This contributed volume is based on talks given at the August 2016 summer school "Fluids Under Pressure," held in Prague as part of the "Prague-Sum" series. Written by experts in their respective fields, chapters explore the complex role that pressure plays in physics, mathematical modeling, and fluid flow analysis. Specific topics covered include: Oceanic and atmospheric dynamics Incompressible flows Viscous compressible flows Well-posedness of the Navier-Stokes equations Weak solutions to the Navier-Stokes equations Fluids Under Pressure will be a valuable resource for graduate students and researchers studying fluid flow dynamics.

Written by a group of international experts in their field, this book is a review of Lagrangian observation, analysis and assimilation methods in physical and biological oceanography. This multidisciplinary text presents new results on nonlinear analysis of Lagrangian dynamics, the prediction of particle trajectories, and Lagrangian stochastic models. It includes historical information, up-to-date developments, and speculation on future developments in Lagrangian-based observations, analysis, and modeling of physical and biological systems. Containing contributions from experimentalists, theoreticians, and modellers in the fields of physical oceanography, marine biology, mathematics, and meteorology, this book will be of great interest to researchers and graduate students looking for both practical applications and information on the theory of transport and dispersion in physical systems, biological modelling, and data assimilation.

This textbook provides an in-depth overview of the hydrodynamics of estuaries and semi-enclosed bodies of water. It begins by describing the typical classification of estuaries, followed by a presentation of the quantitative tools needed to study these basins: conservation of mass, salt, heat, momentum, and the thermodynamic equation of seawater. Further topics explore tides in homogeneous basins, including shallow water tides and tidal residual flows, wind-driven flows in homogeneous basins, density-driven flows, as well as interactions among tides, winds and density gradients. The book proposes a classification of semi-enclosed basins that is based on dominant dynamics, comparing forcing agents and restorative or balancing forces. Introduction to Estuarine Hydrodynamics provides an introduction for advanced students and researchers across a range of disciplines - Earth science, environmental science, biology, chemistry, geology, hydrology, physics - related to the study of estuarine systems.

Explore a thorough and up to date overview of the current knowledge, developments and outstanding challenges in turbulent combustion and application. The balance among various renewable and combustion technologies are surveyed, and numerical and experimental tools are discussed along with recent advances. Covers combustion of gaseous, liquid and solid fuels and subsonic and supersonic flows. This detailed insight into the turbulence-combustion coupling with turbulence and other physical aspects, shared by a number of the world leading experts in the field, makes this an excellent reference for graduate students, researchers and practitioners in the field.

Dynamics of Water Surface Flows and Waves provides theoretical descriptions of the whole life of water surface waves through their birth, propagation, evolution and finally breaking. While initial capillary waves are created via instability at air-water interfaces, potential wave theories adequately describe interactions of waves with current, bathymetry and structure. In the final breaking stage, potential fluid motions in the waves rapidly evolve into vortical turbulent flows that disturb the surfaces, resulting in entrainment of air-bubbles and ejection of sea spray in bursting bubbles floating on the surface. All theories and analytical methods required to understand the series of wave processes, over diverse areas of subjects, including turbulence, diffusion, vortex and capillary dynamics, shallow water approach, and stability analysis, as well as the conventional potential wave theory, are comprehensively covered in this book. All of the mathematical formulas are consistently developed from theorems and linked with physics, which provides theoretical understanding and further interest in wave dynamics. This is an ideal graduate-level textbook or reference for engineers and researchers in the fields of fluid and wave mechanics, coastal and ocean engineering.

Based on research into jets in supersonic crossflow carried out by the authors' team over the past 15 years, this book summarizes and presents many cutting-edge findings and analyses on this subject. It tackles the complicated mixing process of gas jets and atomization process of liquid jets in supersonic crossflow, and studies their physical mechanisms. Advanced experimental and numerical techniques are applied to further readers' understanding of atomization, mixing, and combustion of fuel jets in supersonic crossflow, which can promote superior fuel injection design in scramjet engines. The book offers a valuable reference guide for all researchers and engineers working on the design of scramjet engines, and will also benefit graduate students majoring in aeronautical and aerospace engineering.

The wave equation, a classical partial differential equation, has been studied and applied since the eighteenth century. Solving it in the presence of an obstacle, the scatterer, can be achieved using a variety of techniques and has a multitude of applications. This book explains clearly the fundamental ideas of time-domain scattering, including in-depth discussions of separation of variables and integral equations. The author covers both theoretical and computational aspects, and describes applications coming from acoustics (sound waves), elastodynamics (waves in solids), electromagnetics (Maxwell's equations) and hydrodynamics (water waves). The detailed bibliography of papers and books from the last 100 years cement the position of this work as an essential reference on the topic for applied mathematicians, physicists and engineers.

Understand multiphase flows using multidisciplinary knowledge in physical principles, modelling theories, and engineering practices. This essential text methodically introduces the important concepts, governing mechanisms, and state-of-the-art theories, using numerous real-world applications, examples, and problems. Covers all major types of multiphase flows, including gas-solid, gas-liquid (sprays or bubbling), liquid-solid, and gas-solid-liquid flows. Introduces the volume-time-averaged transport theorems and associated Lagrangian-trajectory modelling and Eulerian-Eulerian multi-fluid modelling. Explains typical computational techniques, measurement methods and four representative subjects of multiphase flow systems. Suitable as a reference for engineering students, researchers, and practitioners, this text explores and applies fundamental theories to the analysis of system performance using a case-based approach.

Geophysical fluid dynamics examines the dynamics of stratified and turbulent motion of fluids in the ocean and outer core, and of gases in the atmosphere. This book explains key notions and fundamental processes of the dynamics of large- and medium-scale atmospheric and oceanic motions from the unifying viewpoint of the rotating shallow water model. The model plays a distinguished role in geophysical fluid dynamics. It has been used for about a century for conceptual understanding of various phenomena, for elaboration of approaches and methods to be used later in more complete models, for development and testing of numerical codes, and for many other purposes. In spite of its simplicity, the model grasps essential features of the complete "primitive equations" models, being their vertically averaged version, and gives an intuitive representation and clear vision of principal dynamical processes. This book is a combination of a course on geophysical fluid dynamics (Part 1), with explanations and illustrations of fundamentals, and problems, as well as a more advanced treatise of a range of principal dynamical phenomena (Part 2), including recently arisen approaches and applications (Part 3). Mathematics and physics underlying dynamical phenomena are explained, with necessary demonstrations. Yet, an important goal of the book is to develop the reader's physical intuition and qualitative insights.

This Element presents a unified computational fluid dynamics framework from rarefied to continuum regimes. The framework is based on the direct modelling of flow physics in a discretized space. The mesh size and time step are used as modelling scales in the construction of discretized governing equations. With the variation-of-cell Knudsen number, continuous modelling equations in different regimes have been obtained, and the Boltzmann and Navier-Stokes equations become two limiting equations in the kinetic and hydrodynamic scales. The unified algorithms include the discrete velocity method (DVM)-based unified gas-kinetic scheme (UGKS), the particlebased unified gas-kinetic particle method (UGKP), and the wave and particle-based unified gas-kinetic wave-particle method (UGKWP). The UGKWP is a multi-scale method with the particle for non-equilibrium transport and wave for equilibrium evolution. The particle dynamics in the rarefied regime and the hydrodynamic flow solver in the continuum regime have been unified according to the cell's Knudsen number.

An introduction to the theory and engineering practice that underpins the component design and analysis of radial flow turbocompressors. Drawing upon an extensive theoretical background and years of practical experience, the authors provide descriptions of applications, concepts, component design, analysis tools, performance maps, flow stability, and structural integrity, with illustrative examples. Features wide coverage of all types of radial compressor over many applications unified by the consistent use of dimensional analysis. Discusses the methods needed to analyse the performance, flow, and mechanical integrity that underpin the design of efficient centrifugal compressors with good flow range and stability. Includes explanation of the design of all radial compressor components, including inlet guide vanes, impellers, diffusers, volutes, return channels, de-swirl vanes and side-streams. Suitable as a reference for advanced students of turbomachinery, and a perfect tool for practising mechanical and aerospace engineers already within the field and those just entering it.

This modern text presents aerodynamic design of aircraft with realistic applications, using CFD software and guidance on its use. Tutorials, exercises, and mini-projects provided involve design of real aircraft, ranging from straight to swept to slender wings, from low speed to supersonic. Supported by online resources and supplements, this toolkit covers topics such as shape optimization to minimize drag and collaborative designing. Prepares seniors and first-year graduate students for design and analysis tasks in aerospace companies. In addition, it is a valuable resource for practicing engineers, aircraft designers, and entrepreneurial consultants.

This book gives a self-contained and up-to-date account of mathematical results in the linear theory of water waves. The study of waves has many applications, including the prediction of behavior of floating bodies (ships, submarines, tension-leg platforms etc.), the calculation of wave-making resistance in naval architecture, and the description of wave patterns over bottom topography in geophysical hydrodynamics. The first section deals with time-harmonic waves. Three linear boundary value problems serve as the approximate mathematical models for these types of water waves. The next section uses a plethora of mathematical techniques in the investigation of these three problems. The techniques used in the book include integral equations based on Green's functions, various inequalities between the kinetic and potential energy and integral identities which are indispensable for proving the uniqueness theorems. The so-called inverse procedure is applied to constructing examples of non-uniqueness, usually referred to as 'trapped nodes.'

This graduate text is indispensable for those wanting to see and understand the mechanics of extreme dynamic events. It describes in detail the mechanics and material models used in understanding impact and penetration events. Covers continuum mechanics, the Hugoniot jump conditions, plasticity theory, damage and failure theory, shock and wave propagation in both Eulerian and Lagrangian frameworks, and the high pressure and high-rate response of materials. Nonlinearity in response of materials and systems is a common theme, showing itself in interesting and surprising ways. Materials are studied through damage to failure, since in armor and protection applications materials are utilized all the way through failure. Continuum and constitutive modelling topics required for modern large-scale numerical simulation techniques are clearly described. Extensive exercises ensure comprehension and explore new topics. This text is appropriate for a variety of graduate courses, including Continuum Mechanics, Advanced Solid Mechanics, and Plasticity and Inelasticity Theory.

Discover a straightforward and holistic look at energy conversion and conservation processes using the exergy concept with this thorough text. Explains the fundamental energy conversion processes in numerous diverse systems, ranging from jet engines and nuclear reactors to human bodies. Provides examples for applications to practical energy conversion processes and systems that use our naturally occurring energy resources, such as fossil fuels, solar energy, wind, geothermal, and nuclear fuels. With more than one-hundred diverse cases and solved examples, readers will be able to perform optimizations for a cleaner environment, a sustainable energy future, and affordable energy generation. An essential tool for practicing scientists and engineers who work or do research in the area of energy and exergy, as well as graduate students and faculty in chemical engineering, mechanical engineering and physics.

This book results from the authors work done on simulation based optimization problems at the Department of Mathematics, University of Trier, and reported in his postdoctoral thesis ("Habilitationsschrift") accepted by the Faculty-IV of this University in 2008. The focus of the work has been to develop mathematical methods and algorithms which lead to efficient and high performance computational techniques to solve such optimization problems in real-life applications. Systematic development of the methods and algorithms are presented here. Practical aspects of implementations are discussed at each level as the complexity of the problems increase, supporting with enough number of computational examples. It consists of two parts: first part deals with time dependent optimization problems with applications in environmental engineering and the second part deals with steady state optimization problems, in which the PDEs are solved using semi-iterative or pseudo-time-stepping techniques, with applications in aerodynamics.

This book will be useful for scientists and engineers who are looking for efficient numerical methods for PDE-constrained optimization problems. It will be helpful for graduate and Ph.D. students in applied mathematics, aerospace engineering, mechanical engineering, civil engineering and computational engineering during their training and research. This also will provide exciting research and development areas involving realistic applications.

Address vector and matrix methods necessary in numerical methods and optimization of linear systems in engineering with this unified text. Treats the mathematical models that describe and predict the evolution of our processes and systems, and the numerical methods required to obtain approximate solutions. Explores the dynamical systems theory used to describe and characterize system behaviour, alongside the techniques used to optimize their performance. Integrates and unifies matrix and eigenfunction methods with their applications in numerical and optimization methods. Consolidating, generalizing, and unifying these topics into a single coherent subject, this practical resource is suitable for advanced undergraduate students and graduate students in engineering, physical sciences, and applied mathematics.

The stratified ocean mixes episodically in small patches where energy is dissipated and density smoothed over scales of centimeters. The net effect of these countless events effects the shape of the ocean's thermocline, how heat is transported from the sea surface to the interior, and how dense bottom water is lifted into the global overturning circulation. This book explores the primary factors affecting mixing, beginning with the thermodynamics of seawater, how they vary in the ocean and how they depend on the physical properties of seawater. Turbulence and double diffusion are then discussed, which determines how mixing evolves and the different impacts it has on velocity, temperature, and salinity. It reviews insights from both laboratory studies and numerical modelling, emphasising the assumptions and limitations of these methods. This is an excellent reference for researchers and graduate students working to advance our understanding of mixing, including oceanographers, atmospheric scientists and limnologists.

Build the skills for determining appropriate error limits for quantities that matter with this essential toolkit. Understand how to handle a complete project and how uncertainty enters into various steps. Provides a systematic, worksheet-based process to determine error limits on measured quantities, and all likely sources of uncertainty are explored, measured or estimated. Features instructions on how to carry out error analysis using Excel and MATLAB (R), making previously tedious calculations easy. Whether you are new to the sciences or an experienced engineer, this useful resource provides a practical approach to performing error analysis. Suitable as a text for a junior or senior level laboratory course in aerospace, chemical and mechanical engineering, and for professionals.

Build the skills for determining appropriate error limits for quantities that matter with this essential toolkit. Understand how to handle a complete project and how uncertainty enters into various steps. Provides a systematic, worksheet-based process to determine error limits on measured quantities, and all likely sources of uncertainty are explored, measured or estimated. Features instructions on how to carry out error analysis using Excel and MATLAB (R), making previously tedious calculations easy. Whether you are new to the sciences or an experienced engineer, this useful resource provides a practical approach to performing error analysis. Suitable as a text for a junior or senior level laboratory course in aerospace, chemical and mechanical engineering, and for professionals.

Computational fluid dynamics (CFD), which involves using computers to simulate fluid flow, is emerging as a powerful approach for elucidating the palaeobiology of ancient organisms. Here, Imran A. Rahman describes its applications for studying fossil echinoderms. When properly configured, CFD simulations can be used to test functional hypotheses in extinct species, informing on aspects such as feeding and stability. They also show great promise for addressing ecological questions related to the interaction between organisms and their environment. CFD has the potential to become an important tool in echinoderm palaeobiology over the coming years.

This second edition extends the rigorous, self-contained exposition of the theory for viscoelastic wave propagation in layered media to include head waves and general ray theory. The theory, not published elsewhere, provides solutions for fundamental wave-propagation and ray-theory problems valid for any media with a linear response, elastic or anelastic. It explains measurable variations in wave speed, particle motion, and attenuation of body waves, surface waves, and head waves induced at anelastic material boundaries that do not occur for elastic waves. This book may be used as a textbook for advanced university courses and as a research reference in seismology, exploration geophysics, engineering, solid mechanics, and acoustics. It provides computation steps for ray-tracing computer algorithms to develop a variety of tomography inferred anelastic models, such as those for the Earth's deep interior and petroleum reserves. Numerical results and problem sets emphasize important aspects of the theory for each chapter.

This book is primarily intended to enable postgraduate research students to enhance their understanding and expertise in Fluid Mechanics and Magnetohydrodynamics (MHD), subjects no longer treated in isolation. The exercises throughout the book often serve to provide additional and quite significant knowledge or to develop selected mathematical skills, and may also fill in certain details or enhance readers' understanding of essential concepts. A previous background or some preliminary reading in either of the two core subjects would be advantageous, and prior knowledge of multivariate calculus and differential equations is expected.

This first volume of two aims to help prepare students of fluid mechanics for their examinations by presenting a clear explanation of theory and application in the form of solutions to typical examination and assignment type questions. Each chapter comprises start-of-chapter learning objectives, a summary of basic theory, end-of-chapter summaries, a range of worked examples, a selection of problems with answers, and assignments to encourage further practice and consolidate understanding.

This book provides a concise introduction to continuum mechanics, with a particular emphasis on fluid dynamics, suitable for upper undergraduate students in applied mathematics and related subjects. Starting with a preliminary chapter on tensors, the main topic of the book begins in earnest with the chapters on continuum kinematics and dynamics. Following chapters cover linear elasticity and both incompressible and compressible fluids. Special topics of note include nonlinear acoustics and the theory of motion of viscous thermal conducting compressible fluids. Based on an undergraduate course taught for over a decade, this textbook assumes only familiarity with multivariate calculus and linear algebra. It includes many exercises with solutions and can serve as textbook for lecture courses at the undergraduate and masters level.