This book collects invited lectures and selected contributions presented at the Enzo Levi and XVIII Annual Meeting of the Fluid Dynamic Division of the Mexican Physical Society in 2012. It is intended for fourth-year undergraduate and graduate students, and for scientists in the fields of physics, engineering and chemistry with an interest in Fluid Dynamics from experimental, theoretical and computational points of view. The invited lectures are introductory in nature and avoid the use of complicated mathematics. The other selected contributions are also suitable for fourth-year undergraduate and graduate students. The Fluid Dynamics applications include oceanography, multiphase flows, convection, diffusion, heat transfer, rheology, granular materials, viscous flows, porous media flows and astrophysics. The material presented in the book includes recent advances in experimental and computational fluid dynamics and is well-suited to both teaching and research.

This book reconsiders the basic approaches behind the BEM method and in particular assesses and validates the equations forming the general momentum theory. One part of the book concerns the validation, using numerical fluid mechanics (CFD), of the different terms in the equations forming the momentum theory. Other parts present new ideas for extending the theory and for enhancing the accuracy of the BEM approach. Besides a general introduction and explanation of the momentum theory, the book also deals with specialized topics, such as diffusor-augmented rotors, wind tunnel corrections, tip corrections, and combined momentum/vortex theory for design of wind turbine rotors. The book contains new as well as already published material, and the author has strived to put the material into a new and more consistent context than what usually is found in similar text books. The book is primarily intended for researchers and experienced students with a basic knowledge in fluid mechanics wishing to understand and expand their knowledge on wind turbine aerodynamics. The book is self-consistent, hence all necessary derivations are shown, and it should not be necessary to seek help in other literature to understand the contents of the book.

This book presents different formulations of the equations governing incompressible viscous flows, in the form needed for developing numerical solution procedures. The conditions required to satisfy the no-slip boundary conditions in the various formulations are discussed in detail. Rather than focussing on a particular spatial discretization method, the text provides a unitary view of several methods currently in use for the numerical solution of incompressible Navier-Stokes equations, using either finite differences, finite elements or spectral approximations. For each formulation, a complete statement of the mathematical problem is provided, comprising the various boundary, possibly integral, and initial conditions, suitable for any theoretical and/or computational development of the governing equations. The text is suitable for courses in fluid mechanics and computational fluid dynamics. It covers that part of the subject matter dealing with the equations for incompressible viscous flows and their determination by means of numerical methods. A substantial portion of the book contains new results and unpublished material.

This monograph presents computational techniques and numerical analysis to study conservation laws under uncertainty using the stochastic Galerkin formulation. With the continual growth of computer power, these methods are becoming increasingly popular as an alternative to more classical sampling-based techniques. The text takes advantage of stochastic Galerkin projections applied to the original conservation laws to produce a large system of modified partial differential equations, the solutions to which directly provide a full statistical characterization of the effect of uncertainties. Polynomial Chaos Methods of Hyperbolic Partial Differential Equations focuses on the analysis of stochastic Galerkin systems obtained for linear and non-linear convection-diffusion equations and for a systems of conservation laws; a detailed well-posedness and accuracy analysis is presented to enable the design of robust and stable numerical methods. The exposition is restricted to one spatial dimension and one uncertain parameter as its extension is conceptually straightforward. The numerical methods designed guarantee that the solutions to the uncertainty quantification systems will converge as the mesh size goes to zero. Examples from computational fluid dynamics are presented together with numerical methods suitable for the problem at hand: stable high-order finite-difference methods based on summation-by-parts operators for smooth problems, and robust shock-capturing methods for highly nonlinear problems. Academics and graduate students interested in computational fluid dynamics and uncertainty quantification will find this book of interest. Readers are expected to be familiar with the fundamentals of numerical analysis. Some background in stochastic methods is useful but notnecessary.

This book deals with the application of spectral methods to problems of uncertainty propagation and quanti?cation in model-based computations. It speci?cally focuses on computational and algorithmic features of these methods which are most useful in dealing with models based on partial differential equations, with special att- tion to models arising in simulations of ?uid ?ows. Implementations are illustrated through applications to elementary problems, as well as more elaborate examples selected from the authors' interests in incompressible vortex-dominated ?ows and compressible ?ows at low Mach numbers. Spectral stochastic methods are probabilistic in nature, and are consequently rooted in the rich mathematical foundation associated with probability and measure spaces. Despite the authors' fascination with this foundation, the discussion only - ludes to those theoretical aspects needed to set the stage for subsequent applications. The book is authored by practitioners, and is primarily intended for researchers or graduate students in computational mathematics, physics, or ?uid dynamics. The book assumes familiarity with elementary methods for the numerical solution of time-dependent, partial differential equations; prior experience with spectral me- ods is naturally helpful though not essential. Full appreciation of elaborate examples in computational ?uid dynamics (CFD) would require familiarity with key, and in some cases delicate, features of the associated numerical methods. Besides these shortcomings, our aim is to treat algorithmic and computational aspects of spectral stochastic methods with details suf?cient to address and reconstruct all but those highly elaborate examples.

The modeling of reactive flows has progressed mainly with advances in aerospace, which gave birth to a new science called aerothermochemistry, as well as through developments in chemical and process engineering. This work examines basic concepts and methods necessary to study reactive flows and transfer phenomena in areas such as fluid mechanics, thermodynamics, and chemistry. The book presents tools of interest to graduate students, researchers in mathematical physics, and engineers who wish to investigate problems of reactive flows. Portions of the text may be used in courses on the physics of liquids or in seminars on mechanics.

Thisbookfocusesonthedynamicsoftheoceanbeingin?uencedbytheEarth'sro- tion and density strati?cation. Fluids in motion are a dif?cult subject of study that traditionally requires advanced knowledge of analytical mathematics, in particularly matrix algebra, differential and integral calculus, and complex analysis. Hence, this fascinating ?eld of science, known as geophysical ?uid dynamics, is accessible only to a limited number of students - those who either are naturally geniuses or those who underwent tough years of intense University study. Fluid processes are inherently complex and analytical solutions describing ?uid dynamics exist only in a few instances and only under highly simpli?ed assu- tions. Computer-based numerical models are required to approximate ?uid beh- ior in more realistic situations. Because of its complexity, universities tend to offer subjects in computational modelling of ?uid dynamics only at postgraduate level. This is a pity given that ?uid processes are truly fascinating in nature and given that the oceans play a signi?cant role in shaping life on Earth. The approach I pursue in this book is different from the traditional approach.

This book gathers the proceedings of the Seventh Symposium on Hybrid RANS-LES Methods, which was held on September 17-19 in Berlin, Germany. The different chapters, written by leading experts, reports on the most recent developments in flow physics modelling, and gives a special emphasis to industrially relevant applications of hybrid RANS-LES methods and other turbulence-resolving modelling approaches. The book addresses academic researchers, graduate students, industrial engineers, as well as industrial R&D managers and consultants dealing with turbulence modelling, simulation and measurement, and with multidisciplinary applications of computational fluid dynamics (CFD), such as flow control, aero-acoustics, aero-elasticity and CFD-based multidisciplinary optimization. It discusses in particular advanced hybrid RANS-LES methods. Further topics include wall-modelled Large Eddy Simulation (WMLES) methods, embedded LES, Lattice-Bolzman methods and turbulence-resolving applications and a comparison of the LES methods with both hybrid RANS-LES and URANS methods. Overall, the book provides readers with a snapshot on the state-of-the-art in CFD and turbulence modelling, with a special focus to hybrid RANS-LES methods and their industrial applications.

This book is primarily concerned with turbulence in superfluid helium. Quantized vorticity has traditionally generated great interest among physicists, but there are now also important engineering applications such as liquid helium cooling of superconducting magnets. Presently much research is done on the relationship between superfluid turbulence and classical turbulence, as intense turbulence can be generated in liquid helium due to its small kinematic viscosity. There is also a close relationship between superfluid behaviour and quantized vorticity in liquid helium and in atomic Bose--Einstein condensates. Putting special emphasis on the interplay between the different disciplines involved, this readable account of recent research will appeal not only to established researchers but also to newcomers and graduate students wishing to enter the field.

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 book was developed using material from teaching courses on fluid mechanics, high-speed flows, aerodynamics, high-enthalpy flows, experimental methods, aircraft design, heat transfer, introduction to engineering, and wind engineering. It precisely presents the theoretical and application aspects of the terms associated with these courses. It explains concepts such as cyclone, typhoon, hurricane, and tornado, by highlighting the subtle difference between them. The text comprehensively introduces the subject vocabulary of fluid mechanics for use in courses in engineering and the physical sciences. This book * Presents the theoretical aspects and applications of high-speed flows, aerodynamics, high-enthalpy flows, and aircraft design. * Provides a ready reference source for readers to learn essential concepts related to flow physics, rarefied, and stratified flows. * Comprehensively covers topics such as laser Doppler anemometer, latent heat of fusion, and latent heat of vaporisation. * Includes schematic sketches and photographic images to equip the reader with a better view of the concepts. This is ideal study material for senior undergraduate and graduate students in the fields of mechanical engineering, aerospace engineering, flow physics, civil engineering, automotive engineering, and manufacturing engineering.

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 is concerned with the prediction of thermodynamic and transport properties of gases and liquids. The prediction of such properties is essential for the solution of many problems encountered in chemical and process engineering as well as in other areas of science and technology. The book aims to present the best of those modern methods which are capable of practical application. It begins with basic scientific principles and formal results which are subsequently developed into practical methods of prediction. Numerous examples, supported by a suite of computer programmes, illustrate applications of the methods. The book is aimed primarily at the student market (for both undergraduate and taught postgraduate courses) but it will also be useful for those engaged in research and for chemical and process engineering professionals.

Flow induced vibration and noise (FIVN) remains a critical research topic. Even after over 50 years of intensive research, accurate and cost-effective FIVN simulation and measurement techniques remain elusive. This book gathers the latest research from some of the most prominent experts in the field. It describes methods for characterizing wall pressure fluctuations, including subsonic and supersonic turbulent boundary layer flows over smooth and rough surfaces using computational methods like Large Eddy Simulation; for inferring wall pressure fluctuations using inverse techniques based on panel vibrations or holographic pressure sensor arrays; for calculating the resulting structural vibrations and radiated sound using traditional finite element methods, as well as advanced methods like Energy Finite Elements; for using scaling approaches to universally collapse flow-excited vibration and noise spectra; and for computing time histories of structural response, including alternating stresses. This book presents the proceedings of the First International Workshop on Flow Induced Noise and Vibration (FLINOVIA), which was held in Rome, Italy, in November 2013. The authors' backgrounds represent a mix of academia, government, and industry, and several papers include applications to important problems for underwater vehicles, aerospace structures and commercial transportation. The book offers a valuable reference guide for all those working in the area of flow-induced vibration and noise.

A few years ago the Helmholtz Association (HGF) consisting of 15 research Institutions including the German Aerospace Center (DLR) started a network research program called 'Virtual Institutes'. The basic idea of this program was to establish research groups formed by Helmholtz research centers and universities to study and develop methods or technologies for future applications and educate young scientists. It should also enable and encourage the partners of this Virtual Institute after 3 years funding to continue their cooperation in other programs. Following this HGF request and chance the DLR Windtunnel Department of the Institute of Aerodynamics and Flow Technology took the initiative and established a network with other DLR institutes and German u- versities RWTH Aachen, University of Stuttgart and Technical University Munich. The main goal of this network was to share the experience in system analysis, ae- dynamics and material science for aerospace for improving the understanding and applicability of some key technologies for future reusable space transportation s- tems. Therefore, the virtual institute was named RESPACE (Key Technologies for Re- Usable Space Systems).

This work describes the different operational regimes and the dominant mechanisms of flows in disperse systems.

The scope of this book is to present in a systematic and unified manner the ray method (in its various forms) for studying nonlinear wave propagation in situations of physical interest (essentially fluid dynamics and plasma physics). The book could be used for an advanced graduate course on nonlinear waves. It should also be of interest to applied mathematicians, physicists and engineers, working in areas related to nonlinear waves.

In these lectures, most of them given at the University of Montreal while he held the Aisenstadt Chair, Roman Jackiw provides a view of fluid dynamics from an entirely novel perspective. He begins by explaining the motivation and reviewing the classical theory, but in a manner different from textbook discussions. Among other topics, he discusses conservation laws and Euler equations, and a method for finding their canonical structure; C. Eckart's Lagrangian and a relativistic generalization for vortex-free motion; nonvanishing vorticity and the Clebsch parameterization for the velocity vector. Jackiw then discusses some specific models for nonrelativistic and relativistic fluid mechanics with more than one spatial dimension, including the Chaplygin gas (whose negative pressure is inversely proportional to density), and the scalar Born-Infeld model. He shows how both the Chaplygin gas and the Born-Infeld model devolve from the parameterization-invariant Nambu-Goto action. As in particle physics, Jackiw shows, fluid mechanics enhanced by supersymmetry, non-Abelian degrees of freedon, and non commuting coordinates. Jackiw discusses the need for a non-Abelian fluid mechanics, and proposes a Lagrangian, which involves a non-Abelian auxiliary field, whose Chern-Simons density should be a total derivative. The generalization to magnetohydrodynamics, which results from including a dynamical non-Abelian guage filed, reduces in the Abelian limit to conventional magnetohydrodynamics. For one-dimensional cases, the models mentioned above are completely integrable, and Jackiw gives the general solution of the Chaplygin gas and the Born-Infeld model on a line, as well as a general solution of the Nambu-Goto theory for a 1-brane (string) in two spatial dimensions. Jackiw discusses the need for a non-Abelian fluid mechanics and proposes a Lagrangian, which involves a non-Abelian auxiliary field whose Chern-Simons density should be a total derivative. The generalization to magnetohydrodynamics, which results from including a dynamical non-Abelian gauge field, reduces in the Abelian limit to conventional magnetohydrodynamics.

This book gives the basic analytical framework for the description of turbulent flows and discusses various types encountered by civil engineers involved in hydraulic analysis and design, as well as environmental engineers. It also presents a detailed exposition of the various dimensions of turbulent flow. The book is extremely useful for practising engineers, particularly in the field of hydraulic analysis and design, building dynamics and environmental engineering.

This book proposes an introduction to the mathematical modeling of the respiratory system. A detailed introduction on the physiological aspects makes it accessible to a large audience without any prior knowledge on the lung. Different levels of description are proposed, from the lumped models with a small number of parameters (Ordinary Differential Equations), up to infinite dimensional models based on Partial Differential Equations. Besides these two types of differential equations, two chapters are dedicated to resistive networks, and to the way they can be used to investigate the dependence of the resistance of the lung upon geometrical characteristics. The theoretical analysis of the various models is provided, together with state-of-the-art techniques to compute approximate solutions, allowing comparisons with experimental measurements. The book contains several exercises, most of which are accessible to advanced undergraduate students.

Vortex flow is one of the fundamental types of fluid and gas motion. These flows are the most spectacular in the form of concentrated vortices, characterized by the localization of vorticity (curl of velocity) in bounded regions of a space, beyond which the vorticity is either absent or rapidly falls down to zero. Concentrated vortices are often observed in nature, exemplified by atmospheric cyclones, whirlwinds and tornados, oceanic vortices, whirlpools on a water s- face, and ring vortices caused by explosive outburst of volcanoes. In technical - vices concentrated vortices form when flow separates from sharp edges of flying vehicles and ships. Among these are vortices flowing off the ends of airplane wings, and intentionally generated vortices for intensification of burning in c- bustion chambers, vortices in cyclonic devices used for mixing or separation of impurities in fluids and gases. One such remarkable and frequent type of conc- trated vortices is a vortex ring which constitutes a vortex tube closed into a t- oidal ring moving in a surrounding fluid like an isolated body out of contact with solid boundaries of the flow region if such boundaries exist. Formation and motion of vortex rings are important part of the dynamics of a continuum medium and have been studied for more than a century.

This book is the result of two decades of research work which started with an accidental observation. One of my students, Dipl. phys. Volkmar Lenz, - ticed that the speckle pattern of laser light scattered by a cuvette containing diluted milk performed a strange motion every time he came near the cuvette with his thumb. After thinkingabout this e?ect we came to the conclusion that this motion can only be caused by scatteringparticles with di?erent velocities, as in the case of the di?raction pattern of an optical grating: A linear motion of the grating does not change the pattern whereas a rotation of the grating does. The observed speckle motion could then be explained qualitatively as produced by the inhomogeneous velocity of the convection within the cuvette which was produced by the heat of the thumb. The theoretical treatment of this e?ect revealed that the velocity gradient of the light scattering medium is responsible for the speckle motion. The idea to use this e?ect for developingmeasurement techniques for velocity gradients arose almost immediately. For that purpose we had to develop not only experimental set-ups to measure the pattern velocity but also the theory which describes the connection between this velocity and the velocity gradient. The result of this work together with the description of a method developed by another group forms the contents of this book. I am indebted to the students who worked in my laboratory and developed the measurement techniques. These were, in temporal order, Dr.

The main idea of the present study is to demonstrate that the qualitative theory of diffe rential equations, when applied to problems in fluid-and gasdynamics, will contribute to the understanding of qualitative aspects of fluid flows, in particular those concerned with geometrical properties of flow fields such as shape and stability of its streamline patterns. It is obvious that insight into the qualitative structure of flow fields is of great importance and appears as an ultimate aim of flow research. Qualitative insight fashions our know ledge and serves as a good guide for further quantitative investigations. Moreover, quali tative information can become very useful, especially when it is applied in close corres pondence with numerical methods, in order to interpret and value numerical results. A qualitative analysis may be crucial for the investigation of the flow in the neighbourhood of singularities where a numerical method is not reliable anymore due to discretisation er rors being unacceptable. Up till now, familiar research methods -frequently based on rigorous analyses, careful nu merical procedures and sophisticated experimental techniques -have increased considera bly our qualitative knowledge of flows, albeit that the information is often obtained indirectly by a process of a careful but cumbersome examination of quantitative data. In the past decade, new methods are under development that yield the qualitative infor mation more directly. These methods, make use of the knowledge available in the qualitative theory of differen tial equations and in the theory of bifurcations."

This textbook presents a systematic study of the qualitative and geometric theory of nonlinear differential equations and dynamical systems. Although the main topic of the book is the local and global behavior of nonlinear systems and their bifurcations, a thorough treatment of linear systems is given at the beginning of the text. All the material necessary for a clear understanding of the qualitative behavior of dynamical systems is contained in this textbook, including an outline of the proof and examples illustrating the proof of the Hartman-Grobman theorem, the use of the Poincare map in the theory of limit cycles, the theory of rotated vector fields and its use in the study of limit cycles and homoclinic loops, and a description of the behavior and termination of one-parameter families of limit cycles. In addition to minor corrections and updates throughout, this new edition includes materials on higher order Melnikov theory and the bifurcation of limit cycles for planar systems of differential equations, including new sections on Francoise's algorithm for higher order Melnikov functions and on the finite codimension bifurcations that occur in the class of bounded quadratic systems.