This book discusses the fundamental principles and equations governing the motion of incompressible Newtonian fluids, and simultaneously introduces analytical and numerical methods for solving a broad range of pertinent problems. Topics include an in-depth discussion of kinematics, elements of differential geometry of lines and surfaces, vortex dynamics, properties and computation of interfacial shapes in hydrostatics, exact solutions, flow at low Reynolds numbers, interfacial flows, hydrodynamic stability, boundary-layer analysis, vortex motion, boundary-integral methods for potential and Stokes flow, principles of computational fluid dynamics (CFD), and finite-difference methods for Navier-Stokes flow.
The discourse includes classical and original topics, as well as derivations accompanied by solved and unsolved problems that illustrate the theoretical results and explain the implementation of the numerical methods. Appendices provide a wealth of information and establish the necessary mathematical and numerical framework.
A unique and comprehensive synthesis of the essential aspects of the discipline, this volume serves as an ideal textbook in several graduate courses on theoretical and computational fluid dynamics, applied mathematics, and scientific computing. The material is an indispensable resource for professionals and researchers in various fields of science, chemical, mechanical, biomechanical, civil and aerospace engineering.

Turbulence is widely recognized as one of the outstanding problems of the physical sciences, but it still remains only partially understood despite having attracted the sustained efforts of many leading scientists for well over a century. In A Voyage Through Turbulence we are transported through a crucial period of the history of the subject via biographies of twelve of its great personalities, starting with Osborne Reynolds and his pioneering work of the 1880s. This book will provide absorbing reading for every scientist, mathematician and engineer interested in the history and culture of turbulence, as background to the intense challenges that this universal phenomenon still presents.

The instability of fluid flows is a key topic in classical fluid mechanics because it has huge repercussions for applied disciplines such as chemical engineering, hydraulics, aeronautics, and geophysics. This modern introduction is written for any student, researcher, or practitioner working in the area, for whom an understanding of hydrodynamic instabilities is essential. Based on a decade's experience of teaching postgraduate students in fluid dynamics, this book brings the subject to life by emphasizing the physical mechanisms involved. The theory of dynamical systems provides the basic structure of the exposition, together with asymptotic methods. Wherever possible, Charru discusses the phenomena in terms of characteristic scales and dimensional analysis. The book includes numerous experimental studies, with references to videos and multimedia material, as well as over 150 exercises which introduce the reader to new problems.

In the present monograph, we develop the kinetic theory of transport phenomena and relaxation processes in the flows of reacting gas mixtures and discuss its applications to strongly non-equilibrium conditions. The main attention is focused on the influence of non-equilibrium kinetics on gas dynamics and transport properties. Closed systems of fluid dynamic equations are derived from the kinetic equations in different approaches. We consider the most accurate approach taking into account the state-to-state kinetics in a flow, as well as simplified multi-temperature and one-temperature models based on quasi-stationary distributions. Within these approaches, we propose the algorithms for the calculation of the transport coefficients and rate coefficients of chemical reactions and energy exchanges in non-equilibrium flows; the developed techniques are based on the fundamental kinetic theory principles. The theory is applied to the modeling of non-equilibrium flows behind strong shock waves, in the boundary layer, and in nozzles. The comparison of the results obtained within the frame of different approaches is presented, the advantages of the new state-to-state kinetic model are discussed, and the limits of validity for simplified models are established. The book can be interesting for scientists and graduate students working on physical gas dynamics, aerothermodynamics, heat and mass transfer, non-equilibrium physical-chemical kinetics, and kinetic theory of gases.

This book unies the common tensor analytical aspects in engineering and physics. Using tensor analysis enables the reader to understand complex physical phenomena from the basic principles in continuum mechanics including the turbulence, its correlations and modeling to the complex Einstein' tensor equation. The development of General Theory of Relativity and the introduction of spacetime geometry would not have been possible without the use of tensor analysis. This textbook is primarily aimed at students of mechanical, electrical, aerospace, civil and other engineering disciplines as well as of theoretical physics. It also covers the special needs of practicing professionals who perform CFD-simulation on a routine basis and would like to know more about the underlying physics of the commercial codes they use. Furthermore, it is suitable for self-study, provided that the reader has a sufficient knowledge of differential and integral calculus. Particular attention was paid to selecting the application examples. The transformation of Cartesian coordinate system into curvilinear one and the subsequent applications to conservation laws of continuum mechanics and the turbulence physics prepares the reader for fully understanding the Einstein tensor equations, which exhibits one of the most complex tensor equation in theoretical physics.

In daily life, we are accustomed to working with length scales of feet or meters, but the building blocks from which our bodies are constructed are many orders of magnitude smaller. The technologies that are being developed to intervene at these minute scales have the potential to improve human health and significantly enrich our lives.
Revolutionary micro/nano technology platforms have led to dramatic advances in sample preparation, analysis and cell culture. From the 1990s through to the very beginning of the twenty-first century, the focus was on the development of manufacturing technologies. Through elegant design and sophisticated fabrication, the micro- to nano-scale manipulation of fluids and particles has become routine. Since then, it has become possible to control molecular interactions at device surfaces, and optical manipulation, imaging and sensing techniques can also be incorporated. Micro/nano technology platforms are already being used to study and direct biological processes at the cellular and sub-cellular level, and to detect disease with greater sensitivity and specificity. The challenges and excitement in the near future will be in engineering these sophisticated, multifunctional devices to seamlessly interface with complex biological systems.
Providing a clear guide that moves from molecules through devices to systems, this book reviews fundamental aspects of microfluidic devices, including fabrication, surface property control, pressure-driven and electrokinetic flow, and functions such as fluid mixing, particle sorting and molecular separations. The integration of optical and plasmonic imaging, optoelectronic tweezers for single particle manipulation, and optical and electrical signal transduction methods for biosensing are shown to provide extraordinary capabilities for bioanalytical and biomedical applications. These represent key areas of research that will lead to the next generation of micro/nano-based systems. Anyone working in this fast-changing field will benefit from this comprehensive review of the latest thinking, while researchers will find much to inspire and direct their work.

Every fluid dynamicist will at some point need to use computation. Thinking about the physics, constraints and the requirements early on will be rewarded with benefits in time, effort, accuracy and expense. How these benefits can be realised is illustrated in this guide for would-be researchers and beginning graduate students to some of the standard methods and common pitfalls of computational fluid mechanics. Based on a lecture course that the author has developed over twenty years, the text is split into three parts. The quick introduction enables students to solve numerically a basic nonlinear problem by a simple method in just three hours. The follow-up part expands on all the key essentials, including discretisation (finite differences, finite elements and spectral methods), time-stepping and linear algebra. The final part is a selection of optional advanced topics, including hyperbolic equations, the representation of surfaces, the boundary integral method, the multigrid method, domain decomposition, the fast multipole method, particle methods and wavelets.

This book aims to bridge the gap between practising mathematicians and the practitioners of turbulence theory. It presents the mathematical theory of turbulence to engineers and physicists, and the physical theory of turbulence to mathematicians. The book is the result of many years of research by the authors to analyse turbulence using Sobolev spaces and functional analysis. In this way the authors have recovered parts of the conventional theory of turbulence, deriving rigorously from the Navier-Stokes equations what had been arrived at earlier by phenomenological arguments. The mathematical technicalities are kept to a minimum within the book, enabling the language to be at a level understood by a broad audience. Each chapter is accompanied by appendices giving full details of the mathematical proofs and subtleties. This unique presentation should ensure a volume of interest to mathematicians, engineers and physicists.

This book presents state-of-the-art lectures on complex flows of fundamental and industrial interest in the subsonic, supersonic and hypersonic regimes. Experimental investigations of unsteady separated flows, high-enthalpy flows, 3D configurations, laminar and transitional flows are addressed. Theoretical predictions of aerodynamic performances are provided along with analyses of supersonic combustion, detonation, simulation of reactive mixing layer and non-equilibrium flow. Computational Fluid Dynamics methods for the simulation of viscous compressible flow, inviscidviscous flow interactions, real-gas effects in rarefied flow, flows about bodies with permeable walls and supersonic turbulent flows are finally developed and analysed.

Provides unified coverage of computational heat transfer and fluid dynamics. Covers basic concepts and then applies computational methods for problem analysis and solution. Contains new chapters on mesh generation and computer modeling of turbulent flow. Includes ANSYS, STAR CCM+, and COMSOL CFD code and tutorials in the appendix. Includes a Solutions Manual for instructor use.

The first of its kind, this book is an in-depth history of hydrodynamics from its eighteenth-century foundations to its first major successes in twentieth-century hydraulics and aeronautics. It documents the foundational role of fluid mechanics in developing a new mathematical physics. It gives full and clear accounts of the conceptual breakthroughs of physicists and engineers who tried to meet challenges in the practical worlds of hydraulics, navigation, blood circulation, meteorology, and aeronautics, and it shows how hydrodynamics at last began to fulfill its early promise to unify the different worlds of flow. Richly illustrated, technically thorough, and sensitive to cross-cultural effects, this history should attract a broad range of historians, scientists, engineers, and philosophers and be a standard reference for anyone interested in fluid mechanics.

Providing a comprehensive grounding in the subject of turbulence, Statistical Theory and Modeling for Turbulent Flows develops both the physical insight and the mathematical framework needed to understand turbulent flow. Its scope enables the reader to become a knowledgeable user of turbulence models; it develops analytical tools for developers of predictive tools. Thoroughly revised and updated, this second edition includes a new fourth section covering DNS (direct numerical simulation), LES (large eddy simulation), DES (detached eddy simulation) and numerical aspects of eddy resolving simulation. In addition to its role as a guide for students, Statistical Theory and Modeling for Turbulent Flows also is a valuable reference for practicing engineers and scientists in computational and experimental fluid dynamics, who would like to broaden their understanding of fundamental issues in turbulence and how they relate to turbulence model implementation. * Provides an excellent foundation to the fundamental theoretical concepts in turbulence. * Features new and heavily revised material, including an entire new section on eddy resolving simulation. * Includes new material on modeling laminar to turbulent transition. * Written for students and practitioners in aeronautical and mechanical engineering, applied mathematics and the physical sciences. * Accompanied by a website housing solutions to the problems within the book.

An introduction to the rheology of polymers, with simple math

Designed for practicing scientists and engineers interested in polymer rheology science, education, consulting, or research and development, "Introduction to Polymer Rheology" is a comprehensive yet accessible guide to the study of the deformation and flow of matter under applied stress. Often considered a complicated topic for beginners, the book makes grasping the fundamentals of polymer rheology easy by presenting information in an approachable way and limiting the use of complex mathematics. By doing so, this introductory overview provides readers with easy access to the key concepts underlying the flow behavior of polymer melts, solutions, and suspensions. Incorporating sample problems that are worked through and explained on the page, as well as numerous practice problems to gauge learning comprehension, the book prepares new students and practitioners for moving on to more advanced concepts.

Comprising twelve chapters, the book covers stress, velocity and rate of deformation, the relationship between stress and rate of deformation (Newtonian fluid), generalized Newtonian fluids, normal stresses and elastic behavior, experimental methods, small and large strain, the molecular origins of rheological behavior, elementary polymer processing concepts, quality control in rheology, and the flow of modified polymers and those with supermolecular structure.

The essential reference for accurately interpreting polymer rheology data, "Introduction to Polymer Rheology" provides readers with an elementary understanding of the key issues and modern approaches to resolving problems in the field.An Instructor's Guide with answers to select problems in the text, 60 new problems with full solutions, hints for effective presentation of the material in the text, and an errata listing is available for professors using the book as a course textbook.

Logan's Turbomachinery: Flowpath Design and Performance Fundamentals, Third Edition is the long-awaited revision of this classic textbook, thoroughly updated by Dr. Bijay Sultanian. While the basic concepts remain constant, turbomachinery design has advanced since the Second Edition was published in 1993. Airfoils in modern turbomachines feature three-dimensional geometries, Computational Fluid Mechanics (CFD) has become a standard design tool, and major advances have been made in the materials and manufacturing technologies that affect turbomachinery design. The new edition adresses these trends to best serve today's students, and design engineers working in turbomachinery industries.

This book addresses the needs of growing community of graduate students and researchers new to the area, for a survey that covers a wide range of pertinent topics, summarizes the current status of the field, and provides the necessary pedagogical materials for newcomers. The investigation of strongly interacting matter under the influence of macroscopic rotational motion is a new, emerging area of research that encompasses a broad range of conventional physics disciplines such as nuclear physics, astrophysics, and condensed matter physics, where the non-trivial interplay between global rotation and spin is generating many novel phenomena. Edited and authored by leading researchers in the field, this book covers the following topics: thermodynamics and equilibrium distribution of rotating matter; quantum field theory and rotation; phase structure of QCD matter under rotation; kinetic theory of relativistic rotating matter; hydrodynamics with spin; magnetic effects in fluid systems with high vorticity and charge; polarization measurements in heavy ion collisions; hydrodynamic modeling of the QCD plasma and polarization calculation in relativistic heavy ion collisions; chiral vortical effect; rotational effects and related topics in neutron stars and condensed matter systems.

In its 3rd revised and extended edition the book offers an overview of the techniques used to solve problems in fluid mechanics on computers and describes in detail those most often used in practice. Included are advanced methods in computational fluid dynamics, like direct and large-eddy simulation of turbulence, multigrid methods, parallel computing, moving grids, structured, block-structured and unstructured boundary-fitted grids, free surface flows. The 3rd edition contains a new section dealing with grid quality and an extended description of discretization methods. The book shows common roots and basic principles for many different methods. The book also contains a great deal of practical advice for code developers and users; it is designed to be equally useful to beginners and experts.The issues of numerical accuracy, estimation and reduction of numerical errors are dealt with in detail, with many examples.

The Navier-Stokes equations describe the motion of fluids and are an invaluable addition to the toolbox of every physicist, applied mathematician, and engineer. The equations arise from applying Newton's laws of motion to a moving fluid and are considered, when used in combination with mass and energy conservation rules, to be the fundamental governing equations of fluid motion. They are relevant across many disciplines, from astrophysics and oceanic sciences to aerospace engineering and materials science. This Student's Guide provides a clear and focused presentation of the derivation, significance and applications of the Navier-Stokes equations, along with the associated continuity and energy equations. Designed as a useful supplementary resource for undergraduate and graduate students, each chapter concludes with a selection of exercises intended to reinforce and extend important concepts. Video podcasts demonstrating the solutions in full are provided online, along with written solutions and other additional resources.

Droplet microfluidics offers tremendous potential as an enabling technology for high-throughput screening. It promises to yield novel techniques for personalised medicine, drug discovery, disease diagnosis, establishing chemical libraries, and the discovery of new materials. Despite the enormous potential to contribute to a broad range of applications, the expected adoption has not yet been seen, partly due to the interdisciplinary nature and the fact that, up until now, information has been scattered across the literature. This book goes a long way to addressing these issues. Edited by two leaders, this book has drawn together expertise from around the globe to form a unified, cohesive resource for the droplet microfluidics community. Starting with the basic theory of droplet microfluidics before introducing its use as a tool, the reader will be treated to chapters on important techniques, including robust passive and active droplet manipulations and applications such as single cell analysis, which is key for drug discovery. This book is a go-to resource for the community yearning to adopt and promote droplet microfluidics into different applications and will interest researchers and practitioners working across chemistry, biology, physics, materials science, micro- and nano-technology, and engineering.

Data-driven methods have become an essential part of the methodological portfolio of fluid dynamicists, motivating students and practitioners to gather practical knowledge from a diverse range of disciplines. These fields include computer science, statistics, optimization, signal processing, pattern recognition, nonlinear dynamics, and control. Fluid mechanics is historically a big data field and offers a fertile ground for developing and applying data-driven methods, while also providing valuable shortcuts, constraints, and interpretations based on its powerful connections to basic physics. Thus, hybrid approaches that leverage both methods based on data as well as fundamental principles are the focus of active and exciting research. Originating from a one-week lecture series course by the von Karman Institute for Fluid Dynamics, this book presents an overview and a pedagogical treatment of some of the data-driven and machine learning tools that are leading research advancements in model-order reduction, system identification, flow control, and data-driven turbulence closures.

This textbook gives an introduction to fluid dynamics based on flows for which analytical solutions exist, like individual vortices, vortex streets, vortex sheets, accretions disks, wakes, jets, cavities, shallow water waves, bores, tides, linear and non-linear free-surface waves, capillary waves, internal gravity waves and shocks. Advanced mathematical techniques ("calculus") are introduced and applied to obtain these solutions, mostly from complex function theory (Schwarz-Christoffel theorem and Wiener-Hopf technique), exterior calculus, singularity theory, asymptotic analysis, the theory of linear and nonlinear integral equations and the theory of characteristics. Many of the derivations, so far contained only in research journals, are made available here to a wider public.

The aim of this book is to offer a direct and self-contained access to some of the new or recent results in fluid mechanics. It gives an authoritative account on the theory of the Euler equations describing a perfect incompressible fluid. First of all, the text derives the Euler equations from a variational principle, and recalls the relations on vorticity and pressure. Various weak formulations are proposed. The book then presents the tools of analysis necessary for their study: Littlewood-Paley theory, action of Fourier multipliers on L spaces, and partial differential calculus. These techniques are then used to prove various recent results concerning vortext patches or sheets, essentially the persistence of the smoothness of the boundary of a vortex patch, even if that smoothness allows singular points, as well as the existence of weak solutions of the vorticity sheet type. The text also presents properties of microlocal (analytic or Gevrey) regularity of the solutions of Euler equations, and provides links of such properties to the smoothness in time of the flow of the solution vector field.

Fluid Mechanics: A Geometrical Point of View emphasizes general principles of physics illustrated by simple examples in fluid mechanics. Advanced mathematics (e.g., Riemannian geometry and Lie groups) commonly used in other parts of theoretical physics (e.g. General Relativity or High Energy Physics) are explained and applied to fluid mechanics. This follows on from the author's book Advanced Mechanics (Oxford University Press, 2013). After introducing the fundamental equations (Euler and Navier-Stokes), the book provides particular cases: ideal and viscous flows, shocks, boundary layers, instabilities, and transients. A restrained look at integrable systems (KdV) leads into a formulation of an ideal fluid as a hamiltonian system. Arnold's deep idea, that the instability of a fluid can be understood using the curvature of the diffeomorphism group, will be explained. Leray's work on regularity of Navier-Stokes solutions, and the modern developments arising from it, will be explained in language for physicists. Although this is a book on theoretical physics, readers will learn basic numerical methods: spectral and finite difference methods, geometric integrators for ordinary differential equations. Readers will take a deep dive into chaotic dynamics, using the Smale horse shoe as an example. Aref's work on chaotic advection is explained. The book concludes with a self-contained introduction to renormalization, an idea from high energy physics which is expected to be useful in developing a theory of turbulence.

Fluid mechanics is an important scientific field with various industrial applications for flows or energy consumption and efficiency issues. This book has as main aim to be a textbook of applied knowledge in real fluids as well as to the Hydraulic systems components and operation, with emphasis to the industrial or real life problems for piping and aerodynamic design geometries. Various problems will be presented and analyzed through this book.

A century ago, Lewis Fry Richardson introduced the concept of energy cascades in turbulence. Since this conceptual breakthrough, turbulence has been studied in diverse systems and our knowledge has increased considerably through theoretical, numerical, experimental and observational advances. Eddy turbulence and wave turbulence are the two regimes we can find in nature. So far, most attention has been devoted to the former regime, eddy turbulence, which is often observed in water. However, physicists are often interested in systems for which wave turbulence is relevant. This textbook deals with wave turbulence and systems composed of a sea of weak waves interacting non-linearly. After a general introduction which includes a brief history of the field, the theory of wave turbulence is introduced rigorously for surface waves. The theory is then applied to examples in hydrodynamics, plasma physics, astrophysics and cosmology, giving the reader a modern and interdisciplinary view of the subject.