This book examines the origins and dynamical characteristics of atmospheric inertia-gravity waves in the Antarctic mesosphere. Gravity waves are relatively small-scale atmospheric waves with a restoring force of buoyancy that can transport momentum upward from the troposphere to the middle atmosphere. In previous studies, the dynamical characteristics of mesospheric gravity waves have not been fully examined using numerical simulations, since performing a numerical simulation with a high resolution and a high model-top requires considerable computational power. However, recent advances in computational capabilities have allowed us to perform numerical simulations using atmospheric general circulation models, which cover the troposphere to the mesosphere with a sufficiently fine horizontal resolution to resolve small-scale gravity waves. The book first describes the simulation of mesospheric gravity waves using a high-resolution non-hydrostatic atmospheric model with a high model top. The accuracy of the numerical results was confirmed by the first Mesosphere-Stratosphere-Troposphere/Incoherent Scattering (MST/IS) radar observation in the Antarctic. It also depicts the origins and propagation processes of mesospheric gravity waves on the basis of the results of the high-resolution numerical model. The behaviors of mesospheric gravity waves can be clearly explained using both fundamental and cutting-edge theories of fluid dynamics

Instabilities of fluid flows and the associated transitions between different possible flow states provide a fascinating set of problems that have attracted researchers for over a hundred years. This book addresses state-of-the-art developments in numerical techniques for computational modelling of fluid instabilities and related bifurcation structures, as well as providing comprehensive reviews of recently solved challenging problems in the field.

Free Surface Flow: Environmental Fluid Mechanics introduces a wide range of environmental fluid flows, such as water waves, land runoff, channel flow, and effluent discharge. The book provides systematic analysis tools and basic skills for study fluid mechanics in natural and constructed environmental flows. As the prediction of changes in free surfaces in rivers, lakes, estuaries and in the ocean directly affects the design of structures that control surface waters, and because planning for the allocation of fresh-water resources in a sustainable manner is an essential goal, this book provides the necessary background and research.

This book presents an introduction to viscoelasticity, in particular, to the theories of dilute polymer solutions and dilute suspensions of rigid particles in viscous and incompressible fluids. These theories are important, not just because they apply to practical problems of industrial interest, but because they form a solid theoretical base upon which mathematical techniques can be built, from which more complex theories can be constructed, to better mimic material behaviour. The emphasis of this book is not on the voluminous current topical research, but on the necessary tools to understand viscoelasticity. This is a compact book for a first year graduate course in viscoelasticity and modelling of viscoelastic multiphase fluids. The Dissipative Particle Dynamics (DPD) is introduced as a particle-based method, relevant in modelling of complex-structured fluids. All the basic ideas in DPD are reviewed. The third edition has been updated and expanded with new results in the meso-scale modelling, links between the fluid modelling to its physical parameters and new matlab programs illustrating the modelling. Particle-based modelling techniques for complex-structure fluids are added together with some sample programs. A solution manual to the problems is included.

Bose-Einstein condensation is a phase transition in which a fraction of particles of a boson gas condenses into the same quantum state known as the Bose-Einstein condensate (BEC). The aim of this book is to present a wide array of findings in the realm of BECs and on the nonlinear Schrodinger-type models that arise therein. The Defocusing Nonlinear Schrodinger Equation is a broad study of nonlinear excitations in self-defocusing nonlinear media. It summarizes state-of-the-art knowledge on the defocusing nonlinear Schrodinger-type models in a single volume and contains a wealth of resources, including over 800 references to relevant articles and monographs and a meticulous index for ease of navigation.

Theory and Modeling of Dispersed Multiphase Turbulent Reacting Flows gives a systematic account of the fundamentals of multiphase flows, turbulent flows and combustion theory. It presents the latest advances of models and theories in the field of dispersed multiphase turbulent reacting flow, covering basic equations of multiphase turbulent reacting flows, modeling of turbulent flows, modeling of multiphase turbulent flows, modeling of turbulent combusting flows, and numerical methods for simulation of multiphase turbulent reacting flows, etc. The book is ideal for graduated students, researchers and engineers in many disciplines in power and mechanical engineering.

This book reports on the EU-funded 7th Framework project, Go4Hybrid (Grey Area Mitigation for Hybrid RANS-LES Methods). It presents new findings concerning the accuracy and reliability of current hybrid RANS-LES methods. It describes improved formulations of both non-zonal and embedded hybrid strategies, together with their validation in a broad range of flow cases, and highlighting some key industrial applications. The book provides students, researchers and professionals in the field of applied computational fluid dynamics with a timely, practice-oriented reference guide.

Introduction to Fluid Mechanics, Second Edition, uses clear images and animations of flow patterns to help readers grasp the fundamental rules of fluid behavior. Everyday examples are provided for practical context, before tackling the more involved mathematic techniques that form the basis for computational fluid mechanics. This fully updated and expanded edition builds on the author's flair for flow visualization with new content. With basic introductions to all essential fluids theory, and exercises to test your progress, this is the ideal introduction to fluids for anyone involved in mechanical, civil, chemical, or biomedical engineering.

This first volume of the proceedings of the 8th conference on "Finite Volumes for Complex Applications" (Lille, June 2017) covers various topics including convergence and stability analysis, as well as investigations of these methods from the point of view of compatibility with physical principles. It collects together the focused invited papers comparing advanced numerical methods for Stokes and Navier-Stokes equations on a benchmark, as well as reviewed contributions from internationally leading researchers in the field of analysis of finite volume and related methods, offering a comprehensive overview of the state of the art in the field. The finite volume method in its various forms is a space discretization technique for partial differential equations based on the fundamental physical principle of conservation, and recent decades have brought significant advances in the theoretical understanding of the method. Many finite volume methods preserve further qualitative or asy mptotic properties, including maximum principles, dissipativity, monotone decay of free energy, and asymptotic stability. Due to these properties, finite volume methods belong to the wider class of compatible discretization methods, which preserve qualitative properties of continuous problems at the discrete level. This structural approach to the discretization of partial differential equations becomes particularly important for multiphysics and multiscale applications. The book is a valuable resource for researchers, PhD and master's level students in numerical analysis, scientific computing and related fields such as partial differential equations, as well as engineers working in numerical modeling and simulations.

This book explores the dynamics of planetary and stellar fluid layers, including atmospheres, oceans, iron cores, and convective and radiative zones in stars, describing the different theoretical, computational and experimental methods used to study these problems in fluid mechanics, including the advantages and limitations of each method for different problems. This scientific domain is by nature interdisciplinary and multi-method, but while much effort has been devoted to solving open questions within the various fields of mechanics, applied mathematics, physics, earth sciences and astrophysics, and while much progress has been made within each domain using theoretical, numerical and experimental approaches, cross-fertilizations have remained marginal. Going beyond the state of the art, the book provides readers with a global introduction and an up-to-date overview of relevant studies, fully addressing the wide range of disciplines and methods involved. The content builds on the CISM course "Fluid mechanics of planets and stars", held in April 2018, which was part of the research project FLUDYCO, supported by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program.

This book is an introduction to the mathematical analysis of p- and hp-finite elements applied to elliptic problems in solid and fluid mechanics, and is suitable for graduate students and researchers who have had some prior exposure to finite element methods (FEM). In the last decade the p-, hp-, and spectral element methods have emerged as efficient and robust approximation methods for several classes of problems in this area. The aim of this book is therefore to establish the exponential convergence of such methods for problems with the piecewise analytic solutions which typically arise in engineering. It looks at the variational formulation of boundary value problems with particular emphasis on the regularity of the solution. The books then studies the p- and hp- convergence of FEM in one and two dimensions, supplying complete proofs. Also covered are hp-FEM for saddle point problems and the techniques for establishing the discrete infsup condition. Finally, hp-FEM in solid mechanics and the issue of locking is addressed in the context of these methods.

This book presents numerical algorithms for solving incompressible fluids, elastic structures and fluid-structure interactions. It collects some of the fundamental finite element methods as well as new approaches. For Stokes and Navier-Stokes equations, the mixed finite element method is employed. An arbitrary Lagrangian Eulerian framework is used for fluids in a moving domain. Schemes for linear and St Venant-Kirchhoff non-linear dynamic elasticity are presented. For fluid-structure interaction, two schemes are analyzed: the first is fully implicit and the second is semi-implicit, where the fluid domain is computed explicitly and consequently the computational time is considerably reduced. The stability of the schemes is proven in this self-contained book. Every chapter is supplied with numerical tests for the reader. These are aimed at Masters students in Mathematics or Mechanical Engineering.

One of the few textbooks in the field, this volume deals with several aspects of the dynamics of colloids. A self-contained treatise, it fills the gap between research literature and existing books for graduate students and researchers. For readers with a background in chemistry, the first chapter contains a section on frequently used mathematical techniques, as well as statistical mechanics.

Some of the topics covered include:

- diffusion of free particles on the basis of the Langevin equation

-the separation of time, length and angular scales;

- the fundamental Fokker-Planck and Smoluchowski equations derived for interacting particles

- friction of spheres and rods, and hydrodynamic interaction of spheres (including three body interactions)

- diffusion, sedimentation, critical phenomena and phase separation kinetics

- experimental light scattering results.

For universities and research departments in industry this textbook makes vital reading.

The book presents a state-of-the-art overview of current developments in the field in a way accessible to attendees coming from a variety of fields. Relevant examples are turbulence research, (environmental) fluid mechanics, lake hydrodynamics and atmospheric physics. Topics discussed range from the fundamentals of rotating and stratified flows, mixing and transport in stratified or rotating turbulence, transport in the atmospheric boundary layer, the dynamics of gravity and turbidity currents eventually with effects of background rotation or stratification, mixing in (stratified) lakes, and the Lagrangian approach in the analysis of transport processes in geophysical and environmental flows. The topics are discussed from fundamental, experimental and numerical points of view. Some contributions cover fundamental aspects including a number of the basic dynamical properties of rotating and or stratified (turbulent) flows, the mathematical description of these flows, some applications in the natural environment, and the Lagrangian statistical analysis of turbulent transport processes and turbulent transport of material particles (including, for example, inertial and finite-size effects). Four papers are dedicated to specific topics such as transport in (stratified) lakes, transport and mixing in the atmospheric boundary layer, mixing in stratified fluids and dynamics of turbidity currents. The book is addressed to doctoral students and postdoctoral researchers, but also to academic and industrial researchers and practicing engineers, with a background in mechanical engineering, applied physics, civil engineering, applied mathematics, meteorology, physical oceanography or physical limnology.

Aeroacoustics of Low Mach Number Flows: Fundamentals, Analysis, and Measurement provides a comprehensive treatment of sound radiation from subsonic flow over moving surfaces, which is the most widespread cause of flow noise in engineering systems. This includes fan noise, rotor noise, wind turbine noise, boundary layer noise, and aircraft noise. Beginning with fluid dynamics, the fundamental equations of aeroacoustics are derived and the key methods of solution are explained, focusing both on the necessary mathematics and physics. Fundamentals of turbulence and turbulent flows, experimental methods and numerous applications are also covered. The book is an ideal source of information on aeroacoustics for researchers and graduate students in engineering, physics, or applied math, as well as for engineers working in this field. Supplementary material for this book is provided by the authors on the website www.aeroacoustics.net. The website provides educational content designed to help students and researchers in understanding some of the principles and applications of aeroacoustics, and includes example problems, data, sample codes, course plans and errata. The website is continuously being reviewed and added to.

This book provides a general introduction to the topic of turbulent flows. Apart from classical topics in turbulence, attention is also paid to modern topics. After studying this work, the reader will have the basic knowledge to follow current topics on turbulence in scientific literature. The theory is illustrated with a number of examples of applications, such as closure models, numerical simulations and turbulent diffusion, and experimental findings. The work also contains a number of illustrative exercises Review from the Textbook & Academic Authors Association that awarded the book with the 2017 Most Promising New Textbook Award: "Compared to other books in this subject, we find this one to be very up-to-date and effective at explaining this complicated subject. We certainly would highly recommend it as a text for students and practicing professionals who wish to expand their understanding of modern fluid mechanics."