses on those aspects of fluid motion that are primarily controlled by the vorticity and are such that the effects of the other fluid properties are secondary.

This book, on the general topic of hydroaerodynamics, investigates a number of exciting applications in this field, addressing specifically issues that allow seemingly paradoxical issues to be dealt with. The first part is devoted to the study of channel flows, in particular the lateral flow of a viscous and viscous-plastic liquid in a ring channel formed by coaxial cylinders. Specifically, the problem of dissipation of mechanical energy in channel flows of highly viscous liquids is addressed and solved. Furthermore, the mechanism leading to hydrodynamic erosion in intra-field pipelines (known as "channelized effect") is identified. Subsequently, a theory for channel flows with mass transfer through porous walls is developed. In the second part, viscous liquid free flows (jets) are investigated. In particular, a dispersion law for turbulent flow is derived and the existence of dynamic invariance in wake flows of variable density is demonstrated. The third part presents new insights from both theoretical and experimental research into concentrated vortex structure formation and development. The conditions for the existence of Taylor-Goertler vortices are determined and the mechanism for their formation is described. Last but not least, the theory of vortex rings, a particularly interesting problem in hydroaerodynamics, is introduced in the last section of this book. Care has been taken, when selecting original theoretical problems of interest, to make the link with related topics in the published literature. At the same time, all experimental research described in this book is given a meaningful physical interpretation and corroborated by suitable theoretical models and computations.

This book is a comprehensive and intensive monograph for scientists, engineers and applied mathematicians, as well as graduate students in fluid dynamics. It starts with a brief review of fundamentals of fluid dynamics, with an innovative emphasis on the intrinsic orthogonal decomposition of fluid dynamic process, by which one naturally identifies the content and scope of vorticity and vortex dynamics. This is followed by a detailed presentation of vorticity dynamics as the basis of later development. In vortex dynamics part the book deals with the formation, motion, interaction, stability, and breakdown of various vortices. Typical vortex structures are analyzed in laminar, transitional, and turbulent flows, including stratified and rotational fluids. Physical understanding of vertical flow phenomena and mechanisms is the first priority throughout the book. To make the book self-contained, some mathematical background is briefly presented in the main text, but major prerequisites are systematically given in appendices. Material usually not seen in books on vortex dynamics is included, such as geophysical vortex dynamics, aerodynamic vortical flow diagnostics and management.

This is the 2nd edition of the book, Flow Visualization: Techniques and Examples, which was published by Imperial College Press in 2000. Many of the chapters have been revised and updated to take into consideration recent changes in a number of flow visualization and measurement techniques, including an updated high quality flow gallery. Unique among similar publications, this book focuses on the practical rather than theoretical aspects. Obtaining high quality flow visualization results is, in many ways, more of an art than a science, and experience plays a key deciding role. The depth and breadth of the material will make this book invaluable to readers of all levels of experience in the field.

With clear illustrations throughout and without recourse to quantum mechanics, the reader is invited to revisit unsolved problems lying at the foundations of theoretical physics. Maxwell and his contemporaries abandoned their search for a geometrical representation of the electric and magnetic fields. The wave-particle dilemma and Bose-Einstein statistical counting have resulted in unsatisfactory non-realistic interpretations. Furthermore, a simple structure of the hydrogen atom that includes hyperfine levels is still wanting.Working with the latest experimental data in photonics a proposed solution to the wave-particle dilemma is suggested based on an array of circular-polarized rays. The Bose-Einstein counting procedure is recast in terms of distinguishable elements. Finally, a vortex model of a 'particle' is developed based on a trapped photon. This consists of a single ray revolving around a toroidal surface, and allows a geometrical definition of mass, electric potential, and magnetic momentum. With the adjustment of two parameters, values to 4 dp for the hyperfine frequencies (MHz) of hydrogen can be obtained for which a computer program is available.