**Context of the present book "Hydrodynamics - Advanced Topics"**

A quick search in virtual book stores may result in more than one hundred titles involving the word "Hydrodynamics". Considering the superposition existing with Fluid Mechanics, the number of titles grows much more. Considering all these titles, why try to organize another book on Hydrodynamics? One answer could be that the researchers always try new points of view to understand and treat the problems related to Hydrodynamics. Even a much known phenomenon may be re-explained from a point of view that introduces different tools (conceptual, numerical or practical) into the discussion of fluids. And eventually, a detail shows to be useful, or even very relevant. So, it is necessary to give the opportunity for the different authors to expose their points of view.

Among the historically relevant books on Hydrodynamics, some should be mentioned here. For example, the volumes "Hydrodynamics" and "Hydraulics", by Daniel Bernoulli (1738) and his father, Johann Bernoulli (1743) present many interesting sketches and the analyses that converged to the so called "Bernoulli equation", later deduced more properly by Leonhard Euler. Although there are unpleasant questions about the authorship of the main ideas, as pointed out by Rouse (1967) and Calero (2008), both books are placed in a "prominent position" in history, because of their significant contributions. The volume written by Sir Horace Lamb (1879), now named "Hydrodynamics", considers the basic equations, the vortex motion, and tidal waves, among other interesting topics. Considering the classical equations and procedures followed to study fluid motion, the books "Fundamentals of Hydro and Aerodynamics" and "Applied Hydro and Aerodynamics" by Prandtl and Tietjens (1934) present the theory and its practical applications in a comprehensive way, influencing the experimental procedures for several decades. For over fifty years, the classical volume of Landau and Lifschitz (1959) remains an extremely valuable work for researchers in fluid mechanics.

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 professionals working with Hydrodynamics.

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

Part 1: Mathematical Models in Fluid Mechanics

X Preface

which the knowledge about fluids is vital.

their points of view.

**Context of the present book "Hydrodynamics - Advanced Topics"**

A quick search in virtual book stores may result in more than one hundred titles involving the word "Hydrodynamics". Considering the superposition existing with Fluid Mechanics, the number of titles grows much more. Considering all these titles, why try to organize another book on Hydrodynamics? One answer could be that the researchers always try new points of view to understand and treat the problems related to Hydrodynamics. Even a much known phenomenon may be re-explained from a point of view that introduces different tools (conceptual, numerical or practical) into the discussion of fluids. And eventually, a detail shows to be useful, or even very relevant. So, it is necessary to give the opportunity for the different authors to expose

Among the historically relevant books on Hydrodynamics, some should be mentioned here. For example, the volumes "Hydrodynamics" and "Hydraulics", by Daniel Bernoulli (1738) and his father, Johann Bernoulli (1743) present many interesting sketches and the analyses that converged to the so called "Bernoulli equation", later deduced more properly by Leonhard Euler. Although there are unpleasant questions about the authorship of the main ideas, as pointed out by Rouse (1967) and Calero (2008), both books are placed in a "prominent position" in history, because of their significant contributions. The volume written by Sir Horace Lamb (1879), now named "Hydrodynamics", considers the basic equations, the vortex motion, and tidal waves, among other interesting topics. Considering the classical equations and procedures followed to study fluid motion, the books "Fundamentals of Hydro and Aerodynamics" and "Applied Hydro and Aerodynamics" by Prandtl and Tietjens (1934) present the theory and its practical applications in a comprehensive way,

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

Part 2: Biological Applications and Biohydrodynamics

Part 3: Detailed Experimental Analyses of Fluids and Flows

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

Part 5: Special Topics on Simulations and Experimental Data

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 XVI Preface

region covered by the marine currents that transport this oil. Gases or liquids, the changes in the quality of the fluids in which we live, certainly affect our quality of life.

The knowledge about fluids, their movements, and their ability to transport physical properties and compounds is thus recognized as important for life. As a consequence, thinking about new solutions for general or specific problems in Hydromechanics may help to attain a sustainable relationship with our environment. Re-contextualizing the classical discussion about the truth, in which it was suggested that the "thinking" is the guarantee of our "existence" (St. Augustine, 386a, b, 400), we can say that we agree that thinking guarantees the human existence, and that there are too many warriors, and too few thinkers. Following this re-contextualized sense, it was also said that the man is a bridge between the "animal" and "something beyond the man" (Nietzsche, 1883). This is an interesting metaphor, because bridges are built crossing fluids (even abysms are filled with fluids). Considering all possible interpretations of this phrase, let us study and understand the fluids, and let us help to build the bridge.
