International Series of Monographs in Natural Philosophy, Volume 32: Random Functions and Turbulence focuses on the use of random functions as mathematical methods. The manuscript first offers information on the elements of the theory of random functions. Topics include determination of statistical moments by characteristic functions; functional transformations of random variables; multidimensional random variables with spherical symmetry; and random variables and distribution functions. The book then discusses random processes and random fields, including stationarity and ergodicity of random processes; influence of finiteness of the interval of averaging; scalar and vector random fields; and statistical moments. The text takes a look at the statistical theory of turbulence. Topics include turbulence with very large Reynolds numbers; emergence of turbulent motion; and energy spectrum in isothermal turbulent shear flow. The book also discusses small-scale and large-scale atmospheric turbulence and applications to numerical weather analysis and prediction. The manuscript is a vital source of data for readers interested in random theory.

This accessible treatment offers the mathematical tools for describing and solving problems related to stochastic vector fields. Advanced undergraduates and graduate students will find its use of generalized functions a relatively simple method of resolving mathematical questions. It will prove a valuable reference for applied mathematicians and professionals in the fields of aerospace, chemical, civil, and nuclear engineering. The author, Professor Emeritus of Engineering at Cornell University, starts with a survey of probability distributions and densities and proceeds to examinations of moments, characteristic functions, and the Gaussian distribution; random functions; and random processes in more dimensions. Extensive appendixes—which include information on Fourier transforms, tensors, generalized functions, and invariant theory—contribute toward making this volume mathematically self-contained.

Fluid flow turbulence is a phenomenon of great importance in many fields of engineering and science.

This is a reissue of Professor Batchelor's text on the theory of turbulent motion, which was first published by Cambridge Unviersity Press in 1953. It continues to be widely referred to in the professional literature of fluid mechanics, but has not been available for several years. This classic account includes an introduction to the study of homogeneous turbulence, including its mathematic representation and kinematics. Linear problems, such as the randomly-perturbed harmonic oscillator and turbulent flow through a wire gauze, are then treated. The author also presents the general dynamics of decay, universal equilibrium theory, and the decay of energy-containing eddies. There is a renewed interest in turbulent motion, which finds applications in atmospheric physics, fluid mechanics, astrophysics, and planetary science.

This monograph describes the phenomena associated with the propagation of electromagnetic and acoustic waves through atmospheric turbulence. Geared toward specialists in radiophysics and atmospheric acoustics and optics, the treatment is also suitable for advanced undergraduates and graduate students. The author stresses applications to phase and amplitude fluctuations, scintillation of stars, radio scattering, and other problems. Part I covers topics from the theory of random fields and turbulence theory, including statistical description. Part II, on the scattering of waves in the turbulent atmosphere, is supplemented by an appendix on scattering of acoustic radiation. Part III offers a detailed presentation of line-of-sight propagation of acoustic and electromagnetic waves through a turbulent medium. Part IV concludes the text with a comparison of theory with experimental data

Now in its fully updated fourth edition, this leading text in its field is an exhaustive monograph on turbulence in fluids in its theoretical and applied aspects. The authors examine a number of advanced developments using mathematical spectral methods, direct-numerical simulations, and large-eddy simulations. The book remains a hugely important contribution to the literature on a topic of great importance for engineering and environmental applications, and presents a very detailed presentation of the field.

Turbulence takes place in practically all flow situations that occur naturally or in modern technological systems. Therefore, considerable effort is being expended in an attempt to understand this very complex physical phenome non and to develop both empirical and mathematical models for its description. Such numerical and analytical computational schemes would allow the reliable prediction and design of turbulent flow processes to be carried out. The purpose of this book is to bring together, in a usable form, some of the fundamental concepts of turbulence along with turbulence models and experimental techniques. It is hoped that these have "general applicability" in current engineering design. The phrase "general applicabil ity" is highlighted because the theory of turbulence is still so much in a formative stage that completely general analyses are not available now, nor will they be available in the immediate future. The concepts and models described herein represent the state-of-the art methods that are now being used to give answers to turbulent flow problems. As in all turbulent flow analysis, the methods are a blend of analytical and empirical input, and the reader should be cognizant of the simplification and restrictions imposed upon the methods when applyingthem to physical situations different from those for which they have been developed.

The theory of turbulence reached its full growth at the end of the 19th century as a result of the work by Boussinesq and Reynolds. It then underwent a long period of stagnation which ended under the impulse given to it by the development of wind tunnels caused by the needs of aviation. Numerous researchers, attempted to put Reynolds' elementary statistical theory into a more precise form.

This volume comprises selected papers presented at the Sixth International Conference on Difference Equations which was held at Augsburg, Germany. It covers all themes in the fields of discrete dynamical systems and ordinary and partial difference equations, classical and contemporary, theoretical and applied. It provides a useful reference text for graduates and researchers working in this area of mathematics.

The present volume comprises the contributions of some of the participants of the NATO Advance Studies Institute "Turbulence, Weak and Strong", held in Cargese, in August 1994. More than 70 scientists, from seniors to young students, have joined to gether to discuss and review new (and not so new) ideas and developments in the study of turbulence. One of the objectives of the School was to incorporate, in the same meeting, two aspects of turbulence, which are obviously linked, and which are often treated sep arately: fully developed turbulence (in two and three dimensions) and weak turbulence (essentially one and two-dimensional systems). The idea of preparing a dictionary rather than ordinary proceedings started from the feeling that the terminology of turbulence includes many long, technical, poorly evocative words, which are usually not understood by people exterior to the field, and which might be worth explaining. Students who start working in the field of turbulence face a sort of curious situation: on one side, they are aware that turbulence is related to the disordered, churning flows of torrents, the pow erful movements of water in the oceans, the violent jet streams in the troposphere, the solar eruptions, and they are certainly excited to pierce the mystery of this fascinating, omnipresent phenomenon.