This second edition of Physical Hydrodynamics is a deeply enriched version of a classical textbook on fluid dynamics. It retains the same pedagogical spirit, based on the authors' experience of teaching university students in the physical sciences, and emphasizes an experimental (inductive) approach rather than the more formal approach found in many textbooks in the field. A new edition was necessary as contact between the mechanics and physics approaches and their communities has increased continuously over the last few decades. Today the field is more widely open to other experimental sciences: materials, environmental, life, and earth sciences, as well as the engineering sciences. Representative examples from these fields have been included where possible, while retaining a general presentation in each case. This book should be useful for researchers and engineers in these various fields. Images have an essential place in fluid mechanics, and the illustrations in this edition have been completely revisited and widely improved. An inset of colour photographs is provided to stimulate the interest of readers. Exercises have also been added at the end of a number of chapters.

This immensely practical guide to PIV provides a condensed, yet exhaustive guide to most of the information needed for experiments employing the technique. This second edition has updated chapters on the principles and extra information on microscopic, high-speed and three component measurements as well as a description of advanced evaluation techniques. What's more, the huge increase in the range of possible applications has been taken into account as the chapter describing these applications of the PIV technique has been expanded.

Progress in fluid mechanics depends heavily on the availability of good experimental data which can inspire new ideas and concepts but which are also necessary to check and validate theories and numerical calculations. With the advent of new recording and image analysis techniques new and promising experimental methods in fluid flows have presented themselves which are rather newly developed techniques such as particle tracking velocimetry (PTV), particle image velocimetry (PIV) and laser fluorescene (LIF). This volume presents state-of-the-art research on these techniques and their application to fluid flow. Selected papers from the EUROMECH conference on Image Analysis are published in this volume.

This book contains contributions by colleagues, former students and friends of Professor Eli Reshotko in celebration of his 60th birth day. Since Professor Reshotko's scientific and engineering contribu tions have been in the areas of hydrodynamic stability, transition to turbulence, and boundary layer flows, it is only appropriate that the articles in this volume be devoted to these and related topics. The first two sections focus on instabilities and transition in sub sonic and supersonic flows, respectively. The third section deals with developing turbulence, while the the final section treats related prob lems in engineering fluid mechanics. The diversity and scope of the articles contained herein exemplify the insight and expertise required in the study of transitional and turbulent flows today - traits which also exemplify Eli Reshotko's contributions to these fields. A few of the articles in this volume were presented at a sym posium in honor of Eli Reshotko's 60th birthday, held in Newport News, Virginia, on July 28, 1991. The symposium was sponsored by lCASE, and organized by M.Y. Hussaini (lCASE) and R. Hirsh (U.S. National Science Foundation). Of those who could not attend, many chose to honor Professor Reshotko by a contribution to the volume dedicated to him. We would like to use this opportunity to express our deep ap preciation to M.Y. Hussaini for initiating this very special tribute to Eli, and to Ms. Emily Todd for her efforts in the volume preparation and in the organization of the symposium."

This title provides the fundamental bases for developing turbulence models on rational grounds. The main different methods of approach are considered, ranging from statistical modelling at various degrees of complexity to numerical simulations of turbulence. Each of these various methods has its own specific performances and limitations, which appear to be complementary rather than competitive. After a discussion of the basic concepts, mathematical tools and methods for closure, the book considers second order closure models.Emphasis is placed upon this approach because it embodies potentials for clarifying numerous problems in turbulent shear flows. Simpler, generally older models are then presented as simplified versions of the more general second order models. The influence of extra physical parameters is also considered. Finally, the book concludes by examining large Eddy numerical simulations methods. Given the book's comprehensive coverage, those involved in the theoretical or practical study of turbulence problems in fluids will find this a useful and informative read.

TUrbulence modeling encounters mixed evaluation concerning its impor tance. In engineering flow, the Reynolds number is often very high, and the direct numerical simulation (DNS) based on the resolution of all spatial scales in a flow is beyond the capability of a computer available at present and in the foreseeable near future. The spatial scale of energetic parts of a turbulent flow is much larger than the energy dissipative counterpart, and they have large influence on the transport processes of momentum, heat, matters, etc. The primary subject of turbulence modeling is the proper es timate of these transport processes on the basis of a bold approximation to the energy-dissipation one. In the engineering community, the turbulence modeling is highly evaluated as a mathematical tool indispensable for the analysis of real-world turbulent flow. In the physics community, attention is paid to the study of small-scale components of turbulent flow linked with the energy-dissipation process, and much less interest is shown in the foregoing transport processes in real-world flow. This research tendency is closely related to the general belief that universal properties of turbulence can be found in small-scale phenomena. Such a study has really contributed much to the construction of statistical theoretical approaches to turbulence. The estrangement between the physics community and the turbulence modeling is further enhanced by the fact that the latter is founded on a weak theoretical basis, compared with the study of small-scale turbulence."

Turbulent ?ows are ubiquitous in most application ?elds, ranging from - gineering to earth sciences and even life sciences. Therefore, simulation of turbulent ?ows has become a key tool in both fundamental and applied - search. The complexity of Navier-Stokes turbulence, which is illustrated by the fact that the number of degrees of freedom of turbulence grows faster 11/4 thanO(Re ), where Re denotes the Reynolds number, renders the Direct Numerical Simulation (DNS) of turbulence inapplicable to most ?ows of - terest. To alleviate this problem, truncated solutions in both frequency and wavenumbermaybesought, whosecomputationalcostismuchlowerandmay ideally be arbitrarily adjusted. The most suitable approach to obtain such a low-cost three-dimensional unsteady simulation of a turbulent ?ow is Large- EddySimulation(LES), whichwaspioneeredtocomputemeteorological?ows in the late 1950s and the early 1960s. One of the main issues raised by LES is a closure problem: because of the non-linearity of the Navier-Stokes equations, the e?ect of unresolved scales must be taken into account to recover a reliable description of resolved scales of motion (Chap. 2). This need to close the governing equations of LES has certainly been the main area of investigation since the 1960s, and numerous closures, alsoreferredtoassubgridmodels, havebeenproposed. Mostexisting subgrid models have been built using simpli?ed viewsof turbulence dynamics, the main physical phenomenon taken into account being the direct kinetic - ergycascade from largeto small scales that is observed in isotropic turbulence and high-Reynolds fully developed turbulent ?ows. The most popular pa- digm for interscale energy transfer modeling is subgrid viscosity (C

This book benefits users, manufacturers and engineers by drawing together an overall view of the technology. It attempts to give the reader an appreciation of the extent to which slurry transport is presently employed, the theoretical basis for pipeline design, the practicalities of design and new developments.

When this volume was first published in 1971, the science of deformation of materials, now usually known as rheology, had branched out into several new and significant areas of research. In particular, the search for compounds with specified desirable properties had produced synthetic materials of great technological importance. This third edition contains authoritative contributions from specialists in the various fields. The aim of the book was to draw together and discuss the problems of physicists, chemists and technologists, and the editors attempted, in so far as it was possible for a science in a state of growth, to trace a unity of thought THAT is seldom apparent in the literature of this subject. The early chapters deal with the physical principles of elasticity, plasticity and viscosity, and relate physical and chemical structure to rheological properties. Individual chapters later in the book contain comparative accounts of a wide range of materials, some naturally occurring and others man-made; the general theoretical laws of rheology are compared with experimental observations.

The field of Large Eddy Simulations is reaching a level of maturity that brings this approach to the mainstream of engineering computations, while it opens opportunities and challenges. The main objective of this volume is to bring together leading experts in presenting the state-of-the-art and emerging approaches for treating complex effects in LES. A common theme throughout is the role of LES in the context of multiscale modeling and simulation.

This comprehensive two-volume reference covers the application of the finite element method to incompressible flows in fluid mechanics, addressing the theoretical background and the development of appropriate numerical methods applied to their solution.
Volume One provides extensive coverage of the prototypical fluid mechanics equation: the advection-diffusion equation. For both this equation and the equations of principal interest - the Navier-Stokes equations (covered in detail in Volume Two) - a discussion of both the continuous and discrete equations is presented, as well as explanations of how to properly march the time-dependent equations using smart implicit methods. Boundary and initial conditions, so important in applications, are carefully described and discussed, including well-posedness. The important role played by the pressure, so confusing in the past, is carefully explained.
The book explains and emphasizes consistency in six areas:
* consistent mass matrix
* consistent pressure Poisson equation
* consistent penalty methods
* consistent normal direction
* consistent heat flux
* consistent forces
Fully indexed and referenced, this book is an essential reference tool for all researchers, students and applied scientists in incompressible fluid mechanics.

Following the highly successful first edition, this text deals with numerical solutions of coupled thermo-hydro-mechanical problems in porous media. Governing equations are newly derived in a general form using both averaging methods (hybrid mixture theory) and an engineering approach. Unique new features of the book include numerical solutions for fully and partially saturated consolidation, subsidence analysis including far field boundary conditions (Infinite Elements), new case studies and also petroleum reservoir simulation. Extended heat and mass transfer in partially saturated porous media, and consideration of phase change, are covered in detail. In addition, large strain, fully and partially saturated, soil dynamics problems are explained. Back analysis for consolidation problems is also included. Significantly, the reader is provided with access to a Finite Element code for coupled thermo-hydro-mechanical problems in partially saturated porous media with full two phase flow and phase change, written according to the theory outlined in the book and obtainable via the Network of the Italian Research Council (COMES). With a range of engineering applications from geotechnical and petroleum engineering through to bioengineering and materials science, this book represents an important resource for students, researchers and practising engineers in all these and related fields.

Thermal and flow processes are ubiquitous in mechanical, aerospace and chemical engineering systems. Experimental methods including thermal and flow diagnostics are therefore an important element in preparation of future engineers and researchers in this field. Due to the interdisciplinary nature of experimentation, a fundamental guidance book is essential in the engineering curriculum and as a technical reference. Thermal and Flow Measurements provides a synthesis of the basic science and engineering of diagnostic methods that students and engineers need to understand, design and apply to measurements in mechanical, aerospace and chemical engineering processes. A clear exposition is given on the basic concepts and application aspects of a wide range of thermal and flow diagnostics, starting from basic sensors, flow visualization, velocimetry, laser optical diagnostics, particle sizing methods, gas sampling methods, to micro-, nano-scale sensors and lidars. The presentation of topics allow readers to see the fundamental principles behind each methodology as well as the application details.

This book deals with the simulation of the incompressible Navier-Stokes equations for laminar and turbulent flows. The book is limited to explaining and employing the finite difference method. It furnishes a large number of source codes which permit to play with the Navier-Stokes equations and to understand the complex physics related to fluid mechanics. Numerical simulations are useful tools to understand the complexity of the flows, which often is difficult to derive from laboratory experiments. This book, then, can be very useful to scholars doing laboratory experiments, since they often do not have extra time to study the large variety of numerical methods; furthermore they cannot spend more time in transferring one of the methods into a computer language. By means of numerical simulations, for example, insights into the vorticity field can be obtained which are difficult to obtain by measurements. This book can be used by graduate as well as undergraduate students while reading books on theoretical fluid mechanics; it teaches how to simulate the dynamics of flow fields on personal computers. This will provide a better way of understanding the theory. Two chapters on Large Eddy Simulations have been included, since this is a methodology that in the near future will allow more universal turbulence models for practical applications. The direct simulation of the Navier-Stokes equations (DNS) is simple by finite-differences, that are satisfactory to reproduce the dynamics of turbulent flows. A large part of the book is devoted to the study of homogeneous and wall turbulent flows. In the second chapter the elementary concept of finite difference is given to solve parabolic and elliptical partial differential equations. In successive chapters the 1D, 2D, and 3D Navier-Stokes equations are solved in Cartesian and cylindrical coordinates. Finally, Large Eddy Simulations are performed to check the importance of the subgrid scale models. Results for turbulent and laminar flows are discussed, with particular emphasis on vortex dynamics. This volume will be of interest to graduate students and researchers wanting to compare experiments and numerical simulations, and to workers in the mechanical and aeronautic industries.

This is an advanced textbook on the subject of turbulence, and is suitable for engineers, physical scientists and applied mathematicians. The aim of the book is to bridge the gap between the elementary accounts of turbulence found in undergraduate texts, and the more rigorous monographs on the subject. Throughout, the book combines the maximum of physical insight with the minimum of mathematical detail. Chapters 1 to 5 may be appropriate as background material for an advanced undergraduate or introductory postgraduate course on turbulence, while chapters 6 to 10 may be suitable as background material for an advanced postgraduate course on turbulence, or act as a reference source for professional researchers. This second edition covers a decade of advancement in the field, streamlining the original content while updating the sections where the subject has moved on. The expanded content includes large-scale dynamics, stratified & rotating turbulence, the increased power of direct numerical simulation, two-dimensional turbulence, Magnetohydrodynamics, and turbulence in the core of the Earth

Five leading specialists reflect on different and complementary approaches to fundamental questions in the study of the Fluid Mechanics and Gas Dynamics equations. Constantin presents the Euler equations of ideal incompressible fluids and discusses the blow-up problem for the Navier-Stokes equations of viscous fluids, describing some of the major mathematical questions of turbulence theory. These questions are connected to the Caffarelli-Kohn-Nirenberg theory of singularities for the incompressible Navier-Stokes equations that is explained in Gallavotti's lectures. Kazhikhov introduces the theory of strong approximation of weak limits via the method of averaging, applied to Navier-Stokes equations. Y. Meyer focuses on several nonlinear evolution equations - in particular Navier-Stokes - and some related unexpected cancellation properties, either imposed on the initial condition, or satisfied by the solution itself, whenever it is localized in space or in time variable. Ukai presents the asymptotic analysis theory of fluid equations. He discusses the Cauchy-Kovalevskaya technique for the Boltzmann-Grad limit of the Newtonian equation, the multi-scale analysis, giving the compressible and incompressible limits of the Boltzmann equation, and the analysis of their initial layers.

This textbook integrates classic principles of flow through porous media with recently developed stochastic analyses to provide new insight on subsurface hydrology. Importantly, each of the authors has extensive experience in both academia and the world of applied groundwater hydrology. The book not only presents theories but also emphasizes their underlying assumptions, limitations, and the potential pitfalls that may occur as a result of blind application of the theories as 'cookie-cutter' solutions. The book has been developed for advanced-level courses on groundwater fluid flow, hydraulics, and hydrogeology, in either civil and environmental engineering or geoscience departments. It is also a valuable reference text for researchers and professionals in civil and environmental engineering, geology, soil science, environmental science, and petroleum and mining engineering.

Large eddy simulation (LES) seeks to simulate the large structures of a turbulent flow. This is the first monograph which considers LES from a mathematical point of view. It concentrates on LES models for which mathematical and numerical analysis is already available and on related LES models. Most of the available analysis is given in detail, the implementation of the LES models into a finite element code is described, the efficient solution of the discrete systems is discussed and numerical studies with the considered LES models are presented.

This is an up-to-date review of recent advances in the study of two-phase flows, with focus on gas-liquid flows, liquid-liquid flows, and particle transport in turbulent flows. The book is divided into several chapters, which after introducing basic concepts lead the reader through a more complex treatment of the subjects. The reader will find an extensive review of both the older and the more recent literature, with abundance of formulas, correlations, graphs and tables. A comprehensive (though non exhaustive) list of bibliographic references is provided at the end of each chapter. The volume is especially indicated for researchers who would like to carry out experimental, theoretical or computational work on two-phase flows, as well as for professionals who wish to learn more about this topic.

Multiphase Particulate Systems in Turbulent Flows: Fluid-Liquid and Solid-Liquid Dispersions provides methods necessary to analyze complex particulate systems and related phenomena including physical, chemical and mathematical description of fundamental processes influencing crystal size and shape, suspension rheology, interfacial area of drops and bubbles in extractors and bubble columns. Examples of mathematical model formulation for different processes taking place in such systems is shown. Discussing connections between turbulent mixing mechanisms and precipitation, it discusses influence of fine-scale structure of turbulence, including its intermittent character, on breakage of drops, bubbles, cells, plant cell aggregates. An important aspect of the mathematical modeling presented in the book is multi-fractal, taking into account the influence of internal intermittency on different phenomena. Key Features Provides detailed descriptions of dispersion processes in turbulent flow, interactions between dispersed entities, and continuous phase in a single volume Includes simulation models and validation experiments for liquid-liquid, gas-liquid, and solid-liquid dispersions in turbulent flows Helps reader learn formulation of mathematical models of breakage or aggregation processes using multifractal theory Explains how to solve different forms of population balance equations Presents a combination of theoretical and engineering approaches to particulate systems along with discussion of related diversity, with exercises and case studies

The dynamics of transitional and turbulent flows is often dominated by organized structures with a life-time much longer than the characteristic time-scale of the surrounding small-scale turbulence. Organized structures may appear as secondary flows as a result of an instability, but they persist in turbulent flows. They manifest themselves as eddies or localized vortices and play an important role in, for example, mixing and transport processes. Although the existence of organized structures has been revealed by many experiments and by numerical simulations, they are somewhat elusive, as there is no consensus on how to define them and technically how to detect them. This volume contains reviewed papers from the IUTAM Symposium entitled "Simulation and Identification of Organized Structures in Flows" which was held in Lyngby, Denmark, on 25th - 29th May, 1997. The purpose of the symposium was to present the latest results from leading scientists within the field of detection and simulation of organized flow structures. Describing various aspects of complex, organized flow motion, including topics such as decomposition techniques, structure definition and recognition, experimental techniques and topological concepts, this volume should be of interest to all researchers active in the field.

The ability to actively or passively manipulate a flow field to bring about a desired change is of immense technological and economical importance. This volume provides a thorough, up-to-date treatment of the basics of flow control and control practices that can be used to produce desired effects. The author explores the frontiers of flow control strategies, especially as applied to turbulent flows. Intended for engineering and physics students, researchers, and practitioners, Flow Control brings together in a single source a wealth of state-of-the-art information on this very active field.

This book is designed to fulfill a dual role. On the one hand it provides a description of the rheological behavior of molten poly mers. On the other, it presents the role of rheology in melt processing operations. The account of rheology emphasises the underlying principles and presents results, but not detailed deriva tions of equations. The processing operations are described qualita tively, and wherever possible the role of rheology is discussed quantitatively. Little emphasis is given to non-rheological aspects of processes, for example, the design of machinery. The audience for which the book is intended is also dual in nature. It includes scientists and engineers whose work in the plastics industry requires some knowledge of aspects of rheology. Examples are the polymer synthetic chemist who is concerned with how a change in molecular weight will affect the melt viscosity and the extrusion engineer who needs to know the effects of a change in molecular weight distribution that might result from thermal degra dation. The audience also includes post-graduate students in polymer science and engineering who wish to acquire a more extensive background in rheology and perhaps become specialists in this area. Especially for the latter audience, references are given to more detailed accounts of specialized topics, such as constitutive relations and process simulations. Thus, the book could serve as a textbook for a graduate level course in polymer rheology, and it has been used for this purpose."

Numerical large-eddy simulation techniques are booming at present and will have a decisive impact on industrial modeling and flow control. The book represents the general framework in physical and spectral space. It also gives the recent subgrid-scale models. Topics treated include compressible turbulence research, turbulent combustion, acoustic predictions, vortex dynamics in non-trivial geometries, flows in nuclear reactors and problems in atmospheric and geophysical sciences. The book addresses numerical analysts, physicists, and engineers.

Recent advances in boundary-layer theory have shown how modern analytical and computational techniques can and should be combined to deepen the understanding of high Reynolds number flows and to design effective calculation strategies. This is the unifying theme of the present volume which addresses laminar as well as turbulent flows.