What do combustion engines, fusion reactors, weather forecast, ocean ?ows, our sun, and stellar explosions in outer space have in common? Of course, the physics and the length and time scales are vastly di?erent in all cases, but it is alsowellknownthatinallofthem,onsomerelevantlengthscales,thematerial ?ows that govern the dynamical and/or secular evolution of the systems are chaotic and often unpredictable: they are said to be turbulent. In fact, the term "turbulence" is used for an enormous variety of p- nomena in very di?erent ?elds, including geophysics, astrophysics, and - gineering. Unfortunately, these communities do not talk to each other too often. Therefore, back in 2005, we organized a workshop on "Interdis- plinary Aspects of Turbulence" at the Ringberg Castle in the Bavarian Alps, to discuss topics such as the basic concepts of turbulence, the di?- ent approaches of modelling and simulations used in the various areas, and also possible tests. This workshop was a great success and the proceedings can be found on the Internet (www.mpa-garching.mpg.de/mpa/publications/ proceedings/proceedings-en.html) as well as pdf-?les of several of the talks presented (www.mpa-garching. mpg.de/hydro/Turbulence/).

This thesis represents the first systematic description of the two-phase flow problem. Two-phase flows of volatile fluids in confined geometries driven by an applied temperature gradient play an important role in a range of applications, including thermal management, such as heat pipes, thermosyphons, capillary pumped loops and other evaporative cooling devices. Previously, this problem has been addressed using a piecemeal approach that relied heavily on correlations and unproven assumptions, and the science and technology behind heat pipes have barely evolved in recent decades. The model introduced in this thesis, however, presents a comprehensive physically based description of both the liquid and the gas phase. The model has been implemented numerically and successfully validated against the available experimental data, and the numerical results are used to determine the key physical processes that control the heat and mass flow and describe the flow stability. One of the key contributions of this thesis work is the description of the role of noncondensables, such as air, on transport. In particular, it is shown that many of the assumptions used by current engineering models of evaporative cooling devices are based on experiments conducted at atmospheric pressures, and these assumptions break down partially or completely when most of the noncondensables are removed, requiring a new modeling approach presented in the thesis. Moreover, Numerical solutions are used to motivate and justify a simplified analytical description of transport in both the liquid and the gas layer, which can be used to describe flow stability and determine the critical Marangoni number and wavelength describing the onset of the convective pattern. As a result, the results presented in the thesis should be of interest both to engineers working in heat transfer and researchers interested in fluid dynamics and pattern formation.

As the first of its kind, this book provides a valuable introduction for scientists and engineers interested in liquid/fluid interfaces and disperse systems to the rapidly developing area of adsorption dynamics. It is the first extensive review available on the subject of dynamics of adsorption and gives a general summary of the current state of adsorption kinetics theory and experiments. Current progress in recently designed set-ups and improved and generalised known methods for studying interfacial relaxations is reviewed. In addition, the role of the electric charge of surfactants in the adsorption process is discussed in terms of a non-equilibrium distribution of adsorbing ions in the diffuse layer.

Present theories of the effect of dynamic adsorption layers on mobile surfaces, such as moving drops and bubbles, based on both diffusion and kinetic controlled adsorption models are described and efficient approximate analytical methods to solve the mathematical problem of coupling surfactant transport and hydrodynamics are introduced. The role of a dynamic adsorption layer in bubble rising, film drainage and film stabilisation and in complex processes such as flotation and microflotation is discussed.

Containing more than 1100 references, the book is essential reading for industrial scientists and graduate and post-graduate students in physical, surface and colloid chemistry, physico-chemical hydrodynamics, water purification and mineral processing.

This book gathers the proceedings of the Fifth Symposium on Hybrid RANS-LES Methods, which was held on March 19-21 in College Station, Texas, USA. 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, 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.

The book introduces readers to and summarizes the current ideas and theories about the basic mechanisms for transport in chaotic flows. Typically no single paradigmatic approach exists as this topic is relevant for fields as diverse as plasma physics, geophysical flows and various branches of engineering. Accordingly, the dispersion of matter in chaotic or turbulent flows is analyzed from different perspectives. Partly based on lecture courses given by the author, this book addresses both graduate students and researchers in search of a high-level but approachable and broad introduction to the topic.

This book presents recent progress in the application of RANS turbulence models based on the Reynolds stress transport equations. A variety of models has been implemented by different groups into different flow solvers and applied to external as well as to turbo machinery flows. Comparisons between the models allow an assessment of their performance in different flow conditions. The results demonstrate the general applicability of differential Reynolds stress models to separating flows in industrial aerodynamics.

This book presents new methods of numerical modelling of tube heat exchangers, which can be used to perform design and operation calculations of exchangers characterized by a complex flow system. It also proposes new heat transfer correlations for laminar, transition and turbulent flows. A large part of the book is devoted to experimental testing of heat exchangers, and methods for assessing the indirect measurement uncertainty are presented. Further, it describes a new method for parallel determination of the Nusselt number correlations on both sides of the tube walls based on the nonlinear least squares method and presents the application of computational fluid dynamic (CFD) modeling to determine the air-side Nusselt number correlations. Lastly, it develops a control system based on the mathematical model of the car radiator and compares this with the digital proportional-integral-derivative (PID) controller. The book is intended for students, academics and researchers, as well as for designers and manufacturers of heat exchangers.

This book is a collection of papers presented at a symposium held in honor of Sidney Leibovich. According all papers deal with mathematical or computational aspects of fluid dynamics applied mostly to atmospheric or oceanographic problems. All contributions are research papers having not only the specialist but also graduate students in mind.

Rationality - as opposed to 'ad-hoc' - and asymptotics - to emphasize the fact that perturbative methods are at the core of the theory - are the two main concepts associated with the Rational Asymptotic Modeling (RAM) approach in fluid dynamics when the goal is to specifically provide useful models accessible to numerical simulation via high-speed computing. This approach has contributed to a fresh understanding of Newtonian fluid flow problems and has opened up new avenues for tackling real fluid flow phenomena, which are known to lead to very difficult mathematical and numerical problems irrespective of turbulence. With the present scientific autobiography the author guides the reader through his somewhat non-traditional career; first discovering fluid mechanics, and then devoting more than fifty years to intense work in the field. Using both personal and general historical contexts, this account will be of benefit to anyone interested in the early and contemporary developments of an important branch of theoretical and computational fluid mechanics.

In this volume, the problems of pattern formation in physics, chemistry and other related fields in complex and nonlinear dissipative systems are studied. Main subjects discussed are formation mechanisms, properties, statistics, characterization and dynamics of periodic and nonperiodic patterns in the electrohydrodynamics in liquid crystals, Rayleigh-Benard convection, crystallization, viscous fingering and Belouzov-Zhabotinsky chemical reaction. Recent developments in topological and defect-mediated chaos, chaos in systems with large degrees of freedom and turbulence-turbulence transitions are also discussed.

This book presents fundamental concepts and seminal results to the study of vortex filaments in equilibrium. It also presents new discoveries in quasi-2D vortex structures with applications to geophysical fluid dynamics and magnetohydrodynamics in plasmas. It fills a gap in the vortex statistics literature by simplifying the mathematical introduction to this complex topic, covering numerical methods, and exploring a wide range of applications with numerous examples. The authors have produced an introduction that is clear and easy to read, leading the reader step-by-step into this topical area. Alongside the theoretical concepts and mathematical formulations, interesting applications are discussed. This combination makes the text useful for students and researchers in mathematics and physics.

This authored monograph provides a detailed discussion of the boundary layer flow due to a moving plate. The topical focus lies on the 2- and 3-dimensional case, considering axially symmetric and unsteady flows. The author derives a criterion for the self-similar and non-similar flow, and the turbulent flow due to a stretching or shrinking sheet is also discussed. The target audience primarily comprises research experts in the field of boundary layer flow, but the book will also be beneficial for graduate students.

The present Volume 4 of the successful monograh package Multiphase Flow Dynamics is devoted to selected Chapters of the multiphase fluid dynamics that are important for practical applications but did not find place in the previous volumes. The state of the art of the turbulence modeling in multiphase flows is presented. As introduction, some basics of the single phase boundary layer theory including some important scales and flow oscillation characteristics in pipes and rod bundles are presented. Then the scales characterizing the dispersed flow systems are presented. The description of the turbulence is provided at different level of complexity: simple algebraic models for eddy viscosity, simple algebraic models based on the Boussinesq hypothesis, modification of the boundary layer share due to modification of the bulk turbulence, modification of the boundary layer share due to nucleate boiling. The role of the following forces on the mathematical description of turbulent flows is discussed: the lift force, the lubrication force in the wall boundary layer, and the dispersion force. A pragmatic generalization of the k-eps models for continuous velocity field is proposed containing flows in large volumes and flows in porous structures. A Methods of how to derive source and sinks terms for multiphase k-eps models is presented. A set of 13 single- and two phase benchmarks for verification of k-eps models in system computer codes are provided and reproduced with the IVA computer code as an example of the application of the theory. This methodology is intended to help other engineers and scientists to introduce this technology step-by-step in their own engineering practice.

In many practical application gases are solved in liquids under given conditions, released under other conditions and therefore affecting technical processes for good of for bad. Useful information on the solubility of oxygen, nitrogen, hydrogen and carbon dioxide in water under large interval of pressures and temperatures is collected, and appropriate mathematical approximation functions are provided. In addition methods for the computation of the diffusion coefficients are described. With this information solution and dissolution dynamics in multiphase fluid flows can be analyzed. For this purpose the non-equilibrium absorption and release on bubble, droplet and film surfaces under different conditions is mathematically described.

A systematic set of internally consistent state equations for diesel fuel gas and liquid valid in broad range of changing pressure and temperature is provided.

This new second edition includes various updates, extensions, improvements and corrections.

In many practical application gases are solved in liquids under given conditions, released under other conditions and therefore affecting technical processes for good of for bad. Useful information on the solubility of oxygen, nitrogen, hydrogen and carbon dioxide in water under large interval of pressures and temperatures is collected, and appropriate mathematical approximation functions are provided. In addition methods for the computation of the diffusion coefficients are described. With this information solution and dissolution dynamics in multiphase fluid flows can be analyzed. For this purpose the non-equilibrium absorption and release on bubble, droplet and film surfaces under different conditions is mathematically described.

A systematic set of internally consistent state equations for diesel fuel gas and liquid valid in broad range of changing pressure and temperature is provided.

This new second edition includes various updates, extensions, improvements and corrections.

Computational Fluid Dynamics: An Introduction grew out of a von Karman Institute (VKI) Lecture Series by the same title ?rst presented in 1985 and repeated with modi?cations every year since that time. The objective, then and now, was to present the subject of computational ?uid dynamics (CFD) to an audience unfamiliar with all but the most basic numerical techniques and to do so in such a way that the practical application of CFD would become clear to everyone. A second edition appeared in 1995 with updates to all the chapters and when that printing came to an end, the publisher requested that the editor and authors consider the preparation of a third edition. Happily, the authors received the request with enthusiasm. The third edition has the goal of presenting additional updates and clari?cations while preserving the introductory nature of the material. The book is divided into three parts. John Anderson lays out the subject in Part I by ?rst describing the governing equations of ?uid dynamics, concentrating on their mathematical properties which contain the keys to the choice of the numerical approach. Methods of discretizing the equations are discussed and transformation techniques and grids are presented. Two examples of numerical methods close out this part of the book: source and vortex panel methods and the explicit method. Part II is devoted to four self-contained chapters on more advanced material. Roger Grundmann treats the boundary layer equations and methods of solution.

It is evident, that for a number of ecological and technical problems in rivers and lakes a better knowledge of sediment transport and sedimentation is needed together with the ability to predict and simulate sediment behaviour. On the other hand, a stagnation of research in these topics could be observed in the last decades. At the Symposium an attempt was made to present new results in mathematics and natural sciences relevant for the sediment problem. New strategies were discussed to tackle the complexity of the problem. Basic theoretical research and laboratory experiments alone are incomplete without a feedback from field observations and measurements. For that reason well-known researchers from both basic and engineering sciences were invited.
Turbulence, non-local phenomena, stability, interaction, feedback systems, self-organization, two-phase flow and chaotic processes, numerical simulations as well as measurement techniques and field results were the keywords of the Symposium. This proceedings are a good source for those interested in the state of the art.

This research monograph deals with a modeling theory of the system of Navier-Stokes-Fourier equations for a Newtonian fluid governing a compressible viscous and heat conducting flows. The main objective is threefold. First , to 'deconstruct' this Navier-Stokes-Fourier system in order to unify the puzzle of the various partial simplified approximate models used in Newtonian Classical Fluid Dynamics and this, first facet, have obviously a challenging approach and a very important pedagogic impact on the university education. The second facet of the main objective is to outline a rational consistent asymptotic/mathematical theory of the of fluid flows modeling on the basis of a typical Navier-Stokes-Fourier initial and boundary value problem. The third facet is devoted to an illustration of our rational asymptotic/mathematical modeling theory for various technological and geophysical stiff problems from: aerodynamics, thermal and thermocapillary convections and also meteofluid dynamics.

This book contains selected papers from the "Fourth International Conference on Computational Methods in Marine Engineering, " held at Instituto Superior Tecnico, Technical University of Lisbon, Portugal in September 2011.

Nowadays, computational methods are an essential tool of engineering, which includes a major field of interest in marine applications, such as the maritime and offshore industries and engineering challenges related to the marine environment and renewable energies. The 2011 Conference included 8 invited plenary lectures and 86 presentations distributed through 10 thematic sessions that covered many of the most relevant topics of marine engineering today. This book contains 16 selected papers from the Conference that cover CFD for Offshore Applications, Fluid-Structure Interaction, Isogeometric Methods for Marine Engineering, Marine/Offshore Renewable Energy, Maneuvering and Seakeeping, Propulsion and Cavitation and Ship Hydrodynamics . The papers were selected with the help of the recognized experts that collaborated in the organization of the thematic sessions of the Conference, which guarantees the high quality of the papers included in this book.

This book provides a practical guide to molecular dynamics and Monte Carlo simulation techniques used in the modelling of simple and complex liquids. Computer simulation is an essential tool in studying the chemistry and physics of condensed matter, complementing and reinforcing both experiment and theory. Simulations provide detailed information about structure and dynamics, essential to understand the many fluid systems that play a key role in our daily lives: polymers, gels, colloidal suspensions, liquid crystals, biological membranes, and glasses. The second edition of this pioneering book aims to explain how simulation programs work, how to use them, and how to interpret the results, with examples of the latest research in this rapidly evolving field. Accompanying programs in Fortran and Python provide practical, hands-on, illustrations of the ideas in the text.

Our new monograph has been inspired by the former one, Earthquake Source Asymmetry, Structural Media, and Rotation Effects (R. Teisseyre, M. Takeo, and E. Majewski, eds, Springer 2006). Some problems, c- cerned primarily but not exclusively with the basic theoretical nature, have appeared to us as worthy of further analysis. Thus, in the present mo- graph we intend to develop new theoretical approaches to the theory of continua that go far beyond the traditional seismological applications. We also try to present the links between the experimental data, the observed rotational seismic waves, and their theoretical evaluation and description. In addition, we consider the basic point motions and deformations, and we intend to find the invariant forms to describe such point motions. We believe that there must exist the basic equations for all point motions and deformations, and we derive such relations within a frame of a continuum theory. Thus, in the considered standard asymmetric theory, we include relations not only for the displacement velocities but also for a spin motion and basic point deformations as well. We include here the axial point - formation and twist point deformation represented by the string-string and string-membrane motions. A twist vector is defined here as a vector p- pendicular to the string-string plane and representing its magnitude. It - comes an important counterpart to spin and a key to the presented theory. We show in the forthcoming chapters that the twist motion describes the oscillations of shear axes.

Modeling of flow and transport in groundwater has become an important focus of scientific research in recent years. Most contributions to this subject deal with flow situations, where density and viscosity changes in the fluid are neglected. This restriction may not always be justified. The models presented in the book demonstrate immpressingly that the flow pattern may be completely different when density changes are taken into account. The main applications of the models are: thermal and saline convection, geothermal flow, saltwater intrusion, flow through salt formations etc. This book not only presents basic theory, but the reader can also test his knowledge by applying the included software and can set up own models.

Geomorphology deals with some of the most striking patterns of nature. From mountain ranges and mid-ocean ridges to river networks and sand dunes, there is a whole family of forms, structures, and shapes that demand rationalization as well as mathematical description. In the various chapters of this volume, many of these patterns are explored and discussed, and attempts are made to both unravel the reasons for their very existence and to describe their dynamics in quantitative terms. Particular focus is placed on lava and mud flows, ice and snow dynamics, river and coastal morphodynamics and landscape formation. Combining a pedagogical approach with up-to-date reviews of forefront research, this volume will serve both postgraduate students and lecturers in search of advanced textbook material, and experienced researchers wishing to get acquainted with the various physical and mathematical approaches in a range of closely related research fields.

Most fluid flows of practical importance are fully three-dimensional, so the non-linear instability properties of three-dimensional flows are of particular interest. In some cases the three-dimensionality may have been caused by a finite amplitude disturbance whilst, more usually, the unperturbed state is three-dimensional. Practical applications where transition is thought to be associated with non-linearity in a three- dimensional flow arise, for example, in aerodynamics (swept wings, engine nacelles, etc.), turbines and aortic blood flow. Here inviscid cross-flow' disturbances as well as Tollmien-Schlichting and GArtler vortices can all occur simultaneously and their mutual non-linear behaviour must be understood if transition is to be predicted. The non-linear interactions are so complex that usually fully numerical or combined asymptotic/numerical methods must be used. Moreover, in view of the complexity of the instability processes, there is also a growing need for detailed and accurate experimental information. Carefully conducted tests allow us to identify those elements of a particular problem which are dominant. This assists in both the formulation of a relevant theoretical problem and the subsequent physical validation of predictions. It should be noted that the demands made upon the skills of the experimentalist are high and that the tests can be extremely sophisticated - often making use of the latest developments in flow diagnostic techniques, automated high speed data gathering, data analysis, fast processing and presentation.