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The average rate at which the radar signal crosses a voltage level is linearly dependent on the root mean square of the turbulent wind component in the direction of the beam (1, 2), and therefore constitutes an anemometer with these characteristics. All tracers within the illuminated volume contribute to the signal. This anemometer therefore senses an average over the space they occupy which is at most equivalent to a cylinder standing half a pulse length high and straddling a diameter equal to the product of the range and beamwidth.
Turbulence-the randomly disordered movement of volumes of air of widely varying size-is one of the characteristic features of atmospheric air flows; its investigation is essential for the solution of several theoretical and practical problems. Until recently, owing to experimental difficulties, research on turbu lence was confmed mainly to the lower half of the troposphere. Theoretical investigations have consequently been based on these data. The rapid development of high-altitude aviation and cases of aircraft encoun tering hazardous turbulence led to a sharp intensification of research on turbu lence in the atmosphere up to 10-12 km, and subsequently at greater altitudes. Such research was confined initially to the characterization of the frequency of occurrence of gusts of different speeds, their relation to altitude, geographical conditions, time of day and year, and so on. At the end of the fifties, when the required measuring equipment and experimental techniques had been developed, it became possible to investigate the complete statistical characteristics of turbu lence: the spectral densities of the velocity fluctuations of air flows, structure functions, etc. These data stimulated the further development of theory related to the specific conditions of the free atmosphere.
Since the human organism is itself an open system, we are naturally curious about the behavior of other open systems with fluxes of matter, energy or information. Of the possible open systems, it is those endowed with many degrees of freedom and strongly deviating from equilibrium that are most challenging. A simple but very significant example of such a system is given by developed turbulence in a continuous medium, where we can discern astonishing features of universality. This two-volume monograph deals with the theory of turbulence viewed as a general physical phenomenon. In addition to vortex hydrodynamic turbulence, it considers various cases of wave turbulence in plasmas, magnets, atmosphere, ocean and space. A sound basis for discussion is provided by the concept of cascade turbulence with relay energy transfer over different scales and modes. We shall show how the initial cascade hypothesis turns into an elegant theory yielding the Kolmogorov spectra of turbulence as exact solutions. We shall describe the further development of the theory discussing stability prob lems and modes of Kolmogorov spectra formation, as well as their matching with sources and sinks. This volume is dedicated to developed wave turbulence in different media.
Based on his over forty years of research and teaching, John C. Wyngaard's textbook is an excellent up-to-date introduction to turbulence in the atmosphere and in engineering flows for advanced students, and a reference work for researchers in the atmospheric sciences. Part I introduces the concepts and equations of turbulence. It includes a rigorous introduction to the principal types of numerical modeling of turbulent flows. Part II describes turbulence in the atmospheric boundary layer. Part III covers the foundations of the statistical representation of turbulence and includes illustrative examples of stochastic problems that can be solved analytically. The book treats atmospheric and engineering turbulence in a unified way, gives clear explanation of the fundamental concepts of modeling turbulence, and has an up-to-date treatment of turbulence in the atmospheric boundary layer. Student exercises are included at the ends of chapters, and worked solutions are available online for use by course instructors.
Radiophysical tools for measuring atmospheric dynamics include sodars, Doppler radars, and Doppler lidars. Among these, coherent Doppler lidars (CDLs) have been considered the best for remote measurement of wind turbulence. This is important not only for understanding the exchange processes in the boundary layer, but also in the applied aspect, such as aviation safety. CDLs significantly extend possibilities of experimental investigation of not only wind turbulence, but also coherent structures such as aircraft wake vortices. The authors of this book conducted field tests of the developed methods of lidar measurements of the wind velocity, atmospheric turbulence parameters, and aircraft wake vortices. This valuable resource, containing over 500 equations based on original results from the authors’ work, gives professionals a comprehensive description of the operating principles of continuous wave and pulsed coherent Doppler lidars. This book studies the possibilities of obtaining information about wind turbulence from data measured by continuous wave and pulsed CDLs. The procedures for estimation are described, as well as algorithms for numerical simulation. Results on the vortex behavior and evolution are then presented.
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.
"If ever a book on turbulence could be called definitive," declared Science, "it is this book by two of Russia's most eminent and productive scientists in turbulence, oceanography, and atmospheric physics." Noted for its clarity as well as its comprehensive treatment, this two-volume set serves as text or reference. 1975 edition.