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.

Modelling Approaches and Computational Methods for Particle-laden Turbulent Flows introduces the principal phenomena observed in applications where turbulence in particle-laden flow is encountered while also analyzing the main methods for analyzing numerically. The book takes a practical approach, providing advice on how to select and apply the correct model or tool by drawing on the latest research. Sections provide scales of particle-laden turbulence and the principal analytical frameworks and computational approaches used to simulate particles in turbulent flow. Each chapter opens with a section on fundamental concepts and theory before describing the applications of the modelling approach or numerical method. Featuring explanations of key concepts, definitions, and fundamental physics and equations, as well as recent research advances and detailed simulation methods, this book is the ideal starting point for students new to this subject, as well as an essential reference for experienced researchers. - Provides a comprehensive introduction to the phenomena of particle laden turbulent flow - Explains a wide range of numerical methods, including Eulerian-Eulerian, Eulerian-Lagrange, and volume-filtered computation - Describes a wide range of innovative applications of these models

1. ABOUT THE DISCIPLINE 'DYNAMIC METEOROLOGY' The name 'dynamic meteorology' is traditional for designating a university course as well as the scientific branch of meteorology as a whole. While there is no need to abandon this name, it needs contemporary treatment and specifications in its definition. A synonym for it could be 'dynamics (more precisely, hydrodynamics or fluid dynamics) of the atmosphere'. It suggests the relationship of this discipline to general hydrodynamics and applied mathematics and its pronounced theoretical nature. Besides the atmosphere, however, our planet has another (liquid) envelope - the hydrosphere (world's ocean), which also concerns ocean dynamics and, therefore, it is necessary to define, from a unified standpoint, the subject and aims of the disciplines dealing with the dynamics of the processes which take place in both fluid spheres. Such a unified standpoint offers the so-called geophysical fluid dynamics. During the past few years this description is encountered quite often in scientific literature concerning the Earth as a planet. Obviously, a scientific branch or a science is created whose subject is our planet and the investigation methods are borrowed from classical fluid dynamics and applied mathematics, including the most recent numerical methods. As can be seen from its very suitable name, it is the dynamics of quite definite geophysical fluids (atmosphere, ocean and even the liquid inside of the Earth) and not of some abstract (often perfect) flUids, as in classical hydrodynamics.

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