The present set of lectures and tutorial reviews deals with various topical aspects related to instabilities of interfacial processes and driven flows from both the theoretical and experimental point of views. New research has been spurred by demands for many applications in material sciences (melting, solidification, electro deposition), biomedical engineering and processing in microgravity environments. This book is intended as both a modern source of reference for researchers in the field as well as an introduction to postgraduate students and non-specialists from related areas.

This book is an introduction to current research on the N- vortex problem of fluid mechanics. Its goal is to describe the Hamiltonian aspects of vortex dynamics so that graduate students and researchers can use the book as an entry point into the rather large literature on integrable and non-integrable vortex problems within the broader context of dynamical systems. It is as self-contained as possible: the only training required of the reader is a good background in advanced calculus and ordinary and partial differential equations at the level of a typical undergraduate engineering, physics, or applied mathematics major. Exercises of varying difficulty are found at the end of each chapter which often require the reader to fill in details of proofs or complete examples.

This volume includes versions of papers selected from those presented at the THIESEL 2000 Conference on Thermofluidynamic Processes in Diesel Engines, held at the Universidad Politecnica de Valencia, during the period of September th th 13 to 15 , 2000. The papers are grouped into seven thematic areas: State of the Art and Prospective, Fuels for Diesel Engines, Injection System and Spray Formation, Combustion and Pollutant Formation, Modelling, Experimental Techniques, and Air Management. These areas cover most of the technologies and research strategies that may allow Light Duty and Heavy Duty Diesel engines to comply with current and forthcoming emission standards, while maintaining or improving fuel consumption. The main objectives of the conference were to bring together ideas and experience from Industry and Universities to facilitate interchange of information and to promote discussion of future research and development needs. The technical papers emphasised the use diagnostic and simulation techniques and their relationship to engineering practice and the advancement of the Diesel engine. We hope that this approach, which proved to be successful at the Conference, is reflected in this volume. We thank all those who contributed to the success of the Conference, and particularly the members of the Advisory Committee who assessed abstracts and chaired many of the technical sessions. Weare also grateful to participants who presented their work or contributed to the many discussions. Finally, the Conference benefitted from financial support from the organisations listed below and we are glad to have this opportunity to record our gratitude.

The book describes recent developments in aeroacoustic measurements in wind tunnels and the interpretation of the resulting data. The reader will find the latest measurement techniques described along with examples of the results.

This well-written book explains the theory of spectral methods and their application to the computation of viscous incompressible fluid flows in clear and elementary terms. It begins with an introduction to the fundamentals of spectral methods and then moves on to cover, in particular, the Fourier and Chebyshev methods. Examples are included. Chapters 6 and 7 handle streamfunction-vorticity and velocity-pressure fomulations of the Navier-Stokes equations. Chapter 8 and 9 address special topics such as self- adaptive coordinate transform, treatment of singularities, and domain decomposition. The work will be useful to those teaching in the field at the graduate level, as well as to researchers working in the area.

In January 1992, the Sixth Workshop on Optimization and Numerical Analysis was held in the heart of the Mixteco-Zapoteca region, in the city of Oaxaca, Mexico, a beautiful and culturally rich site in ancient, colonial and modern Mexican civiliza tion. The Workshop was organized by the Numerical Analysis Department at the Institute of Research in Applied Mathematics of the National University of Mexico in collaboration with the Mathematical Sciences Department at Rice University, as were the previous ones in 1978, 1979, 1981, 1984 and 1989. As were the third, fourth, and fifth workshops, this one was supported by a grant from the Mexican National Council for Science and Technology, and the US National Science Foundation, as part of the joint Scientific and Technical Cooperation Program existing between these two countries. The participation of many of the leading figures in the field resulted in a good representation of the state of the art in Continuous Optimization, and in an over view of several topics including Numerical Methods for Diffusion-Advection PDE problems as well as some Numerical Linear Algebraic Methods to solve related pro blems. This book collects some of the papers given at this Workshop."

As computational fluid dynamics (CFD) is applied to ever more demanding fluid flow problems, the ability to compute numerical fluid flow solutions to a user specified tolerance as well as the ability to quantify the accuracy of an existing numerical solution are seen as essential ingredients in robust numerical simulation. Although the task of accurate error estimation for the nonlinear equations of CFD seems a daunting problem, considerable effort has centered on this challenge in recent years with notable progress being made by the use of advanced error estimation techniques and adaptive discretization methods. To address this important topic, a special course wasjointly organized by the NATO Research and Technology Office (RTO), the von Karman Insti tute for Fluid Dynamics, and the NASA Ames Research Center. The NATO RTO sponsored course entitled "Error Estimation and Solution Adaptive Discretization in CFD" was held September 10-14, 2002 at the NASA Ames Research Center and October 15-19, 2002 at the von Karman Institute in Belgium. During the special course, a series of comprehensive lectures by leading experts discussed recent advances and technical progress in the area of numerical error estimation and adaptive discretization methods with spe cific emphasis on computational fluid dynamics. The lecture notes provided in this volume are derived from the special course material. The volume con sists of 6 articles prepared by the special course lecturers."

Explains the motivation and reviewing the classical theory in a new form; Discusses conservation laws and Euler equations; For one-dimensional cases, the models presented are completely integrable

It was long ago that group analysis of differential equations became a powerful tool for studying nonlinear equations and boundary value problems. This analysis was especially fruitful in application to the basic equations of mechanics and physics because the invariance principles are already involved in their derivation. It is in no way a coincidence that the equations of hydrodynamics served as the first object for applying the new ideas and methods of group analysis which were developed by 1. V. Ovsyannikov and his school. The authors rank themselves as disciples of the school. The present monograph deals mainly with group-theoretic classification of the equations of hydrodynamics in the presence of planar and rotational symmetry and also with construction of exact solutions and their physical interpretation. It is worth noting that the concept of exact solution to a differential equation is not defined rigorously; different authors understand it in different ways. The concept of exact solution expands along with the progress of mathematics (solu tions in elementary functions, in quadratures, and in special functions; solutions in the form of convergent series with effectively computable terms; solutions whose searching reduces to integrating ordinary differential equations; etc. ). We consider it justifiable to enrich the set of exact solutions with rank one and rank two in variant and partially invariant solutions to the equations of hydrodynamics."

The workshop "Nonhnear MHD Waves and Turbulence" was held at the - servatoire de Nice, December 1-4, 1998 and brought together an international group of experts in plasma physics, fluid dynamics and applied mathematics. The aim of the meeting was to survey the current knowledge on two main topics: (i) propagation of plasma waves (like Alfven, whistler or ion-acoustic waves), their instabilities and the development of a nonlinear dynamics lea ding to solitonic structures, wave collapse or weak turbulence; (ii) turbulence in magnetohydrodynamic flows and its reduced description in the presence of a strong ambient magnetic fleld. As is well known, both aspects play an important role in various geophysical or astrophysical media such as the - gnetospheres of planets, the heliosphere, the solar wind, the solar corona, the interplanetary and interstellar media, etc. This volume, which includes expanded versions of oral contributions pre sented at this meeting, should be of interest for a large community of resear chers in space plasmas and nonlinear sciences. Special effort was made to put the new results into perspective and to provide a detailed literature review. A main motivation was the attempt to relate more closely the theoretical un derstanding of MHD waves and turbulence (both weak and strong) with the most recent observations in space plasmas. Some papers also bring interesting new insights into the evolution of hydrodynamic or magnetohydrodynamic structures, based on systematic asymptotic methods."

In this book, the necessary background for understanding viscoelasticity is covered; both the continuum and microstructure approaches to modelling viscoelastic materials are discussed, since neither approach alone is sufficient.

The focus is on the main physical ideas and mathematical methods of the microscopic theory of fluids, starting with the basic principles of statistical mechanics. The detailed derivation of results is accompanied by explanation of their physical meaning. The same approach refers to several specialized topics of the liquid state, most of which are recent developments, such as: a perturbation approach to the surface tension, an algebraic perturbation theory of polar nonpolarizable fluids and ferrocolloids, a semi-phenomenological theory of the Tolman length and some others.

The origins of turbulent flow and the transition from laminar to turbulent flow are among the most important unsolved problems of fluid mechanics and aerodynamics. Besides being a fundamental question of fluid mechanics, there are any number of applications for information regarding transition location and the details of the subsequent turbulent flow. The JUT AM Symposium on Laminar-Turbulent Transition, co-hosted by Arizona State University and the University of Arizona, was held in Sedona, Arizona. Although four previous JUT AM Symposia bear the same appellation (Stuttgart 1979, Novosibirsk 1984, Toulouse 1989, and Sendai 1994) the topics that were emphasized at each were different and reflect the evolving nature of our understanding of the transition process. The major contributions of Stuttgart 1979 centered on nonlinear behavior and later stages of transition in two-dimensional boundary layers. Stability of closed systems was also included with Taylor vortices in different geometries. The topics of Novosibirsk 1984 shifted to resonant wave interactions and secondary instabilities in boundary layers. Pipe- and channel-flow transition were discussed as model problems for the boundary layer. Investigations of free shear layers were presented and a heavy dose of supersonic papers appeared for the first time. The character of Toulouse 1989 was also different in that 3-D boundary layers, numerical simulations, streamwise vortices, and foundation papers on receptivity were presented. Sendai 1994 saw a number of papers on swept wings and 3-D boundary layers. Numerical simulations attacked a broader range of problems.

Advances in Mechanics and Mathematics (AMMA) is intended to bridge the gap by providing multi-disciplinary publications. This volume, AMMA 2002, includes two parts with three articles by four subject experts. Part 1 deals with nonsmooth static and dynamic systems. A systematic mathematical theory for multibody dynamics with unilateral and frictional constraints and a brief introduction to hemivariational inequalities together with some new developments in nonsmooth semi-linear elliptic boundary value problems are presented. Part 2 provides a comprehensive introduction and the latest research on dendritic growth in fluid mechanics, one of the most profound and fundamental subjects in the area of interfacial pattern formation, a commonly observed phenomenon in crystal growth and solidification processes.

This book is devoted to recent developments in the field of rotating fluids, in particular the study of Taylor--Couette flow, spherical Couette flow, planar Couette flow, as well as rotating annulus flow. Besides a comprehensive overview of the current state of the art, possible future directions in this research field are investigated. The first part of this volume presents several new results in the classical Taylor--Couette system covering diverse theoretical, experimental and numerical work on bifurcation theory, influence of boundary conditions, counter-rotating flows, spiral vortices and many others. The second part focuses on spherical Couette flows, including isothermal flows, thermal convective motion, as well as magnetohydrodynamics in spherical shells. The remaining parts are devoted to Goertler vortices, rotating annulus flows, as well as superfluid Couette flows. The present book will be of interest to all researchers and graduate students working actively in the field.

The subject of wave phenomena is well-known for its inter-disciplinary nature. Progress in this field has been made both through the desire to solve very practical problems, arising in acoustics, optics, radiophysics, electronics, oceanography, me teorology and so on, and through the development of mathematical physics which emphasized that completely different physical phenomena are governed by the same (or similar) equations. In the immense literature on physics of waves there is no lack of good presentations of particular branches or general textbooks on mathematical physics. But if one restricts the attention to pulse propagation phenomena, one no tices that many useful facts are scattered among the various books and journals, and their connections are not immediately apparent. For example, the problems involv ing acoustic pulse propagation in bubbly liquids and those related to electromagnetic pulses in resonant media are usually treated without much cross reference in spite of their obvious connections. The authors of this book have attempted to write a coherent account of a few pulse propagation problems selected from different branches of applied physics. Although the basic material on linear pulse propagation is included, some topics have their own unique twists, and a comprehensive treatment of this body of material can hardly be found in other sources. First of all, the problem of pulse propagation in non equilibrium media (unstable or admitting attenuation) is far more delicate than it is apparent at a first glance."

Transports in fluids can be approached from two complementary perspectives. In the Eulerian view of mixing, the focus is on the concentration field. In the Langrangian view, fluid parcels are followed around as they move with the flow, experiencing chaotic or stochastic motion. This book examines both pictures, presenting a number of theoretical and experimental lectures on various aspects of transport and mixing of active and passive particles in geophysical flows.

Magnetohydrodynamics (MHD) studies the interaction between the flow of an electrically conducting fluid and magnetic fields. It involves such diverse topics as the evolution and dynamics of astrophysical objects, thermonuclear fusion, metallurgy and semiconductor crystal growth, etc. Although the first ideas in magnetohydrodynamics appeared at the beginning of the last century, the "explosion" in theoretical and experimental studies occurred in the 1950s-60s.

This state-of-the-art book aims at revising the evolution of ideas in various branches of magnetohydrodynamics (astrophysics, earth and solar dynamos, plasmas, MHD turbulence and liquid metals) and reviews current trends and challenges.

The Origin of Species Charles Darwin The origin of turbulence in fluids is a long-standing problem and has been the focus of research for decades due to its great importance in a variety of engineering applications. Furthermore, the study of the origin of turbulence is part of the fundamental physical problem of turbulence description and the philosophical problem of determinism and chaos. At the end of the nineteenth century, Reynolds and Rayleigh conjectured that the reason of the transition of laminar flow to the 'sinuous' state is in stability which results in amplification of wavy disturbances and breakdown of the laminar regime. Heisenberg (1924) was the founder of linear hydrody namic stability theory. The first calculations of boundary layer stability were fulfilled in pioneer works of Tollmien (1929) and Schlichting (1932, 1933). Later Taylor (1936) hypothesized that the transition to turbulence is initi ated by free-stream oscillations inducing local separations near wall. Up to the 1940s, skepticism of the stability theory predominated, in particular due to the experimental results of Dryden (1934, 1936). Only the experiments of Schubauer and Skramstad (1948) revealed the determining role of insta bility waves in the transition. Now it is well established that the transition to turbulence in shear flows at small and moderate levels of environmental disturbances occurs through development of instability waves in the initial laminar flow. In Chapter 1 we start with the fundamentals of stability theory, employing results of the early studies and recent advances."

obtained are still severely limited to low Reynolds numbers (about only one decade better than direct numerical simulations), and the interpretation of such calculations for complex, curved geometries is still unclear. It is evident that a lot of work (and a very significant increase in available computing power) is required before such methods can be adopted in daily's engineering practice. I hope to l"Cport on all these topics in a near future. The book is divided into six chapters, each. chapter in subchapters, sections and subsections. The first part is introduced by Chapter 1 which summarizes the equations of fluid mechanies, it is developed in C apters 2 to 4 devoted to the construction of turbulence models. What has been called "engineering methods" is considered in Chapter 2 where the Reynolds averaged equations al"C established and the closure problem studied ( 1-3). A first detailed study of homogeneous turbulent flows follows ( 4). It includes a review of available experimental data and their modeling. The eddy viscosity concept is analyzed in 5 with the l"Csulting alar-transport equation models such as the famous K-e model. Reynolds stl"Css models (Chapter 4) require a preliminary consideration of two-point turbulence concepts which are developed in Chapter 3 devoted to homogeneous turbulence. We review the two-point moments of velocity fields and their spectral transforms ( 1), their general dynamics ( 2) with the particular case of homogeneous, isotropie turbulence ( 3) whel"C the so-called Kolmogorov's assumptions are discussed at length."

Groundwater constitutes the most important reservoir of available clean water. Due to its overexploitation, some anthropogenic mismanagement on the surface and the overloading of the cleanup potential of subsurface, many of the groundwater systems used for water supply are in jeopardy. The problem is very severe in dry-lands, but also in urban, industrial, agricultural and traffic areas.

This book first addresses the recharge fluxes relating both to the quantity and quality of groundwater. In order to face the threats to the water supply and to be able to maintain a sustainable water management policy, detailed knowledge is needed on the surface-to-subsurface transformation link in the water cycle. Secondly, a comparison of both the traditional and modern approaches to determine groundwater recharge is presented. The traditional approach to determine groundwater recharge is based on water balance estimates and hydraulic considerations, which yield instantaneous values at best but do not integrate the totality of recharge pathways in time and space. In contrast, environmental tracers integrate these factors. Finally, the fate of groundwater recharge in the subsurface by hydraulic and geologic means is explained in detail, in order to stimulate adapted groundwater-management strategies and to better assess consequences of climate changes on groundwater resources as a whole.

Six new chapters (14-19) deal with topics of current interest: multi-component convection diffusion, convection in a compressible fluid, convenction with temperature dependent viscosity and thermal conductivity, penetrative convection, nonlinear stability in ocean circulation models, and numerical solution of eigenvalue problems.

"Nanotechnology" isa broad term that includes aspects of materials science, mesoscopicphysics, organicandinorganicchemistry, na- electronics, atmosphericchemistry, airpollution, and other?elds. The technology is very muchincurrent focus-at the beginning of the Third Millennium-and raises hopes for environmentally benign, resource-lean manufacturing of products of manykinds. One precursor to present-day nanotechnology used porous coatings, comprised of "ultra?ne" particles withdimensions inthe nanometer range, for absorption of thermal radiation on thermocouples, bolometers, and the like. These particles were prepared by gas-phase syntheses, speci?cally using species formed by nucleation andgrowth from a metalvapor - dergoing coolingby collisions withinert gas molecules. Such "inert gas evaporation" was explored inthe 1920s and 1930s see, for example, A.H. Pfund, Phys. Rev. 35 (1930) 1434]andwas investigated in moredetail in the 1960s and 1970s see, for example, K. Kimoto et al., Jpn. J. Appl. Phys. 2 (1963) 702; C.G. Granqvist and R.A. Buhrman, J. Appl. Phys.47 (1976) 2200]. Improved analytical capabilities(electron microscopy)as well as new applications (selective absorption of solar energy) were twoofthe r- sons for the renewed interest. Today, gas-phase synthesis of nanoparticles constitutesthe foundation for a pro?table butstill small industry. Aerosols, i.e., dispersions or suspensions of particles ina gas, form the background ?eld for contemporaryefforts in gas-phase nanotechnology. Interest inaerosol researchhistorically arose from the issues of atmospheric chemistry and physics, human health protection, and airpollution. Today, aerosol researchengagesa vast array of efforts inthese and related ?elds, andelsewherein work identi?ed as nanotechnology.

The book provides a broad overview of the full spectrum of state-of-the-art computational activities in multiphase flow as presented by top practitioners in the field. It starts with well-established approaches and builds up to newer methods. These methods are illustrated with applications to a broad spectrum of problems involving particle dispersion and deposition, turbulence modulation, environmental flows, fluidized beds, bubbly flows, and many others.

The simulation of technological and environmental flows is very important for many industrial developments. A major challenge related to their modeling is to involve the characteristic turbulence that appears in most of these flows. The traditional way to tackle this question is to use deterministic equations where the effects of turbulence are directly parametrized, i. e. , assumed as functions of the variables considered. However, this approach often becomes problematic, in particular if reacting flows have to be simulated. In many cases, it turns out that appropriate approximations for the closure of deterministic equations are simply unavailable. The alternative to the traditional way of modeling turbulence is to construct stochastic models which explain the random nature of turbulence. The application of such models is very attractive: one can overcome the closure problems that are inherent to deterministic methods on the basis of relatively simple and physically consistent models. Thus, from a general point of view, the use of stochastic methods for turbulence simulations seems to be the optimal way to solve most of the problems related to industrial flow simulations. However, it turns out that this is not as simple as it looks at first glance. The first question concerns the numerical solution of stochastic equations for flows of environmental and technological interest. To calculate industrial flows, 3 one often has to consider a number of grid cells that is of the order of 100 .