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This is a comprehensive account of the asymptotic theory of slender vortices with diffusion cores. Addressed to both graduate students and researchers it describes the mathematical model and its numerical analysis. The asymptotic analysis involves two length and two time scales. Consistency conditions and time invariance of moments of vorticity are given and applied to numerical solutions. The authors also describe consistency conditions between the large circumferential and axial velocity in the core.
This book is a comprehensive and intensive book for graduate students in fluid dynamics as well as scientists, engineers and applied mathematicians. Offering a systematic introduction to the physical theory of vortical flows at graduate level, it considers the theory of vortical flows as a branch of fluid dynamics focusing on shearing process in fluid motion, measured by vorticity. It studies vortical flows according to their natural evolution stages,from being generated to dissipated. As preparation, the first three chapters of the book provide background knowledge for entering vortical flows. The rest of the book deals with vortices and vortical flows, following their natural evolution stages. Of various vortices the primary form is layer-like vortices or shear layers, and secondary but stronger form is axial vortices mainly formed by the rolling up of shear layers. Problems are given at the end of each chapter and Appendix, some for helping understanding the basic theories, and some involving specific applications; but the emphasis of both is always on physical thinking.
This is a comprehensive account of the asymptotic theory of slender vortices with diffusion cores. Addressed to both graduate students and researchers it describes the mathematical model and its numerical analysis. The asymptotic analysis involves two length and two time scales. Consistency conditions and time invariance of moments of vorticity are given and applied to numerical solutions. The authors also describe consistency conditions between the large circumferential and axial velocity in the core.
This 2006 book details exact solutions to the Navier-Stokes equations for senior undergraduates and graduates or research reference.
This book is a comprehensive and intensive monograph for scientists, engineers and applied mathematicians, as well as graduate students in fluid dynamics. It starts with a brief review of fundamentals of fluid dynamics, with an innovative emphasis on the intrinsic orthogonal decomposition of fluid dynamic process, by which one naturally identifies the content and scope of vorticity and vortex dynamics. This is followed by a detailed presentation of vorticity dynamics as the basis of later development. In vortex dynamics part the book deals with the formation, motion, interaction, stability, and breakdown of various vortices. Typical vortex structures are analyzed in laminar, transitional, and turbulent flows, including stratified and rotational fluids. Physical understanding of vertical flow phenomena and mechanisms is the first priority throughout the book. To make the book self-contained, some mathematical background is briefly presented in the main text, but major prerequisites are systematically given in appendices. Material usually not seen in books on vortex dynamics is included, such as geophysical vortex dynamics, aerodynamic vortical flow diagnostics and management.
Fluid Vortices is a comprehensive, up-to-date, research-level overview covering all salient flows in which fluid vortices play a significant role. The various chapters have been written by specialists from North America, Europe and Asia, making for unsurpassed depth and breadth of coverage. Topics addressed include fundamental vortex flows (mixing layer vortices, vortex rings, wake vortices, vortex stability, etc.), industrial and environmental vortex flows (aero-propulsion system vortices, vortex-structure interaction, atmospheric vortices, computational methods with vortices, etc.), and multiphase vortex flows (free-surface effects, vortex cavitation, and bubble and particle interactions with vortices). The book can also be recommended as an advanced graduate-level supplementary textbook. The first nine chapters of the book are suitable for a one-term course; chapters 10--19 form the basis for a second one-term course.
Many important phenomena in fluid motion are evident in vortex flow, i.e., flows in which vortical structures are significant in determining the whole flow. This book, which consists of lectures given at a NATO ARW held in Grenoble (France) in June 1992, provides an up-to-date account of current research in the study of these phenomena by means of numerical methods and mathematical modelling. Such methods include Eulerian methods (finite difference, spectral and wavelet methods) as well as Lagrangian methods (contour dynamics, vortex methods) and are used to study such topics as 2- or 3-dimensional turbulence, vorticity generation by solid bodies, shear layers and vortex sheets, and vortex reconnection. For researchers and graduate students in computational fluid dynamics, numerical analysis, and applied mathematics.
Every scientific subject probably conceals unexplored or little investigated strata, which may show up at the proper time when favourable conditions coincide (practical demands, a circle of scientists prepared to recognize the novelty and capable of giving impetus to the development of a new theory, etc.). Something like this occurred in early seventies for magnetohydrodynamics, which at the time was considered to be a relatively complete branch of hydro dynamics with no apparent broad, unexplored areas. It was unexpectedly realized that, in addition to the traditional methods of affecting an electrically conducting medium, there is yet another way, one which subsequently lead to a new direction in magnetohydrodynamics. In the Soviet scientific literature this direction has been termed 'electrically induced vortex flows', the essence of which are hydrodynamic effects due to the interaction of an electric current passing through the fluid with its own magnetic field. It cannot be said that this direction was created ex nihilo: individual studies related to the flows driven in a current-carrying medium in the absence of external magnetic fields appeared in the sixties; in the thirties the flows them selves were known to take place within electrical arcs; and yet the first observa tions on the behaviour of liquid current-carrying conductors were made at the beginning of this century.
Vortex methods have matured in recent years, offering an interesting alternative to finite difference and spectral methods for high resolution numerical solutions of the Navier Stokes equations. In the past three decades, research into the numerical analysis aspects of vortex methods has provided a solid mathematical background for understanding the accuracy and stability of the method. At the same time vortex methods retain their appealing physical character, which was the motivation for their introduction. This book presents and analyzes vortex methods as a tool for the direct numerical simulation of impressible viscous flows. It will interest graduate students and researchers in numerical analysis and fluid mechanics and also serve as an ideal textbook for courses in fluid dynamics.
The aerodynamics of aircraft at high angles of attack is a subject which is being pursued diligently, because the modern agile fighter aircraft and many of the current generation of missiles must perform well at very high incidence, near and beyond stall. However, a comprehensive presentation of the methods and results applicable to the studies of the complex aerodynamics at high angle of attack has not been covered in monographs or textbooks. This book is not the usual textbook in that it goes beyond just presenting the basic theoretical and experimental know-how, since it contains reference material to practical calculation methods and technical and experimental results which can be useful to the practicing aerospace engineers and scientists. It can certainly be used as a text and reference book for graduate courses on subjects related to high angles of attack aerodynamics and for topics related to three-dimensional separation in viscous flow courses. In addition, the book is addressed to the aerodynamicist interested in a comprehensive reference to methods of analysis and computations of high angle of attack flow phenomena and is written for the aerospace scientist and engineer who is familiar with the basic concepts of viscous and inviscid flows and with computational methods used in fluid dynamics.