Random Functions And Turbulence

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.

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

Turbulence is a research field where high expectations have met with recurrent frustration. It is a common perception among physicists, mathematicians and engineers that there is a "big mystery" behind the phenomenon of turbulence. Its history has also remained anything but well researched. Unlike topics such as quantum theory, which began to attract physics historians as long as fifty years ago, turbulence has - until now - received only little professional historical investigation. In this book, which complements his earlier SpringerBrief "The Turbulence Problem", the author sketches the history of turbulence from the vantage point of its roots (Part I), the basic concepts (Part II) and the formation of a scientific community that regarded turbulence as a research field in its own right (Part III). From this perspective turbulence research appears to undertake an odyssey through uncharted territories. The book follows this development up until a conference in Marseille in the year 1961, which marked the inauguration of turbulence in the words of its organizer as “a new science”. The epilogue contains some observations about turbulence research since 1961. This book provides a rich source of information for all those interested in the history of this major field of basic and applied science.

Wave Propagation and Scattering in Random Media, Volume 2, presents the fundamental formulations of wave propagation and scattering in random media in a unified and systematic manner. The topics covered in this book may be grouped into three categories: waves in random scatterers, waves in random continua, and rough surface scattering. Random scatterers are random distributions of many particles. Examples are rain, fog, smog, hail, ocean particles, red blood cells, polymers, and other particles in a state of Brownian motion. Random continua are the media whose characteristics vary randomly and continuously in time and space. Examples are clear air turbulence, jet engine exhaust, tropospheric and ionospheric turbulence, ocean turbulence, and biological media such as tissue and muscle. Rough surface examples are the ocean surface, planetary surfaces, interfaces between different biological media, and the surface roughness of an optical fiber. This book is intended for engineers and scientists interested in optical, acoustic, and microwave propagation and scattering in atmospheres, oceans, and biological media, and particularly for those involved in communication through such media and remote sensing of the characteristics of these media.

This textbook presents a modern account of turbulence, one of the greatest challenges in physics. The state-of-the-art is put into historical perspective five centuries after the first studies of Leonardo and half a century after the first attempt by A.N. Kolmogorov to predict the properties of flow at very high Reynolds numbers. Such "fully developed turbulence" is ubiquitous in both cosmical and natural environments, in engineering applications and in everyday life. First, a qualitative introduction is given to bring out the need for a probabilistic description of what is in essence a deterministic system. Kolmogorov's 1941 theory is presented in a novel fashion with emphasis on symmetries (including scaling transformations) which are broken by the mechanisms producing the turbulence and restored by the chaotic character of the cascade to small scales. Considerable material is devoted to intermittency, the clumpiness of small-scale activity, which has led to the development of fractal and multifractal models. Such models, pioneered by B. Mandelbrot, have applications in numerous fields besides turbulence (diffusion limited aggregation, solid-earth geophysics, attractors of dynamical systems, etc). The final chapter contains an introduction to analytic theories of the sort pioneered by R. Kraichnan, to the modern theory of eddy transport and renormalization and to recent developments in the statistical theory of two-dimensional turbulence. The book concludes with a guide to further reading. The intended readership for the book ranges from first-year graduate students in mathematics, physics, astrophysics, geosciences and engineering, to professional scientists and engineers.