The field of shock compression science has a long and rich history involving contributions of mathematicians, physicists and engineers over approximately two hundred years. The middle of the nineteenth century was an especially ac tive period with the contributions of Riemann, Rankine and Hugoniot, among others. The middle of the twentieth century saw another increase in activity re lated to shock compression of condensed matter as a result of military applica tions. It was also recognized that shock compression provided a means of sub jecting solids and liquids to extreme states of temperature and pressure difficult to achieve by static means. It has thus become an academic study in its own right. The principal modem contributions to this science were summarized in the landmark paper by Rice, McQueen and Walsh [Solid State Physics, Vol. 6, pp. 1-63, 1958]. As this field has continued to mature, interest has increased in tracing the early papers that have served as the foundations of the field. Cheret [Shock Compression of Condensed Matter - 1989, Elsevier Sci. Pub. B. V. , pp 11-19, 1990) has contributed to this literature with his review of the life of Hugoniot on the one-hundredth anniversary of the publication of Hugoniot's classic paper on the propagation of discontinuous waves in gases. This contribution prompted additional historical investigation involving the precursors to Hugoniot.

This book is one of three volumes entitled "ECARP-European Computational Aerodynamics Research Project", which was supported by the European Union in the Aeronautics Area of the Industrial and Materials Technology Programme. This volume contains optimization techniques for a number of inviscid and viscous problems like drag reduction, inverse, multipoint, wing-pylon-nacelle and riblets (Part A); and methodologies for solving the Navier Stokes equations on parallel architectures for compressible viscous flows in two and three dimensions (Part B). The main objective of this book is to disseminate information about cost effective methodologies for practical design problems and parallel CFD to be used by computer scientists and multidisciplinary engineers.

The problems of ocean dynamics present more and more com plex tasks for investigators, based on the continuously sophisti cation of theoretical models, which are applied with the help of universal and efficient algorithms of numerical mathematics. The present level of our knowledge in the field of mathemat ical physics and numerical mathematics allows one to give rather complete theoretical analysis of basic statements of problems as well as numerical algorithms. Our task is to perform such analy sis and also to analyze the results of calculations in order to improve our knowledge of the mechanism of large-scale hy drological processes occurring in the World Ocean. The new level of numerical mathematics has essentially influenced, the formation of new solution methods of ocean dynamics prob lems, among which an important one is the splitting method, which has been already widely practised in various fields of science and engineering. A number of monographs by N. N. Yanenko, A. A. Samarsky, G. . Marchuk (Rozhdestvensky and Yanenko 1968; Samarsky and Andreyev 1976; Marchuk 1970, 1980b) and others are devoted to the description of this methods. But the methods of the splitting theory require extensive creative work for their application to concrete problems, which are peculiar, as a rule, in problem formulation. The success of the application of these methods is related to the deep understanding of the essence of the described processes. In the last decades fundamental works of Arakawa, K."

This volume consists of papers selected from the proceedings of the Fifth International Symposium on Applications of Laser Techniques to Fluid Mechanics, held at the Calouste Gulbenkian Foundation in Lisbon from 9 to 12 July, 1990. Relative to previous meetings in the Lisbon series the scope of this symposium was broadened by expanding the topical coverage to include all laser techniques used in fluid mechanics. This change recognized the trend amongst experimental fluid dynamicists to employ laser techniques for the mea surement of many different quantities, including concentration, temperature, particle size, and velocity, and the need for researchers to have a forum in which to communicate their work and share their common interests. The Fifth Symposium contained twenty-three sessions of formal presentations and a lively Open Forum ses sion. In addition, Dr. H. J. Pfeiffer organized a special Workshop on the Use of Computers in Flow Mea surements which contained five sessions on frequency domain processors, correIa tors, special detectors, and biasing."

This textbook treats Hydro- and Fluid Dynamics, the engineering science dealing with forces and energies generated by fluids in motion, playing a vital role in everyday life. Practical examples include the flow motion in the kitchen sink, the exhaust fan above the stove, and the air conditioning system in our home. When driving a car, the air flow around the vehicle body induces some drag which increases with the square of the car speed and contributes to excess fuel consumption. Engineering applications encompass fluid transport in pipes and canals, energy generation, environmental processes and transportation (cars, ships, aircrafts). This book deals with the topic of applied hydrodynamics. The lecture material is grouped into two complementary sections: ideal fluid flow and real fluid flow. The former deals with two- and possibly three-dimensional fluid motions that are not subject to boundary friction effects, while the latter considers the flow regions affected by boundary friction and turbulent shear. The lecture material is designed as an intermediate course in fluid dynamics for senior undergraduate and postgraduate students in Civil, Environmental, Hydraulic and Mechanical Engineering. It is supported by notes, applications, remarks and discussions in each chapter. Moreover a series of appendices is added, while some major homework assignments are developed at the end of the book, before the bibliographic references.

A modern introduction to methods of statistical mechanics in turbulence, this volume explains the methodology of non-equilibrium statistical mechanics and how it plays an increasingly important role in modern turbulence research. The range of relevant tools and methods is so wide and developing so fast, that until now there has not been a single book covering the subject. This much-needed book is comprised of three harmonized lecture courses by world class experts in statistical physics and turbulence: John Cardy introduces Field Theory and Non-Equilibrium Statistical Mechanics; Gregory Falkovich discusses Turbulence Theory as part of Statistical Physics; and Krzysztof Gawedzki examines Soluble Models of Turbulent Transport. To encourage readers to deepen their understanding of the theoretical material, each chapter contains exercises with solutions. Essential reading for students and researchers in the field of theoretical turbulence, this volume will also interest any scientist or engineer who applies knowledge of turbulence and non-equilibrium physics to their work.

Turbulence modeling both addresses a fundamental problem in physics, 'the last great unsolved problem of classical physics, ' and has far-reaching importance in the solution of difficult practical problems from aeronautical engineering to dynamic meteorology. However, the growth of supercom puter facilities has recently caused an apparent shift in the focus of tur bulence research from modeling to direct numerical simulation (DNS) and large eddy simulation (LES). This shift in emphasis comes at a time when claims are being made in the world around us that scientific analysis itself will shortly be transformed or replaced by a more powerful 'paradigm' based on massive computations and sophisticated visualization. Although this viewpoint has not lacked ar ticulate and influential advocates, these claims can at best only be judged premature. After all, as one computational researcher lamented, 'the com puter only does what I tell it to do, and not what I want it to do. ' In turbulence research, the initial speculation that computational meth ods would replace not only model-based computations but even experimen tal measurements, have not come close to fulfillment. It is becoming clear that computational methods and model development are equal partners in turbulence research: DNS and LES remain valuable tools for suggesting and validating models, while turbulence models continue to be the preferred tool for practical computations. We believed that a symposium which would reaffirm the practical and scientific importance of turbulence modeling was both necessary and timely."

The primary purpose of this text is to document many of the lessons that have been learned during the author s more than forty years in the field of blast and shock. The writing therefore takes on an historical perspective, in some sense, because it follows the author s experience. The book deals with blast waves propagating in fluids or materials that can be treated as fluids.

It begins by distinguishing between blast waves and the more general category of shock waves. It then examines several ways of generating blast waves, considering the propagation of blast waves in one, two and three dimensions as well as through the real atmosphere. One section treats the propagation of shocks in layered gases in a more detailed manner.

The book also details the interaction of shock waves with structures in particular reflections, progressing from simple to complex geometries, including planar structures, two-dimensional structures such as ramps or wedges, reflections from heights of burst, and three-dimensional structures.

Intended for those with a basic knowledge of algebra and a solid grasp of the concepts of conservation of mass and energy, the text includes an introduction to blast wave terminology and conservation laws as well as a discussion of units and the importance of consistency."

Singularities in Fluids, Plasmas and Optics, which contains the proceedings of a NATO Workshop held in Heraklion, Greece, in July 1992, provides a survey of the state of the art in the analysis and computation of singularities in physical problems drawn from fluid mechanics, plasma physics and nonlinear optics. The singularities include curvature singularities on fluid interfaces, the onset of turbulence in 3-D inviscid flows, focusing singularities for laser beams, and magnetic reconnection. The highlights of the book include the nonlinear Schrodinger equation for describing laser beam focusing, the method of complex variables for the analysis and computation of singularities on fluid interfaces, and studies of singularities for the 3-D Euler equations. The book is suitable for graduate students and researchers in these areas."

In the present book the reader will find a review of methods for constructing a certain class of asymptotic solutions, which we call self-stabilizing solutions. This class includes solitons, kinks, traveling waves, etc. It can be said that either the solutions from this class or their derivatives are localized in the neighborhood of a certain curve or surface. For the present edition, the book published in Moscow by the Nauka publishing house in 1987, was almost completely revised, essentially up-dated, and shows our present understanding of the problems considered. The new results, obtained by the authors after the Russian edition was published, are referred to in footnotes. As before, the book can be divided into two parts: the methods for constructing asymptotic solutions ( Chapters I-V) and the application of these methods to some concrete problems (Chapters VI-VII). In Appendix a method for justification some asymptotic solutions is discussed briefly. The final formulas for the asymptotic solutions are given in the form of theorems. These theorems are unusual in form, since they present the results of calculations. The authors hope that the book will be useful to specialists both in differential equations and in the mathematical modeling of physical and chemical processes. The authors express their gratitude to Professor M. Hazewinkel for his attention to this work and his support.

This technical book considers the application side of LDA techniques. Starting from the basic theories that are crucial for each LDA user, the main subject of the book is focused on diverse application methods. In details, it deals with universal methodical techniques that have been mostly developed in the last 15 years. The book thus gives for the first time an application reference for LDA users in improving the optical conditions and enhancing the measurement accuracies. It also provides the guidelines for simplifying the measurements and correcting measurement errors as well as for clarifying the application limits and extending the application areas of LDA techniques. Beside the treatments of some traditional optical and flow mechanical features influencing the measurement accuracies, the book shows a broad spectrum of LDA application methods in the manner of measuring the flow turbulence, resolving the secondary flow structures, and quantifying the optical aberrations at measurements of internal flows etc.. Thus, it also supports the further developments of both the hard- and software of LDA instrumentations.

This book is devoted to an investigation of the basic problems of the the- ory of random fields which are characterized by certain singular properties (e. g., unboundedness, or vanishing) of their spectral densities. These ran- dom fields are called, the random fields with singular spectrum, long-memory fields, random fields with long-range dependence, fields with slowly decaying correlations or strongly dependent random fields by various authors. This phenomenon has been observed empirically by many scientists long before suitable mathematical models were known. The methods and results differ significantly from the theory of weakly dependent random fields. The first chapter presents basic concepts of the spectral theory of random fields, some examples of random processes and fields with singular spectrum, Tauberian and Abelian theorems for the covariance function of singular ran- dom fields. In the second chapter limit theorems for non-linear functionals of random fields with singular spectrum are proved. Chapter 3 summarizes some limit theorems for geometric functionals of random fields with long-range dependence. Limit distributions of the solutions of Burgers equation with random data via parabolic and hyperbolic rescaling are presented in chapter 4. And chapter 5 presents some problems of statistical analysis of random fields with singular spectrum. I would like to thank the editor, Michiel Hazewinkel, for his support. I am grateful to the following students and colleagues: 1. Deriev, A. Olenko, K. Rybasov, L. Sakhno, M. Sharapov, A. Sikorskii, M. Silac-BenSic. I would also like to thank V.Anh, O. Barndorff-Nielsen,Yu. Belyaev, P.

This study is one of the first attempts to bridge the theoretical models of variational dynamics of perfect fluids and some practical approaches worked out in chemical and mechanical engineering in the field newly called thermo-hydrodynamics. In recent years, applied mathematicians and theoretical physicists have made significant progress in formulating analytical tools to describe fluid dynamics through variational methods. These tools are much loved by theoretists, and rightly so, because they are quite powerful and beautiful theoretical tools. Chemists, physicists and engineers, however, are limited in their ability to use these tools, because presently they are applicable only to "perfect fluids" (i. e. those fluids without viscosity, heat transfer, diffusion and chemical reactions). To be useful, a model must take into account important transport and rate phenomena, which are inherent to real fluid behavior and which cannot be ignored. This monograph serves to provide the beginnings of a means by which to extend the mathematical analyses to include the basic effects of thermo-hydrodynamics. In large part a research report, this study uses variational calculus as a basic theoretical tool, without undo compromise to the integrity of the mathematical analyses, while emphasizing the conservation laws of real fluids in the context of underlying thermodynamics --reversible or irreversible. The approach of this monograph is a new generalizing approach, based on Nother's theorem and variational calculus, which leads to the energy-momentum tensor and the related conservation or balance equations in fluids.

Aircraft concepts are always driven by the requirements of the desired m- sion. A di?erent purpose for the use of the aircraft consequently results in a di?erent design. Therefore, depending on the intended outcome, con?i- ing requirements need to be ful?lled, for example, e?cient cruise speed and greatercargocapabilities,in combinationwith shorttake-o?andlanding ?eld lengths, or high speed and agility combined with variable payload demands. Due to the highly complex, non-linear physical environment in which aircraft operate, this task demands that the most advanced methods and tools are employed, to gain the necessary understanding of ?ow phenomena, and to exploit the ?ow physics to achieve maximum aircraft e?ciency. Inthe naturalsciences,researcherstry to create andextend humankno- edge by understanding and explaining the mechanisms of physical processes. In engineering, a designer is limited by certain requirements, and in order to ful?l these requirements the necessary technical tools need to be designed. In general, for a given problem the corresponding scienti?c or technical solution is sought. In order to successfully advance from a problem towards a solution, three main methods may be used. The two classical methods include theory and experiment, which are now being complemented by a third method, - scribedasnumericalsimulation.Theexperimentalapproachis basedonph- ical observation, measurement of relevant values, and methodical variation of the subject matter. For example, such experiments are used to gain a ph- ical understanding as well as to validate and investigate design alternatives.

The origins of turbulent ?ow and the transition from laminar to turbulent ?ow are the most important unsolved problems of ?uid mechanics and aerodynamics. - sides being a fundamental question of ?uid mechanics, there are numerous app- cations relying on information regarding transition location and the details of the subsequent turbulent ?ow. For example, the control of transition to turbulence is - pecially important in (1) skin-friction reduction of energy ef?cient aircraft, (2) the performance of heat exchangers and diffusers, (3) propulsion requirements for - personic aircraft, and (4) separation control. While considerable progress has been made in the science of laminar to turbulent transition over the last 30 years, the c- tinuing increase in computer power as well as new theoretical developments are now revolutionizing the area. It is now starting to be possible to move from simple 1D eigenvalue problems in canonical ?ows to global modes in complex ?ows, all - companied by accurate large-scale direct numerical simulations (DNS). Here, novel experimental techniques such as modern particle image velocimetry (PIV) also have an important role. Theoretically the in?uence of non-normality on the stability and transition is gaining importance, in particular for complex ?ows. At the same time the enigma of transition in the oldest ?ow investigated, Reynolds pipe ?ow tran- tion experiment, is regaining attention. Ideas from dynamical systems together with DNS and experiments are here giving us new insights.

This volume contains the selected papers presented at the EUROTHERM SEMINAR No. 17 - Heat Transfer in Radiating and Combusting Systems held at Cascais from October 8th- 10th, 1990. The EUROTHERM COMMITTEE was created by representatives of the member countries of the European Communities for the organization and coordination of European Scientific events in the field of thermal sciences and their applications. The book is focused on the integration of the heat transfer and combustion. These two subjects have traditionally been considered separate disciplines. In reality, the two are closely interwoven. The central purpose of the book is to generate an effective cross fertilisation of the two at both the fundamental and applied levels. The book reports on: mathematical simulations of heat transfer in reacting systems, new measurements of and measurement techniques for the radiation properties of the intervening medium, and data and theoretical analyses which clarify the physical nature of the complex interactions between the radiation/convection heat transfer processes and the combustion and turbulence of real reacting flows.

In 1858 Hermann von Helmholtz published a paper that today is recognized as the foundation of vortex dynamics.

To celebrate the sesquicentennial of Helmholtz s paper, IUTAM sponsored a symposium that was held at the technical university of Denmark in October 2008. The papers presented at the symposium gave a good overview of where the field of vortex dynamics stands today. This volume contains almost all of the papers presented as lectures at the symposium, and also a few of the poster papers. In this volume the reader will find up-to-date, state-of-theart papers on Point vortices, vortex sheets, vortex filaments, vortex rings, vortex patches, vortex streets, the vortex dynamics of swimming and flying, vortex knots, vortices in turbulent flows, vortices in computational fluid dynamics, the topology of vortex wakes, stability of vortex configurations, vortices on a sphere, geophysical vortices, cosmic vortices and much more."

Professor Sluzalec is a well-known and respected authority in the field of Computational Mechanics, and his personal experience forms the basis of the book. Introduction to Nonlinear Thermomechanics provides both an elementary and advanced exposition of nonlinear thermomechanics. The scope includes theoretical aspects and their rational application in thermal problems, thermo-elastoplasticity, finite strain thermoplasticity and coupled thermoplasticity. The use of numerical techniques for the solution of problems and implementation of basic theory is included. Engineers, technicians, researchers, and advanced students will find the book an extremely useful compendium of solutions to problems. The scope is such that it would also be an effective teaching aid.

The International Union of Theoretical and Applied Mechanics (IUTAM) decided in 1992 to sponsor the fourth Symposium on Laminar-Turbulent Transition, Sendai/Japan, 1994. The objectives of the present Symposium were to deepen the fundamental knowledge of stability and laminar turbulent transition in three-dimensional and compressible flows and to contribute to recent developing technologies in the field. This Symposium followed the three previous IUTAM-Symposia (Stuttgart 1979, Novosibirsk 1984 and Toulouse 1989). The Scientific Committee selected two keynote lectures and 62 technical papers. The Symposium was held on the 5th to 9th of September, 1994, at the Sendai International Center in Sendai. The participants were 82 scientists from 10 countries. The keynote lectures have critically reviewed recent development of researches concerning the laminar-to-turbulent transition phenomena from the fundamental and the application aspects. Many papers presented were concerned about the detailed mechanism of the boundary layer transition (receptivity, secondary instability, turbulent spot and bypass transition). Particular emphasis was further placed on the transition of three-dimensional boundary layers on rotation systems and on swept wings. Attention was also given to compressible hypersonic flows."

The problems of transient interaction of deformable bodies with surrounding media are of great practical and theoretical importance. When solving the problems of this kind, the main difficulty is in the necessity to integrate jointly the system of equations which describe motion of the body and the system of equations which describe motion of the medium under the boundary conditions predetermined at the unknown (movable) curvilinear interfaces. At that, the position of these interfaces should be determined as part of the solution process. That is why, the known exact solutions in this area of mechanics of continuum have been derived mainly for the cases of idealized rigid bodies. Different aspects of the problems of transient interaction of bodies and structures with continuum (derivation of the efficient mathematical mod els for the phenomenon, development of the theoretical and experimental methods to be used for study of the transient problems of mechanics, etc.) were considered in the books by S.U. Galiev, A.N. Guz, V.D. Kubenko, V.B. Poruchikov, L.L Slepyan, A.S. Volmir, and Yu.S. Yakovlev. The results presented by these authors make interest when solving a great variety of problems and show a necessity of joint usage of the results obtained in differ ent areas: aerohydrodynamics, theory of elasticity and plasticity, mechanics of soils, theory of shells and plates, applied and computational mathemat ics, etc.

The first Symposium Transsonicum took pl.ace in Aachen thirteen years ago during a period of decreasing governmental. and industrial. support for transonic flow research. Since then, there has been a strong revival. in interest in transonic flow research so that the number of partici pants at the second symposium remained about the same as at the first even in spite of tight financial. means and Limited governmental. support. During both meetings the number of participants reached the upper Limit of the number desirabl.e for such a symposium. Participants came from aU over the worl.d and there was a weU bal.anced distribution of participants from aU countries interested in transonic flow research. The discussions - mostLy conducted in EngLish - were stimul.ating and there was a great deal. of interest in the l.ectures as was shown by the good attendance even during the l.ast session on Saturday morning."

G.I. Taylor, one of the most distinguished physical scientists of this century, used his deep insight and originality to increase our understanding of phenomena such as the turbulent flow of fluids. His interest in the science of fluid flow was not confined to theory; he was one of the early pioneers of aeronautics, and designed a new type of anchor that was inspired by his passion for sailing. Taylor spent most of his working life in the Cavendish Laboratory in Cambridge, where he investigated the mechanics of fluid and solid materials; his discoveries and ideas have had application throughout mechanical, civil, and chemical engineering, meteorology, oceanography and materials science. He was also a noted research leader, and his group in Cambridge became one of the most productive centers for the study of fluid mechanics. How was Taylor able to be innovative in so many different ways? This interesting and unusual biography helps answer that question. Professor Batchelor, himself a student and close collaborator of Taylor, is ideally placed to describe Taylor's life, achievements and background. He does so without introducing any mathematical details, making this book enjoyable reading for a wide range of people--and especially those whose own interests have brought them into contact with the legacy of Taylor.

This work of applied mathematics focuses on the functional study of the nonlinear boundary value problems relating to water flow in porous media, a topic which has not up to now been explored in book form. The author shows that abstract theory may be sometimes easier and richer in consequences for applications than standard classical approaches are. The volume deals with diffusion type models, emphasizing the mathematical treatment of their nonlinear aspects.

We are extremely grateful to Springer-Verlag and to Prof. Dr. W. BeiglbOck for bring ing out the English edition of our book. We are also thankful to Dr. R. S. Wadhwa for a qualified translation. While preparing the manuscript for translation, we took the opportunity to go through the whole text, make necessary amendments, supplement the original material with new results, and considerably enlarge the lists of references. We hope that this book will serv to strengthen the bonds of international coopera tion in this field. July 1986 The authors Translator's Note The final form of the bibliography contains a (free) English translation of all the Russian books and papers published in the USSR. This has been done at the request of the authors and with the concurrence of Prof. BeiglMck. The titles are not always exact, and some of the works have already been translated into English or other European languages. Unfortunately, the authors were not in a position to provide detailed information on this subject. R.S. Wadhwa Preface to the Russian Edition What shall I do ... With their weightlessness In this ponderous world? M. Tsvetaeva, The Poet This book deals with the behavior of a liquid in zero-gravity or conditions close to it. The surge of interest in zero-gravity problems stems from the progress attained in the field of spaceflight, where such conditions can be attained for long periods of time."