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This book is intended to serve as an introduction to the multidisciplinary ?eld of anomalous diffusion in complex systems such as turbulent plasma, convective rolls, zonal ?ow systems, stochastic magnetic ?elds, etc. In spite of its great importance, turbulent transport has received comparatively little treatment in published mo- graphs. This book attempts a comprehensive description of the scaling approach to turbulent diffusion. From the methodological point of view, the book focuses on the general use of correlation estimates, quasilinear equations, and continuous time random walk - proach. I provide a detailed structure of some derivations when they may be useful for more general purposes. Correlation methods are ?exible tools to obtain tra- port scalings that give priority to the richness of ingredients in a physical pr- lem. The mathematical description developed here is not meant to provide a set of “recipes” for hydrodynamical turbulence or plasma turbulence; rather, it serves to develop the reader’s physical intuition and understanding of the correlation mec- nisms involved.
This book grew out of an introductory course that I was invited to teach on a number of occasions to senior and graduate level students at the University of Kid. I have cherished these opportunities in part because I was never required to conduct examinations or give grades. For the students, however, my good fortune presented special problems that induced my sympathy: in addition to having to contend with a foreign language, they would eventually have to confront an examiner with his own ideas about what they should have learned. Although I always left a copy of my lecture notes with this person, they were too sketchy to be of much use. The present book is an attempt to solve some of these problems. The content is intended to be as broad as possible within the limitations of an introductory one-semester course. It aims at providing an insightful view of present understanding, emphasizing the methods and the history of their development. In particular I have tried to expose the power of intuitive reasoning - the nature of tensor invariants, the usefulness of dimensional analysis, and the relevance of scales of physical quantities in the inference of relationships. I know of no other subject that has benefited more from these important tools, which seem to be widely neglected in the teaching of more fundamental disciplines.
The rather excessive public preoccupation of the immediate past with what has been labeled the 'environmental crisis' is now fortunately being replaced by a more sus tained and rational concern with pollution problems by public administrators, engineers, and scientists. It is to be expected that members of the engineering profes sion will in the future widely be called upon to design disposal systems for gaseous and liquid wastes which meet strict pollution control regulations and to advise on possible improvements to existing systems of this kind. The engineering decisions involved will have to be based on reasonably accurate quantitative predictions of the effects of pollutants introduced into the atmosphere, ocean, lakes and rivers. A key input for such calculations comes from the theory of turbulent diffusion, which enables the prediction of the concentrations in which pollutants may be found in the neighborhood of a release duct, such as a chimney or a sewage outfall. Indeed the role of diffusion theory in pollution prediction may be likened to the role of applied mechanics (,strength of materials') in the design of structures for adequate strength. At least a certain group of engineers will have to be proficient in applying this particular branch of science to practical problems. At present, training in the theory of turbulent diffusion is available only at the gra duate level and then only in a very few places.
Turbulence, mixing and the mutual interaction of turbulence and chemistry continue to remain perplexing and impregnable in the fron tiers of fluid mechanics. The past ten years have brought enormous advances in computers and computational techniques on the one hand and in measurements and data processing on the other. The impact of such capabilities has led to a revolution both in the understanding of the structure of turbulence as well as in the predictive methods for application in technology. The early ideas on turbulence being an array of complicated phenomena and having some form of reasonably strong coherent struc ture have become well substantiated in recent experimental work. We are still at the very beginning of understanding all of the aspects of such coherence and of the possibilities of incorporating such structure into the analytical models for even those cases where the thin shear layer approximation may be valid. Nevertheless a distinguished body of "eddy chasers" has come into existence. The structure of mixing layers which has been studied for some years in terms of correlations and spectral analysis is also getting better understood. Both probability concepts such as intermittency and conditional sampling as well as the concept of large scale structure and the associated strain seem to indicate possibilities of distinguishing and synthesizing 'engulfment' and molecular mixing.
The analysis and control of mixing is of great interest because of the potential for optimizing the performance of many flow processes. This monograph presents a unique overview of the physics, mathematics and state-of-the-art theoretical/numerical modeling and experimental investigations of mixing. It approaches the subject of mixing from many angles: presents theoretical and experimental results, discusses laminar and turbulent flows, considers macro and micro scales, elaborates on purely advective and advective-diffusive flows, and considers conceptual and industrial-relevant mixing devices. This monograph provides an essential reading for graduate students and postdoctoral researches interested in the investigation of mixing, and constitutes an indispensable reference for mechanical, chemical and aeronautical engineers, and applied mathematicians in universities and industries.
The 35th OHOLO Conference, which provided the basis for the present book covered a broad range of topics. Basic studies and newly developed methods in modeling atmospheric flows are discussed, besides analyses of concentration fluctuations in different atmospheric conditions, and techniques of data acquisition. The book gives an excellent state-of-the-art impression of the situation in turbulent diffusion and transport.
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