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This volume, number 109 of the Les Houches Summer School series, presents the lectures held in August 2017 on the subject of turbulent flows in climate dynamics. Leading scientists in the fields of climate dynamics, atmosphere and ocean dynamics, geophysical fluid dynamics, physics and non-linear sciences present their views on this fast growing and interdisciplinary field of research, by venturing upon fundamental problems of atmospheric convection, clouds, large scale circulation, and predictability. Climate is controlled by turbulent flows. Turbulent motions are responsible for the bulk of the transport of energy, momentum, and water vapor in the atmosphere, which determine the distribution of temperature, winds, and precipitation on Earth. The aim of this book is to survey what is known about how turbulent flows control climate, what role they may play in climate change, and to outline where progress in this important area can be expected, given today's computational and observational capabilities. This book reviews the state-of-the-art developments in this field and provides an essential background to future studies. All chapters are written from a pedagogical perspective, making the book accessible to masters and PhD students and all researchers wishing to enter this field.

This book gathers contributions to the 21st biannual symposium of the German Aerospace Aerodynamics Association (STAB) and the German Society for Aeronautics and Astronautics (DGLR). The individual chapters reflect ongoing research conducted by the STAB members in the field of numerical and experimental fluid mechanics and aerodynamics, mainly for (but not limited to) aerospace applications, and cover both nationally and EC-funded projects. Special emphasis is given to collaborative research projects conducted by German scientists and engineers from universities, research-establishments and industries. By addressing a number of cutting-edge applications, together with the relevant physical and mathematics fundamentals, the book provides readers with a comprehensive overview of the current research work in the field. The book's primary emphasis is on aerodynamic research in aeronautics and astronautics, and in ground transportation and energy as well.

This book presents a snapshot of the state-of-art in the field of turbulence modeling, with an emphasis on numerical methods. Topics include direct numerical simulations, large eddy simulations, compressible turbulence, coherent structures, two-phase flow simulation and many more. It includes both theoretical contributions and experimental works, as well as chapters derived from keynote lectures, presented at the fourth Turbulence and Interactions Conference (TI 2015), which was held on June 11-14 in Cargèse, Corsica, France. This multifaceted collection, which reflects the conference´s emphasis on the interplay of theory, experiments and computing in the process of understanding and predicting the physics of complex flows and solving related engineering problems, offers a timely guide for students, researchers and professionals in the field of applied computational fluid dynamics, turbulence modeling and related areas.

This book gathers contributions to the 20th biannual symposium of the German Aerospace Aerodynamics Association (STAB) and the German Society for Aeronautics and Astronautics (DGLR). The individual chapters reflect ongoing research conducted by the STAB members in the field of numerical and experimental fluid mechanics and aerodynamics, mainly for (but not limited to) aerospace applications, and cover both nationally and EC-funded projects. Special emphasis is given to collaborative research projects conducted by German scientists and engineers from universities, research-establishments and industries. By addressing a number of cutting-edge applications, together with the relevant physical and mathematics fundamentals, the book provides readers with a comprehensive overview of the current research work in the field. Though the book's primary emphasis is on the aerospace context, it also addresses further important applications, e.g. in ground transportation and energy.

This volume collects the edited and reviewed contribution presented in the 7th iTi Conference in Bertinoro, covering fundamental and applied aspects in turbulence. In the spirit of the iTi conference, the volume is produced after the conference so that the authors had the opportunity to incorporate comments and discussions raised during the meeting. In the present book, the contributions have been structured according to the topics: I Theory II Wall bounded flows III Pipe flow IV Modelling V Experiments VII Miscellaneous topics

This volume collects the edited and reviewed contributions presented in the 6th iTi Conference in Bertinoro, covering fundamental and applied aspects in turbulence. In the spirit of the iTi conference, the volume has been produced after the conference so that the authors had the possibility to incorporate comments and discussions raised during the meeting. In the present book the contributions have been structured according to the topics : I Theory II Wall bounded flowsIII Particles in flows IV Free flows V Complex flows The volume is dedicated to the memory of Prof. Konrad Bajer who prematurely passed away in Warsaw on August 29, 2014.

This book presents contributions to the 19th biannual symposium of the German Aerospace Aerodynamics Association (STAB) and the German Society for Aeronautics and Astronautics (DGLR). The individual chapters reflect ongoing research conducted by the STAB members in the field of numerical and experimental fluid mechanics and aerodynamics, mainly for (but not limited to) aerospace applications, and cover both nationally and EC-funded projects. Special emphasis is given to collaborative research projects conducted by German scientists and engineers from universities, research-establishments and industries. By addressing a number of cutting-edge applications, together with the relevant physical and mathematics fundamentals, the book provides readers with a comprehensive overview of the current research work in the field. Though the book's primary emphasis is on the aerospace context, it also addresses further important applications, e.g. in ground transportation and energy.

The book presents a snapshot of the state-of-art in the field of turbulence modeling and covers the latest developments concerning direct numerical simulations, large eddy simulations, compressible turbulence, coherent structures, two-phase flow simulation and other related topics. It provides readers with a comprehensive review of both theory and applications, describing in detail the authors'own experimental results. The book is based on the proceedings of the third Turbulence and Interactions Conference (TI 2012), which was held on June 11-14 in La Saline-les-Bains, La Réunion, France and includes both keynote lectures and outstanding contributed papers presented at the conference. This multifaceted collection, which reflects the conference´s emphasis on the interplay of theory, experiments and computing in the process of understanding and predicting the physics of complex flows and solving related engineering problems, offers a practice-oriented guide for students, researchers and professionals in the field of computational fluid dynamics, turbulence modeling and related areas.

This book reflects the results of the 2nd and 3rd International Workshops on Turbulent Spray Combustion. The focus is on progress in experiments and numerical simulations for two-phase flows, with emphasis on spray combustion. Knowledge of the dominant phenomena and their interactions allows development of predictive models and their use in combustor and gas turbine design. Experts and young researchers present the state-of-the-art results, report on the latest developments and exchange ideas in the areas of experiments, modelling and simulation of reactive multiphase flows.The first chapter reflects on flame structure, auto-ignition and atomization with reference to well-characterized burners, to be implemented by modellers with relative ease. The second chapter presents an overview of first simulation results on target test cases, developed at the occasion of the 1st International Workshop on Turbulent Spray Combustion. In the third chapter, evaporation rate modelling aspects are covered, while the fourth chapter deals with evaporation effects in the context of flamelet models. In chapter five, LES simulation results are discussed for variable fuel and mass loading. The final chapter discusses PDF modelling of turbulent spray combustion.In short, the contributions in this book are highly valuable for the research community in this field, providing in-depth insight into some of the many aspects of dilute turbulent spray combustion.

This book presents contributions to the 18th biannual symposium of the German Aerospace Aerodynamics Association (STAB). The individual chapters reflect ongoing research conducted by the STAB members in the field of numerical and experimental fluid mechanics and aerodynamics, mainly for (but not limited to) aerospace applications, and cover both nationally and EC-funded projects. By addressing a number of essential research subjects, together with their related physical and mathematics fundamentals, the book provides readers with a comprehensive overview of the current research work in the field, as well as its main challenges and new directions. Current work on e.g. high aspect-ratio and low aspect-ratio wings, bluff bodies, laminar flow control and transition, active flow control, hypersonic flows, aeroelasticity, aeroacoustics and biofluid mechanics is exhaustively discussed here.

Turbulence, mixing and the mutual interaction of turbulence and chemistry continue to remain perplexing and impregnable in the fron­ tiers of fluid mechanics. The past ten years have brought enormous advances in computers and computational techniques on the one hand and in measurements and data processing on the other. The impact of such capabilities has led to a revolution both in the understanding of the structure of turbulence as well as in the predictive methods for application in technology. The early ideas on turbulence being an array of complicated phenomena and having some form of reasonably strong coherent struc­ ture have become well substantiated in recent experimental work. We are still at the very beginning of understanding all of the aspects of such coherence and of the possibilities of incorporating such structure into the analytical models for even those cases where the thin shear layer approximation may be valid. Nevertheless a distinguished body of'eddy chasers'has come into existence. The structure of mixing layers which has been studied for some years in terms of correlations and spectral analysis is also getting better understood. Both probability concepts such as intermittency and conditional sampling as well as the concept of large scale structure and the associated strain seem to indicate possibilities of distinguishing and synthesizing'engulfment'and molecular mixing.

The origins of turbulent flow and the transition from laminar to turbulent flow are among the most important unsolved problems of fluid mechanics and aerodynamics. Besides being a fundamental question of fluid mechanics, there are any number of applications for information regarding transition location and the details of the subsequent turbulent flow. The JUT AM Symposium on Laminar-Turbulent Transition, co-hosted by Arizona State University and the University of Arizona, was held in Sedona, Arizona. Although four previous JUT AM Symposia bear the same appellation (Stuttgart 1979, Novosibirsk 1984, Toulouse 1989, and Sendai 1994) the topics that were emphasized at each were different and reflect the evolving nature of our understanding of the transition process. The major contributions of Stuttgart 1979 centered on nonlinear behavior and later stages of transition in two-dimensional boundary layers. Stability of closed systems was also included with Taylor vortices in different geometries. The topics of Novosibirsk 1984 shifted to resonant wave interactions and secondary instabilities in boundary layers. Pipe- and channel-flow transition were discussed as model problems for the boundary layer. Investigations of free shear layers were presented and a heavy dose of supersonic papers appeared for the first time. The character of Toulouse 1989 was also different in that 3-D boundary layers, numerical simulations, streamwise vortices, and foundation papers on receptivity were presented. Sendai 1994 saw a number of papers on swept wings and 3-D boundary layers. Numerical simulations attacked a broader range of problems.

The IUTAM Symposium on Flow in Collapsible Tubes and Past Other Highly Compliant Boundaries was held on 26-30 March, 2001, at the University of Warwick. As this was the first scientific meeting of its kind we considered it important to mark the occasion by producing a book. Accordingly, at the end of the Symposium the Scientific Committee met to discuss the most appropriate format for the book. We wished to avoid the format of the conventional conference book consisting of a large number of short articles of varying quality. It was agreed that instead we should produce a limited number of rigorously refereed and edited articles by selected participants who would aim to sum up the state of the art in their particular research area. The outcome is the present book. Peter W. Ca rpenter, Warwick Timothy J. Pedley, Cambridge May, 2002. VB SCIENTIFIC COMMITTEE Co-Chair: P.W. Carpenter, Engineering, Warwiek, UK Co-Chair: TJ. Pedley, DAMTP, Cambridge, UK V.V. Babenko, Hydromechanics, Kiev, Ukraine R. Bannasch, Bionik & Evolutionstechnik, TU Berlin, Germany C.D. Bertram, Biomedical Engineering, New South Wales, Australia M. Gad-el-Hak, Aerospace & Mechanical Engineering, Notre Dame, USA J.B. Grotberg, Biomedical Engineering, Michigan, USA. R.D. Kamm, Mechanical Engineering, MIT, USA Y. Matsuzaki, Aerospace Engineering, N agoya, Japan P.K. Sen, Applied Mechanics, IIT Delhi, India L. van Wijngaarden, Twente, Netherlands K-S. Yeo, Mechanical Engineering, NU Singapore.

This volume contains the papers presented at the IUTAM Symposium on Geometry and Statistics of Turbulence, held in November 1999, at the Shonan International Village Center, Hayama (Kanagawa-ken), Japan. The Symposium was proposed in 1996, aiming at organizing concen­ trated discussions on current understanding of fluid turbulence with empha­ sis on the statistics and the underlying geometric structures. The decision of the General Assembly of International Union of Theoretical and Applied Mechanics (IUTAM) to accept the proposal was greeted with enthusiasm. Turbulence is often characterized as having the properties of mixing, inter­ mittency, non-Gaussian statistics, and so on. Interest is growing recently in how these properties are related to formation and evolution of struc­ tures. Note that the intermittency is meant for passive scalars as well as for turbulence velocity or rate of dissipation. There were eighty-eight participants in the Symposium. They came from thirteen countries, and fifty-seven papers were presented. The presenta­ tions comprised a wide variety of fundamental subjects of mathematics, statistical analyses, physical models as well as engineering applications. Among the subjects discussed are (a) Degree of self-similarity in cascade, (b) Fine-scale structures and degree of Markovian property in turbulence, (c) Dynamics of vorticity and rates of strain, (d) Statistics associated with vortex structures, (e) Topology, structures and statistics of passive scalar advection, (f) Partial differential equations governing PDFs of velocity in­ crements, (g) Thermal turbulences, (h) Channel and pipe flow turbulences, and others.

The International Union of Theoretical and Applied Mechanics (IUTAM) decided in 1992 to sponsor the fourth Symposium on Laminar-Turbulent Transition, Sendai/Japan, 1994. The objectives of the present Symposium were to deepen the fundamental knowledge of stability and laminar­ turbulent transition in three-dimensional and compressible flows and to contribute to recent developing technologies in the field. This Symposium followed the three previous IUTAM-Symposia (Stuttgart 1979, Novosibirsk 1984 and Toulouse 1989). The Scientific Committee selected two keynote lectures and 62 technical papers. The Symposium was held on the 5th to 9th of September, 1994, at the Sendai International Center in Sendai. The participants were 82 scientists from 10 countries. The keynote lectures have critically reviewed recent development of researches concerning the laminar-to-turbulent transition phenomena from the fundamental and the application aspects. Many papers presented were concerned about the detailed mechanism of the boundary layer transition (receptivity, secondary instability, turbulent spot and bypass transition). Particular emphasis was further placed on the transition of three-dimensional boundary layers on rotation systems and on swept wings. Attention was also given to compressible hypersonic flows.

This volume collects the edited and reviewed contributions presented in the 5th iTi Conference in Bertinoro covering fundamental aspects in turbulent flows. In the spirit of the iTi initiative, the volume is produced after the conference so that the authors had the possibility to incorporate comments and discussions raised during the meeting.Turbulence presents a large number of aspects and problems, which are still unsolved and which challenge research communities in engineering and physical sciences both in basic and applied research. The book presents recent advances in theory related to new statistical approaches, effect of non-linearities and presence of symmetries. This edition presents new contributions related to the physics and control of laminar-turbulent transition in wall-bounded flows, which may have a significant impact on drag reduction applications. Turbulent boundary layers, at increasing Reynolds number, are the main subject of both computational and experimental long research programs aimed at improving our knowledge on scaling, energy distribution at different scales, structure eduction, roughness effects to name only a few. Like previous editions several numerical and experimental analysis of complex flows, mostly related to applications, are presented.The structure of the present book is as such that contributions have been bundled according to covering topics i.e. I Theory, II Stability, III Wall bounded flows, IV, Complex flows, V Acoustic, VI Numerical methods.The volume is dedicated to the memory of Prof. Rudolf Friedrich who prematurely died in Münster/Germany on the 16th of August 2012. In his honor the conference has started with a special session dedicated to his work.

The subject of laminar-turbulent transition is of considerable practical importance and has a wide range of engineering applications. For this reason, the International Union of Applied Mechanics decided to sponsor a third Symposium on'Laminar-Turbulent Transition', which would be organised by the ONERA Toulouse Research Center and held at'Ecole Nationale Superieure de l'Aeronautique et de l'Espace'in 1989. It was supposed that like the two previous IUTAM Symposia (Stuttgart 1979 and Novosibirsk 1984) the symposium would be devoted to experimental of laminar-turbulent transition In fluids, i.e. the and theoretical studies physical problem of transition and mathematical modelling in shear flows. The contributed papers were selected by the Scientific Committee from extended abstracts. The larger number of highly qualified papers submitted for presentation led us to include in the program poster sessions, which could be held during morning, lunch and afternoon breaks, and to take the decision that the symposium should last five days (from Monday 11 to Friday 15 September). An excursion on Wednesday offering a well deserved rest and the occasion of new personal exchanges between the participants seems to have been appreciated by all. The symposium consisted of 8 invited lectures and 62 contributed pa­ pers presented either on oral or poster sessions.

The last two decades have witnessed an intensifying effort in learning how to manage flow turbulence: it has in fact now become one of the most challenging and prized techno­ logical goals in fluid dynamics. The goal itself is of course not new. More than a hundred years ago, Reynolds already listed factors conducive to laminar and to turbulent flow (including among them curvature and acceleration). Further­ more, it is in retrospect clear that there were several early instances ot successful turbulence management. Examples are the reduction in drag achieved with a ring-trip placed on the front of a sphere or the insertion of a splitter-plate behind a circular cylinder; by the early 1950s there were numerous exercises at boundary layer control. Although many of these studies were interesting and suggestive, they led. to no spectacularly successful practical application, and the effort petered out in the late 1950s. The revival of interest in these problems in recent years can be attributed to the emergence of several new factors. First of all, fresh scientific insight into the structure of turbulence, in particular the accumulated evidence for the presence of significant order in turbulent flow, has been seen to point to new methods of managing turbulence. A second major reason has been the growing realisation that the rate at which the world is consuming its reserves of fossil fuels is no longer negligible; the economic value of greater energy effi­ ciency and lower drag has gone up significantly.

In 1976 a similar titled IUTAM Symposium (Structure of Turbulence and Drag Reduction) was held in Washington. However, the progress made during the last thirteen years as weil as the much promising current research desired a second one this year. In Washington drag reduction by additives and by direct manipulation of the walls (compliant walls and heated surfaces) were discussed. In the meantime it became evident that drag reduction also occurs when turbulence is influenced by geometrical means, e.g. by influencing the pressure distribution by the shape of the body (airfoils) or by the introduction of streamwise perturbances on a body (riblets). In the recent years turbulence research has seen increasing attention being focused on the investigation of coherent structures, mainly in Newtonian fluids. We all know that these structures are a significant feature of turbulent flows, playing an important role in the energy balance in such flows. However their place in turbulence theories as weil as the factors influencing their development are still poorly understood. Consequently, the investigation of phenomena in which the properties of coherent structures are alte red provides a promising means of improving our understanding of turbulent flows in general.

The IUTAM Symposium on Nonlinear Instability of Nonparallel Flows was held at Clarkson University, Potsdam, NY 13699-5725, USA from 26 to 31 July 1993. It consisted of 9 general speeches, 35 lectures and 15 poster-seminar presentations. The papers were grouped in fairly focused sessions on boundary layers, shear flows, vortices, wakes, nonlinear waves and jets. The symposium was fol­ lowed by a workshop in which the subject matter discussed was sum­ marized and some further work for future investigation was recom­ mended. The highlights of the workshop will be reported elsewhere. In this book many of the papers that describe the ideas presented at the symposium are collected to provide a reference for researchers in charting the future course of their studies in the area of nonlinear instability of nonparallel flows. The papers in this book are grouped under the following headings: • Boundary layers and shear flows • Compressibility and thermal effects • Vortices and wakes • Nonlinear waves and jets In the lead paper ofthis book M. E. Goldstein describes an asymp­ totic theory of nonlinear interaction between two spatially growing oblique waves on nonparallel boundary and free-shear layers. The wave interaction originates from the nonlinear critical layer and is responsive to weakly nonparallel effects. The theory results in a sys­ tem of integral differential equations which appear to be relevant near the upper branch of the neutral curve.

Separated flows and jets are closely linked in a variety of applications. They are of great importance in various fields of fluid mechanics including vehicle efficiency, technical branches concerned with gas/liquid flows, atmospheric effects on various constructions, etc. Knowledge of the physics of separated flows and jets and the development of reliable control techniques are prerequisite for future progress in the field. These aspects were in focus during the IUTAM-Symposium which was held in Novosibirsk, 9-13 July, 1990. This volume contains a selection of papers presenting recent results of theoretical and numerical studies as well as experimental work on separated flows and jets. The topics include sub- and supersonic, laminar and turbulent separation as well as organized structures in separated flows and jets. The reader will find here the state of the art and major trends for research in this field of aero-hydrodynamics.

This book is an outgrowth of the NSF-CBMS conference Nonlinear Waves £3 Weak Turbulence held at Case Western Reserve University in May 1992. The principal speaker at the conference was Professor V. E. Zakharov who delivered a series of ten lectures outlining the historical and ongoing developments in the field. Some twenty other researchers also made presentations and it is their work which makes up the bulk of this text. Professor Zakharov's opening chapter serves as a general introduction to the other papers, which for the most part are concerned with the application of the theory in various fields. While the word'turbulence'is most often associated with f:l. uid dynamics it is in fact a dominant feature of most systems having a large or infinite number of degrees of freedom. For our purposes we might define turbulence as the chaotic behavior of systems having a large number of degrees of freedom and which are far from thermodynamic equilibrium. Work in field can be broadly divided into two areas: • The theory of the transition from smooth laminar motions to the disordered motions characteristic of turbulence. • Statistical studies of fully developed turbulent systems. In hydrodynamics, work on the transition question dates back to the end of the last century with pioneering contributions by Osborne Reynolds and Lord Rayleigh.

The existence and crucial role played by large-scale, organized motions in turbulent flows are now recognized by industrial, applied and fundamental researchers alike. It has become increasingly evident that coherent structures influence mixing, noise, vibration, heat transfer, drag, etc... The accelera­ tion of the development of both experimental and computational programs devoted to this topic has been evident at several recent international meet­ ings. One of the first questions which experimentalists or numerical analysts are faced with is: how can these structures be separated from the background turbulence? This is a nontrivial task because the coherent structures are gen­ erally embedded in a random field and the technique used to determine when and where certain structures are passing, or their averaged characteristics (in the more probable or dominant role sense) is directly related to the definition of the coherent structure. Several methods or approaches are available and the choice of a particular one is generally dependent on the desired informa­ tion. This choice depends not only on the definition of the structure, but also on the experimental and numerical capabilities available to the researcher.

The European Drag Reduction Meeting has been held on 15th and 16th November 1990 in London. This was the fifth of the annual European meetings on drag reduction in engineering flows. The main objective of this meeting was to discuss up-to-date results of drag reduction research carried out in Europe. The organiser has adopted the philosophy of discussing the yesterday's results rather than the last year's results. No written material has therefore been requested for the meeting. It was only after the meeting the submission of papers was requested to the participants, from which 16 papers were selected for this proceedings volume. The meeting has attracted a record number of participants with a total of 52 researchers from seven European countries, U. K., France, Germany, the Netherlands, Italy, Switzerland and U. S. S. R. as well as from Japan, Canada and Australia. The subjects covered in this proceedings volume include riblets, LEBUs (Large Eddy Break-Up device), surface roughness, compliant surfaces and polymer additives. Riblets seem to be one of the most extensively studied devices in the past years. Reflecting this situation in the European community, there are six papers on riblets covering their practical applications to aircraft and to a model ship, near-wall coherent structure of the boundary layer and effects of flow three-dimensionality. Possibility of heat-transfer enhancement with riblets and potential use in the laminar flow are also investigated. An analytical model is developed for the boundary-layer with a LEBU device.

This fourth issue on'progress in turbulence'is based on the fourth ITI conference (ITI interdisciplinary turbulence initiative), which took place in Bertinoro, North Italy. Leading researchers from the engineering and physical sciences presented latest results in turbulence research. Basic as well as applied research is driven by the rather notorious difficult and essentially unsolved problem of turbulence. In this collection of contributions clear progress can be seen in different aspects, ranging from new quality of numerical simulations to new concepts of experimental investigations and new theoretical developments. The importance of turbulence is shown for a wide range of applications including: combustion, energy, flow control, urban flows, are few examples found in this volume. A motivation was to bring fundamentals of turbulence in connection with renewable energy. This lead us to add a special topic relevant to the impact of turbulence on the wind energy conversion. The structure of the present book is as such that contributions have been bundled according to covering topics i.e. I Basic Turbulence Aspects, II Particle Laden Flows, III Modeling and Simulations, IV, Experimental Methods, V Special Flows, VI Atmospheric Boundary Layer, VII Boundary Layer, VIII Wind Energy and IX Convection. This book is dedicated to the memory of Prof. Tim Nickels. Shortly after giving an invited lecture at the 4th ITI conference, the turbulence community lost a world-class scientist, a friend and devoted family man.

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 Görtler 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.

The articles in this volume are based on recent research on the phenomenon of turbulence in fluid flows collected by the Institute for Mathematics and its Applications. This volume looks into the dynamical properties of the solutions of the Navier-Stokes equations, the equations of motion of incompressible, viscous fluid flows, in order to better understand this phenomenon. Although it is a basic issue of science, it has implications over a wide spectrum of modern technological applications. The articles offer a variety of approaches to the Navier-Stokes problems and related issues. This book should be of interest to both applied mathematicians and engineers.

This collection of articles has its origin in a meeting which took place June 12-15, 1989, on the grounds of Salve Regina College in Newport, Rhode Island. The meeting was blessed by beautiful, balmy weather and an idyllic setting. The sessions themselves took place in Ochre Court, one of the elegant and stately old summer cottages for which Newport is acclaimed. Lectures were presented in the grand ballroom overlooking the famous Cliff Walk and Block Island Sound. Counter to general belief, the pleasant surroundings did not appear to encourage truancy or in any other way diminish the quality of the meeting. On the contrary, for the four days of the meeting there was a high level of excitement and optimism about the new perspectives in turbulence, a tone that carried over to lively dinner and evening discussions. The participants represented a broad range of backgrounds, extending from pure mathemat­ ics to experimental engineering. A dialogue began with the first speakers which cut across the boundaries and gave to the meeting a mood of unity which persisted.

The combination of increasing airport congestion and the ad­ vent of large transports has caused increased interest in aircraft wake turbulence. A quantitative understanding of the interaction between an aircraft and the vortex wake of a preceding aircraft is necessary for planning future high density air traffic patterns and control systems. The nature of the interaction depends on both the characteristics of the following aircraft and the characteristics of the wake. Some of the questions to be answered are: What deter­ mines the full characteristics of the vortex wake? What properties of the following aircraft are important? What is the role of pilot response? How are the wake characteristics related to the genera­ ting aircraft parameters? How does the wake disintegrate and where? Many of these questions were addressed at this first Aircraft Wake Turbulence Symposium sponsored by the Air Force Office of Sci­ entific Research and The Boeing Company. Workers engaged in aero­ dynamic research, airport operations, and instrument development came from several count ries to present their results and exchange information. The new results from the meeting provide a current picture of the state of the knowledge on vortex wakes and their interactions with other aircraft. Phenomena previously regarded as mere curiosities have emerged as important tools for understanding or controlling vortex wakes. The new types of instability occurring within the wake may one day be used for promoting early dis integration of the hazardous twin vortex structure.

The thrust of modern research on turbulence in fluids is concerned with coherent structures and modelling. Riblets have been shown to reduce drag, and the papers presented in this volume tackle the main question of the mechanism responsible for this behaviour in turbulent flow. The contributions in this volume were presented at the Sixth Drag Reduction Meeting held at Eindhoven during November 1991. This volume will be a useful reference work for engineers, physicists and applied mathematicians interested in the topic of fluid turbulence.

Challenging problems involvrllg jet and plume phenomena are common to many areas of fundamental and applied scientific research, and an understanding of plume and jet behaviour is essential in many geophysical and industrial contexts. For example, in the field of meteorology, where pollutant dispersal takes place by means of atmospheric jets and plumes formed either naturally under conditions of convectively-driven flow in the atmospheric boundary layer, or anthropogenically by the release of pollutants from tall chimneys. In other fields of geophysics, buoyant plumes and jets are known to play important roles in oceanic mixing processes, both at the relatively large scale (as in deep water formation by convective sinking) and at the relatively small scale (as with plume formation beneath ice leads, for example). In the industrial context, the performances of many engineering systems are determined primarily by the behaviour of buoyant plumes and jets. For example, (i) in sea outfalls, where either sewage or thermal effluents are discharged into marine and/or freshwater environments, (ii) in solar ponds, where buoyant jets are released under density interfaces, (iii) in buildings, where thermally-generated plumes affect the air quality and ventilation properties of architectural environments, (iv) in rotating machinery where fluid jet~ are used for cooling purposes, and (v) in long road and rail tunnels, where safety and ventilation prcedures rely upon an understanding of the behaviour of buoyant jets. In many other engineering and oceanographic contexts, the properties of jets and plumes are of great importance.

The aim of this Advanced Research Workshop was to bring together Physicists, Applied Mathematicians and Fluid Dynamicists, including very specially experimentalists, to review the available knowledge on the global structural aspects of turbulent flows, with an especial emphasis on open systems, and to try to reach a consensus on their possible relationship to recent advances in the understanding of the behaviour of low dimensional dynamical systems and amplitude equations. A lot has been learned during recent years on the non-equilibrium behaviour of low dimen­ sional dynamical systems, including some fluid flows (Rayleigh-Benard, Taylor-Couette, etc.). These are mostly closed flows and many of the global structural features of the low dimensional systems have been observed in them, including chaotic behaviour, period doubling, intermit­ tency, etc.. It has also been shown that some of these flows are intrinsically low dimensional, which accounts for much of the observed similarities. Open flows seem to be different, and experimental observations point to an intrinsic high dimensionality. However, some of the tran­ sitional features of the low dimensional systems have been observed in them, specially in the intermittent behaviour of subcritical flows (pipes, channels, boundary layers with suction, etc.), and in the large scale geometry of coherent structures of free shear flows (mixing layers, jets and wakes).

The study of wall-bounded turbulent ows is of considerable interest from both scienti c and practical view points. As such it has attracted a great deal of research over the last 100 years. Much research has concentratedon ows over smooth walls since these are simpler from experimental, numerical and theoretical standpoints. The ow over rough walls has still received considerable attention but progress has necessarilybeenslower.Perhapsthemostessentialproblem(certainlyfromaprac- cal point of view) is to be able to predict the skin-frictiondrag acting on a plate (or a body) given a certain known roughness characteristic of the surface. Unfortunately this has proved to be very dif cult since even the simplest rough surfaces can be characterised by a number of different parameters and we still cannot directly c- nectthese tothe uiddynamicdragin a givensituation.Varioustheoriesandmodels have been proposed in order to make progress but there is still some disagreement in the community as to the correct understanding of these important ows.

This third issue on “progress in turbulence” is based on the third ITI conference (ITI interdisciplinary turbulence initiative), which took place in Bertinoro, North Italy. Researchers from the engineering and physical sciences gathered to present latest results on the rather notorious difficult and essentially unsolved problem of turbulence. This challenge is driving us in doing basic as well as applied research. Clear progress can be seen from these contributions in different aspects. New - phisticated methods achieve more and more insights into the underlying compl- ity of turbulence. The increasing power of computational methods allows studying flows in more details. Increasing demands of high precision large turbulence - periments become aware. In further applications turbulence seem to play a central issue. As such a new field this time the impact of turbulence on the wind energy conversion process has been chosen. Beside all progress our ability to numerically calculate high Reynolds number turbulent flows from Navier-Stokes equations at high precision, say the drag co- ficient of an airfoil below one percent, is rather limited, not to speak of our lack of knowledge to compute this analytically from first principles. This is rather - markable since the fundamental equations of fluid flow, the Navier-Stokes eq- tions, have been known for more than 150 years.

th This volume contains the papers presented at the 16 DGLR/STAB-Symposium held at the Eurogress Aachen and organized by RWTH Aachen University, Germany, November, 3 - 4, 2008. STAB is the German Aerospace Aerodynamics Association, founded towards the end of the 1970's, whereas DGLR is the German Society for Aeronautics and Astronautics (Deutsche Gesellschaft für Luft- und Raumfahrt - Lilienthal Oberth e.V.). The mission of STAB is to foster development and acceptance of the discipline “Aerodynamics” in Germany. One of its general guidelines is to concentrate resources and know-how in the involved institutions and to avoid duplication in research work as much as possible. Nowadays, this is more necessary than ever. The experience made in the past makes it easier now, to obtain new knowledge for solving today's and tomorrow's problems. STAB unites German scientists and engineers from universities, research-establishments and industry doing research and project work in numerical and experimental fluid mechanics and aerodynamics for aerospace and other applications. This has always been the basis of numerous common research activities sponsored by different funding agencies. Since 1986 the symposium has taken place at different locations in Germany every two years. In between STAB workshops regularly take place at the DLR in Göttingen.

This volume contains seven keynote lectures of the TI 2006 conference that was held in Porquerolles, May 29-June 2, 2006. These lectures address the latest developments in direct numerical simulations, large eddy simulations, compressible turbulence, coherent structures, bubbly channel flows, combustion. The keynote lectures are extended manuscripts that were not published in the special issues of the journals'Computers and Fluids'and'Flow, Turbulence and Combustion'. The present monograph is a snapshot of the state-of-the-art in the field of turbulence with a view on theory, experiments and numerical simulations.

This book is based on the proceedings of the COSNet/CSIRO Workshop on Turbulence and Coherent Structures held at the Australian National University in Canberra in January 2006.It codifies recent developments in our understanding of the dynamics and statistical dynamics of turbulence and coherent structures in fluid mechanics, atmospheric and oceanic dynamics, plasma physics, and dynamical systems theory. It brings together articles by internationally acclaimed researchers from around the world including Dijkstra (Utrecht), Holmes (Princeton), Jimenez (UPM and Stanford), Krommes (Princeton), McComb (Edinburgh), Chong (Melbourne), Dewar (ANU), Watmuff (RMIT) and Frederiksen (CSIRO).The book will prove a useful resource for researchers as well as providing an excellent reference for graduate students working in this frontier area.

This volume contains the contributions to the 15. Symposium of the STAB (German Aero-space Aerodynamics Association). In this association all those German scientists and engineers from universities, research establishments and industry are involved, who are doing research and project work in numerical and experimental fluid mechanics and aerodynamics, mainly for aerospace but for other applications, too. Many of the contributions are presenting results from national and European Community sponsored projects. The volume gives a broad overview over the ongoing work in this field in Germany, with the topics being high-aspect ratio wings, low aspect-ratio wings, bluff bodies, laminar flow control and transition, active flow control, hypersonic flows, aeroelasticity, aeroacoustics, mathematical fundamentals/ numerical simulation, physical fundamentals, and facilities.

Besides turbulence there is hardly any other scientific topic which has been considered as a prominent scientific challenge for such a long time. The special interest in turbulence is not only based on it being a difficult scientific problem but also on its meaning in the technical world and our daily life. This carefully edited book comprises recent basic research as well as research related to the applications of turbulence. Therefore, both leading engineers and physicists working in the field of turbulence were invited to the iTi Conference on Turbulence held in Bad Zwischenahn, Gemany 25th - 28th of September 2005. Discussed topics include, for example, scaling laws and intermittency, thermal convection, boundary layers at large Reynolds numbers, isotropic turbulence, stochastic processes, passive and active scalars, coherent structures, numerical simulations, and related subjects.

This volume contains the contributions to the 14. Symposium of the STAB (German Aerospace Aerodynamics Association). In this association all those German scientists and engineers from universities, research establishments and industry are involved, who are doing research and project work in numerical and experimental fluid mechanics and aerodynamics, mainly for aerospace but for other applications, too. Many of the contributions are presenting results from national and European Community sponsored projects. The volume gives a broad overview over the ongoing work in this field in Germany, with the topics being high-aspect ratio wings, low aspect-ratio wings, bluff bodies, laminar flow control and transition, active flow control, hypersonic flows, aeroelasticity, aeroacoustics, mathematical fundamentals/ numerical simulation, physical fundamentals, and facilities.

This volume contains articles based on lectures given at the Workshop on Transition and Turbulence Control, hosted by the Institute for Mathematical Sciences, National University of Singapore, 8-10 December 2004. The lecturers included 13 of the world's foremost experts in the control of transitioning and turbulent flows. The chapters cover a wide range of subjects in the broad area of flow control, and will be useful to researchers working in this area in academia, government laboratories and industry. The coverage includes control theory, passive, active and reactive methods for controlling transitional and turbulent wall-bounded flows, noise suppression and mixing enhancement of supersonic turbulent jets, compliant coatings, modern flow diagnostic systems, and swept wing instabilities.

The dynamics of transition from laminar to turbulent flow remains to this day a major challenge in theoretical and applied mechanics. A series of IUTAM symposia held over the last twenty five years at well-known Centres of research in the subject - Novosibirsk, Stuttgart, Toulouse, Sendai and Sedona (Arizona) - has proved to be a great catalyst which has given a boost to research and our understanding of the field. At this point of time, the field is changing significantly with several emerging directions. The sixth IUTAM meeting in the series, which was held at the Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore, India, focused on the progress after the fifth meeting held at Sedona in 1999. The s- posium, which adhered to the IUTAM format of a single session, included seven invited lectures, fifty oral presentations and eight posters. During the course of the symposium, the following became evident. The area of laminar-turbulent transition has progressed considerably since 1999. Better theoretical tools, for handling nonlinearities as well as transient behaviour are now available. This is accompanied by an en- mous increase in the level of sophistication of both experiments and direct numerical simulations. The result has been that our understanding of the early stages of the transition process is now on much firmer footing and we are now able to study many aspects of the later stages of the transition process.

Elementary vortices – those tubular swirling vortical structures with concentrated vorticity commonly observed in various kinds of turbulent flows – play key roles in turbulence dynamics (e.g. enhancement of mixing, diffusion and resistance) and characterize turbulence statistics (e.g. intermittency). Because of their dynamical importance, manipulation of elementary vortices is expected to be effective and useful in turbulence control as well as in construction of turbulence modeling. The most advanced research works on elementary vortices and related problems were presented and discussed at the IUTAM Symposium in Kyoto, Japan, 26-28 October 2004. This book contains 40 contributions presented there, the subjects of which cover vortex dynamics, coherent structures, chaotic advection and mixing, statistical properties of turbulence, rotating and stratified turbulence, instability and transition, dynamics of thin vortices, finite-time singularity, and superfluid turbulence. The book should be useful for readers of graduate and advanced levels in the field of fluid turbulence.

This book is an essential reference for engineers and scientists working in the field of turbulence. It covers a variety of applications, such as: turbulence measurements; mathematical and numerical modeling of turbulence; thermal hydraulics; applications for civil, mechanical and nuclear engineering; environmental fluid mechanics; river and open channel flows; coastal problems; ground water.

The 20th Liège Colloquium was particularly well attended and these proceedings demonstrate the significant progress achieved in understanding, modelling, and observing geostrophic and near-geostrophic turbulence. The book contains more than 50 review papers and original contributions covering most aspects of the field of mesoscale/synoptic coherent structures in geophysical (oceanographic) turbulence. The properties of isolated vortices (generation, evolution, decay), their interactions with other vortices, with larger scale currents and/or with topography are investigated theoretically and by means of numerical and physical models. Observation of these dynamically important features in different parts of the world ocean are reported. Of particular interest will be the fourteen contributions by scientists from the USSR which emphasize the international character of the meeting. The book thus constitutes a useful and complete overview of the current state-of-the-art.

Bottom Turbulence

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.