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86 results in Nonlinear Science and Fluid Dynamics

Page 1 of 5

Fundamentals of Transport Phenomena
  • Anthony T. Paxton
  • Coming soon
  • Expected online publication date:
    September 2025
    Print publication:
    30 September 2025
  • Fluid mechanics, solid-state diffusion and heat conduction are deeply interconnected through the mathematics and physical principles that define them. This concise and authoritative book reveals these connections, providing a detailed picture of their important applications in astrophysics, plasmas, energy systems, aeronautics, chemical engineering and materials science. This sophisticated and focused text offers an alternative to more expansive volumes on heat, mass and momentum transfer and is ideal for students and researchers working on fluid dynamics, mass transfer or phase transformations and industrial scientists seeking a rigourous understanding of chemical or materials processes. Accessible yet in-depth, this modern treatment distils the essential theory and application of these closely related topics, includes numerous real-world applications and can be used for teaching a range of related courses in physics, engineering and materials science departments.

Fluid Mechanics
  • Lectures on Theoretical Physics
  • Volume 4
  • David Tong
  • Coming soon
  • Expected online publication date:
    May 2025
    Print publication:
    31 May 2025
  • Take anything in the universe, put it in a box, and heat it up. Regardless of what you start with, the motion of the substance will be described by the equations of fluid mechanics. This remarkable universality is the reason why fluid mechanics is important. The key equation of fluid mechanics is the Navier-Stokes equation. This textbook starts with the basics of fluid flows, building to the Navier-Stokes equation while explaining the physics behind the various terms and exploring the astonishingly rich landscape of solutions. The book then progresses to more advanced topics, including waves, fluid instabilities, and turbulence, before concluding by turning inwards and describing the atomic constituents of fluids. It introduces ideas of kinetic theory, including the Boltzmann equation, to explain why the collective motion of 1023 atoms is, under the right circumstances, always governed by the laws of fluid mechanics.

A First Course in Magnetohydrodynamics
  • David Alan Clarke
  • Coming soon
  • Expected online publication date:
    May 2025
    Print publication:
    31 May 2025
  • This text introduces readers to magnetohydrodynamics (MHD), the physics of ionised fluids. Traditionally MHD is taught as part of a graduate curriculum in plasma physics. By contrast, this text - one of a very few - teaches MHD exclusively from a fluid dynamics perspective, making it uniquely accessible to senior undergraduate students. Part I of the text uses the MHD Riemann problem as a focus to introduce the fundamentals of MHD: Alfvén's theorem; waves; shocks; rarefaction fans; etc. Part II builds upon this with presentations of broader areas of MHD: fluid instabilities; viscid hydrodynamics; steady-state MHD; and non-ideal MHD. Throughout the text, more than 125 problems and several projects (with solutions available to instructors) reinforce the main ideas. Optionally, large-font lesson plans for a 'flipped-style' class are also available to instructors. This book is suitable for advanced undergraduate and beginning graduate students, requiring no previous knowledge of fluid dynamics or plasma physics.

Population Balance of Particles in Flows
  • From Aerosols to Crystallisation
  • Stelios Rigopoulos
  • Published online:
    14 November 2024
    Print publication:
    21 November 2024
  • The population balance methodology provides a powerful framework for studying polydisperse entities such as aerosols, crystals and bubbles. This self-contained and accessible book explains how this theoretical framework can be employed across a wide range of scientific, engineering and environmental problems. The methodology is explained step-by-step, showing readers how to use these techniques by formulating the population balance problem, choosing models and implementing appropriate solution methods. Particular focus is given to the coupling of the population balance with fluid mechanics and computational fluid dynamics (CFD), in both laminar and turbulent flows. Applications of the population balance methodology are explored in case studies including nanoparticle synthesis, soot formation and crystallisation, and sample open-source code is provided. This book will be valuable to researchers across a range of disciplines including chemical and mechanical engineering, physics and environmental science, and can be used as a resource for advanced undergraduate and graduate courses.

Hamiltonian Systems
  • Dynamics, Analysis, Applications
  • Edited by Albert Fathi, Philip J. Morrison, Tere M-Seara, Sergei Tabachnikov
  • Published online:
    10 May 2024
    Print publication:
    09 May 2024
  • Dynamical systems that are amenable to formulation in terms of a Hamiltonian function or operator encompass a vast swath of fundamental cases in applied mathematics and physics. This carefully edited volume represents work carried out during the special program on Hamiltonian Systems at MSRI in the Fall of 2018. Topics covered include KAM theory, polygonal billiards, Arnold diffusion, quantum hydrodynamics, viscosity solutions of the Hamilton–Jacobi equation, surfaces of locally minimal flux, Denjoy subsystems and horseshoes, and relations to symplectic topology.

Flow Control
  • A Fluid Instability Approach
  • Thomas C. Corke
  • Published online:
    04 April 2024
    Print publication:
    11 April 2024
  • This book provides a comprehensive treatment of passive and active flow control in fluid dynamics, with an emphasis on utilizing fluid instabilities for enhancing control performance. Examples are given from a wide range of technologically important flow fields occurring in aerospace applications, from low-subsonic to hypersonic Mach numbers. This essential book can be used for both research and teaching on the topics of fluid instabilities, fluid measurement and flow actuator techniques, and problem sets are provided at the end of each chapter to reinforce key concepts and further extend readers' understanding of the field. The solutions manual is available as a online resource for instructors. The text is well suited for both graduate students in fluid dynamics and for practising engineers in the aerodynamics design field.

Multiphase Flow with Solid Particles
  • Pawel Kosinski
  • Published online:
    05 October 2023
    Print publication:
    19 October 2023
  • Multiphase flow is an area of fluid dynamics that describes interactions between two or more phases of matter and is relevant across a wide range of industrial processes and natural environmental systems, from the transport of natural resources to volcanic ash flow. This book covers the topic in detail, providing clear explanations of the underlying physics behind the complex behaviour of solid particles in fluids. The forces involved in particle-fluid interactions are first used to describe the interactions between the particles, and the fundamentals of contact mechanics are then outlined and applied to model interparticle collisions. The book is illustrated with frequent worked examples and algorithms, enabling the reader to develop the required tools for simulating the flow of fluids with solid particles. This self-contained text will appeal to physicists, applied mathematicians and mechanical engineers working in this important area of research.

A Student's Guide to the Navier-Stokes Equations
  • Justin W. Garvin
  • Published online:
    10 March 2023
    Print publication:
    09 February 2023
  • 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.

Turbulent Flows
  • Stephen B. Pope
  • Published online:
    20 January 2023
    Print publication:
    10 August 2000
  • This is a graduate text on turbulent flows, an important topic in fluid dynamics. It is up-to-date, comprehensive, designed for teaching, and is based on a course taught by the author at Cornell University for a number of years. The book consists of two parts followed by a number of appendices. Part I provides a general introduction to turbulent flows, how they behave, how they can be described quantitatively, and the fundamental physical processes involved. Part II is concerned with different approaches for modelling or simulating turbulent flows. The necessary mathematical techniques are presented in the appendices. This book is primarily intended as a graduate level text in turbulent flows for engineering students, but it may also be valuable to students in applied mathematics, physics, oceanography and atmospheric sciences, as well as researchers and practising engineers.

Physics of Wave Turbulence
  • Sébastien Galtier
  • Published online:
    08 December 2022
    Print publication:
    22 December 2022
  • 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.

Nanoscale Hydrodynamics of Simple Systems
  • Jesper Schmidt Hansen
  • Published online:
    22 September 2022
    Print publication:
    29 September 2022
  • Written for graduate students and researchers, Nanoscale Hydrodynamics of Simple Systems covers fundamental aspects of nanoscale hydrodynamics and extends this basis to examples. Covering classical, generalised and extended hydrodynamic theories, the title also discusses their limitations. It introduces the reader to nanoscale fluid phenomena and explores how fluid dynamics on this extreme length scale can be understood using hydrodynamic theory and detailed atomistic simulations. It also comes with additional resources including a series of explanatory videos on the installation of the code package, as well as discussion, analysis and visualisations of simulations. This title primarily focusses on training the reader to identify when classical theory breaks down, how to extend and generalise the theory, as well as assimilate how simulations and theory together can be used to gain fundamental knowledge about the fluid dynamics of small-scale systems.

Introductory Incompressible Fluid Mechanics
  • Frank H. Berkshire, Simon J. A. Malham, J. Trevor Stuart
  • Published online:
    05 January 2022
    Print publication:
    02 December 2021
  • This introduction to the mathematics of incompressible fluid mechanics and its applications keeps prerequisites to a minimum – only a background knowledge in multivariable calculus and differential equations is required. Part One covers inviscid fluid mechanics, guiding readers from the very basics of how to represent fluid flows through to the incompressible Euler equations and many real-world applications. Part Two covers viscous fluid mechanics, from the stress/rate of strain relation to deriving the incompressible Navier-Stokes equations, through to Beltrami flows, the Reynolds number, Stokes flows, lubrication theory and boundary layers. Also included is a self-contained guide on the global existence of solutions to the incompressible Navier-Stokes equations. Students can test their understanding on 100 progressively structured exercises and look beyond the scope of the text with carefully selected mini-projects. Based on the authors' extensive teaching experience, this is a valuable resource for undergraduate and graduate students across mathematics, science, and engineering.

Introduction to Turbulent Transport of Particles, Temperature and Magnetic Fields
  • Analytical Methods for Physicists and Engineers
  • Igor Rogachevskii
  • Published online:
    10 September 2021
    Print publication:
    05 August 2021
  • Turbulence and the associated turbulent transport of scalar and vector fields is a classical physics problem that has dazzled scientists for over a century, yet many fundamental questions remain. Igor Rogachevskii, in this concise book, systematically applies various analytical methods to the turbulent transfer of temperature, particles and magnetic field. Introducing key concepts in turbulent transport including essential physics principles and statistical tools, this interdisciplinary book is suitable for a range of readers such as theoretical physicists, astrophysicists, geophysicists, plasma physicists, and researchers in fluid mechanics and related topics in engineering. With an overview to various analytical methods such as mean-field approach, dimensional analysis, multi-scale approach, quasi-linear approach, spectral tau approach, path-integral approach and analysis based on budget equations, it is also an accessible reference tool for advanced graduates, PhD students and researchers.

Partial Differential Equations
  • Classical Theory with a Modern Touch
  • A. K. Nandakumaran, P. S. Datti
  • Published online:
    20 May 2020
    Print publication:
    29 October 2020
  • Suitable for both senior undergraduate and graduate students, this is a self-contained book dealing with the classical theory of the partial differential equations through a modern approach; requiring minimal previous knowledge. It represents the solutions to three important equations of mathematical physics – Laplace and Poisson equations, Heat or diffusion equation, and wave equations in one and more space dimensions. Keen readers will benefit from more advanced topics and many references cited at the end of each chapter. In addition, the book covers advanced topics such as Conservation Laws and Hamilton-Jacobi Equation. Numerous real-life applications are interspersed throughout the book to retain readers' interest.

Introduction to Experimental Nonlinear Dynamics
  • A Case Study in Mechanical Vibration
  • Lawrence N. Virgin
  • Published online:
    13 September 2019
    Print publication:
    28 March 2000
  • Nonlinear behavior can be found in such highly disparate areas as population biology and aircraft wing flutter. Largely because of this extensive reach, nonlinear dynamics and chaos have become very active fields of study and research. This book uses an extended case study - an experiment in mechanical vibration - to introduce and explore the subject of nonlinear behavior and chaos. Beginning with a review of basic principles, the text then describes a cart-on-a-track oscillator and shows what happens when it is gradually subjected to greater excitation, thereby encountering the full spectrum of nonlinear behavior, from simple free decay to chaos. Experimental mechanical vibration is the unifying theme as the narrative evolves from a local, linear, largely analytical foundation toward the rich and often unpredictable world of nonlinearity. Advanced undergraduate and graduate students, as well as practising engineers, will find this book a lively, accessible introduction to the complex world of nonlinear dynamics.

Numerical Bifurcation Analysis of Maps
  • From Theory to Software
  • Yuri A. Kuznetsov, Hil G. E. Meijer
  • Published online:
    15 March 2019
    Print publication:
    28 March 2019
  • This book combines a comprehensive state-of-the-art analysis of bifurcations of discrete-time dynamical systems with concrete instruction on implementations (and example applications) in the free MATLAB® software MatContM developed by the authors. While self-contained and suitable for independent study, the book is also written with users in mind and is an invaluable reference for practitioners. Part I focuses on theory, providing a systematic presentation of bifurcations of fixed points and cycles of finite-dimensional maps, up to and including cases with two control parameters. Several complementary methods, including Lyapunov exponents, invariant manifolds and homoclinic structures, and parts of chaos theory, are presented. Part II introduces MatContM through step-by-step tutorials on how to use the general numerical methods described in Part I for simple dynamical models defined by one- and two-dimensional maps. Further examples in Part III show how MatContM can be used to analyze more complicated models from modern engineering, ecology, and economics.

Chaotic Dynamics
  • Fractals, Tilings, and Substitutions
  • Geoffrey R. Goodson
  • Published online:
    30 January 2019
    Print publication:
    28 December 2016
  • This undergraduate textbook is a rigorous mathematical introduction to dynamical systems and an accessible guide for students transitioning from calculus to advanced mathematics. It has many student-friendly features, such as graded exercises that range from straightforward to more difficult with hints, and includes concrete applications of real analysis and metric space theory to dynamical problems. Proofs are complete and carefully explained, and there is opportunity to practice manipulating algebraic expressions in an applied context of dynamical problems. After presenting a foundation in one-dimensional dynamical systems, the text introduces students to advanced subjects in the latter chapters, such as topological and symbolic dynamics. It includes two-dimensional dynamics, Sharkovsky's theorem, and the theory of substitutions, and takes special care in covering Newton's method. Mathematica code is available online, so that students can see implementation of many of the dynamical aspects of the text.

Turbulence and Random Processes in Fluid Mechanics
  • 2nd edition
  • M. T. Landahl, E. Mollo-Christensen
  • Published online:
    12 October 2018
    Print publication:
    25 September 1992
  • Fluid flow turbulence is a phenomenon of great importance in many fields of engineering and science. Turbulence and related areas have continued to be subjects of intensive research over the last century. In this second edition of their successful textbook Professors Landahl and Mollo-Christensen have taken the opportunity to include recent developments in the field of chaos and its applications to turbulent flow. This timely update continues the original theme of the book: presenting the fundamental concepts and basic methods of fluid flow turbulence which enable the reader to follow the literature and understand current research. The emphasis upon the dynamic processes that create and maintain turbulent flows gives this book an original approach. This book should be useful to graduate students and researchers in fluid dynamics and, in particular, turbulence and related fields.

Fluid Mechanics
  • 2nd edition
  • Gregory Falkovich
  • Published online:
    04 August 2018
    Print publication:
    12 April 2018
  • The multidisciplinary field of fluid mechanics is one of the most actively developing fields of physics, mathematics and engineering. This textbook, fully revised and enlarged for the second edition, presents the minimum of what every physicist, engineer and mathematician needs to know about hydrodynamics. It includes new illustrations throughout, using examples from everyday life, from hydraulic jumps in a kitchen sink to Kelvin–Helmholtz instabilities in clouds, and geophysical and astrophysical phenomena, providing readers with a better understanding of the world around them. Aimed at undergraduate and graduate students as well as researchers, the book assumes no prior knowledge of the subject and only a basic understanding of vector calculus and analysis. It contains forty-one original problems with very detailed solutions, progressing from dimensional estimates and intuitive arguments to detailed computations to help readers understand fluid mechanics.

Turbulence
  • The Legacy of A. N. Kolmogorov
  • Uriel Frisch
  • Published online:
    28 May 2018
    Print publication:
    30 November 1995
  • This textbook presents a modern account of turbulence, one of the greatest challenges in physics. The state-of-the-art is put into historical perspective five centuries after the first studies of Leonardo and half a century after the first attempt by A. N. Kolmogorov to predict the properties of flow at very high Reynolds numbers. Such 'fully developed turbulence' is ubiquitous in both cosmical and natural environments, in engineering applications and in everyday life. The intended readership for the book ranges from first-year graduate students in mathematics, physics, astrophysics, geosciences and engineering, to professional scientists and engineers. Elementary presentations of dynamical systems ideas, of probabilistic methods (including the theory of large deviations) and of fractal geometry make this a self-contained textbook.

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