**Introduction**

Why is it important to study Hydrodynamics? The answer may be strictly technical, but it may also involve some kind of human feeling about our environment and our (eventual) limitations to deal with its fluidic constituents.

As teachers, when talking to our students about the importance of quantifying fluids, we (authors) go to the blackboard and draw, in blue color, a small circumference in the center of the board, and add the obvious name 'Earth'. Some words are then said, in the sense that Hydrodynamics is important, because we are beings strictly adapted to live immersed in a fluidic environment (air), and because we are beings composed basically by simple fluidic solutions (water solutions), encapsulated in fine carbon membranes. Then, with a red chalk, we draw two crosses: one inside and the other outside the circumference, explaining: "our environment is very limited. We can only survive in the space covered by the blue line. No one of us can survive in the inner part of this sphere, or in the outer space. Despite all films, games, and books about contacts with aliens, and endless journeys across the universe, our present knowledge only allows to suggest that it is most probable that the human being will extinct while in this fine fluid membrane, than to create sustainable artificial environments in the cosmos".

Sometimes, to add some drama, we project the known image of the earth on a wall (the image of the blue sphere), and then we blow a soap bubble explaining that the image gives the false impression that the entire sphere is our home. But our "home" is better represented by the liquid film of the soap bubble (only the film) and then we touch the bubble, exploding it, showing its fragility.

In the sequence, we explain that a first reason to understand fluids would be, then, to guarantee the maintenance of the fluidic environment (the film) so that we could also guarantee our survival as much as possible. Further, as we move ourselves and produce our things immersed in fluid, it is interesting to optimize such operations in order to facilitate our survival. Still further, because our organisms interchange heat and mass in cellular and corporal scales between different fluids, the understanding of these transports permits us to understand the spreading of diseases, the delivering of medicines to cells, and the use of physical properties of fluids in internal treatments. Thus, understanding these transports allows us to improve our quality of life. Finally, the observation of the inner part of the sphere, the outer space and its constituents, shows that many "highly energetic" phenomena behave like the fluids around us. It gives us the hope that the knowledge of fluids can help, in the future, to quantify, reproduce, control and use energy sources similar to those of the stars, allowing us to "move through the cosmos", to create sustainable artificial environments and to leave this "limited film" when necessary. Of course, this "speech" may be viewed as a sort of escapism, related to a fiction of the future. In fact, the day-by-day activities show that we are spending our time with "more important" things, like fighting among us for the dividends of the next fashion wave (or the next technical wave), the hierarchy among nations, or the hierarchy of the cultures of the different nations. So, fighters, warriors, or generals still seem to be the agents that write our history. But global survival, or, in other words, the guarantee of any future history, will need other agents, devoted to other activities. The hope lies on the generation of knowledge, in which the knowledge about fluids is vital.

Preface XI

influencing the experimental procedures for several decades. For over fifty years, the classical volume of Landau and Lifschitz (1959) remains an extremely valuable work

In addition to the usual themes, like the basic equations and turbulence, this book also covers themes like the relativistic fluid dynamics and the dynamics of superfluids. Each of the major topics considered in the studies of fluid mechanics can be widely discussed, generating specific texts and books. An example is the theory of boundary layers, in which the book of Schlichting (1951) has been considered an indispensable reference, because it condenses most of the basic concepts on this subject. Further, still considering specific topics, Stoker (1957) and Lighthill (1978) wrote about waves in fluids, while Chandrasekhar (1961) and Drazin and Reid (1981) considered hydrodynamic and hydromagnetic stability. It is also necessary to mention the books of Batchelor (1953), Hinze (1958), and Monin and Yaglom (1965), which are notable examples of texts on turbulence and statistical fluid mechanics, showing basic concepts and comparative studies between theory and experimental data. A more recent example may be the volume written by Kundu e Cohen (2008), which furnishes a chapter on "biofluid mechanics" The list of the "relevant books" is obviously not complete, and grows continuously, because new ideas are continuously added to the existing knowledge.

The present book is one of the results of a project that generated three volumes, in which recent studies on Hydrodynamics are described. The remaining two titles are "Hydrodynamics - Natural Water Bodies", and "Hydrodynamics - Optimizing Methods and Tools". Along the chapters of the present volume, the authors show the application of concepts of Hydrodynamics in different fields, using different points of view and methods. The editors thank all authors for their efforts in presenting their chapters and conclusions, and hope that this effort will be welcomed by the

The book "Hydrodynamics - Advanced Topics" is organized in the following manner:

Hydrodynamics is a very rich area of study, involving some of the most intriguing theoretical problems, considering our present level of knowledge. General nonlinear solutions, closed statistical equations, explanation of sudden changes, for example, are wanted in different areas of research, being also a matter of study in Hydromechanics. Further, any solution in this field depends on many factors, or many "boundary conditions". The changing of the boundary conditions is one of the ways through which the human being affects its fluidic environment. Changes in a specific site can impose catastrophic consequences in a whole region. For example, the permanent leakage of petroleum in one point in the ocean may affect the life along the entire

Part 4: Radiation-, Electro-, Magnetohydrodynamics and Magnetorheology

Part 5: Special Topics on Simulations and Experimental Data

for researchers in fluid mechanics.

professionals working with Hydrodynamics.

Part 1: Mathematical Models in Fluid Mechanics Part 2: Biological Applications and Biohydrodynamics Part 3: Detailed Experimental Analyses of Fluids and Flows
