Über die Autorin bzw. den Autor

JEFFREY S. MARSHALL, PhD, is a professor in the Department of Mechanical Engineering and a research engineer at the Iowa Institute of Hydraulic Research at the University of Iowa, Iowa City.

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A comprehensive, modern account of the flow of inviscid incompressible fluids

This one-stop resource for students, instructors, and professionals goes beyond analytical solutions for irrotational fluids to provide practical answers to real-world problems involving complex boundaries. It offers extensive coverage of vorticity transport as well as computational methods for inviscid flows, and it provides a solid foundation for further studies in fluid dynamics.

Inviscid Incompressible Flow supplies a rigorous introduction to the continuum mechanics of fluid flows. It derives vector representation theorems, develops the vorticity transport theorem and related integral invariants, and presents theorems associated with the pressure field. This self-contained sourcebook describes both solution methods unique to two-dimensional flows and methods for axisymmetric and three-dimensional flows, many of which can be applied to two-dimensional flows as a special case. Finally, it examines perturbations of equilibrium solutions and ensuing stability issues.

Important features of this powerful, timely volume include:

• Focused, comprehensive coverage of inviscid incompressible fluids
• Four entire chapters devoted to vorticity transport and solution of vortical flows
• Theorems and computational methods for two-dimensional, axisymmetric, and three-dimensional flows
• A companion Web site containing subroutines for calculations in the book
• Clear, easy-to-follow presentation

Inviscid Incompressible Flow, the only all-in-one presentation available on this topic, is a first-rate teaching and learning tool for graduate- and senior undergraduate-level courses in inviscid fluid dynamics. It is also an excellent reference for professionals and researchers in engineering, physics, and applied mathematics.

Aus dem Klappentext

A comprehensive, modern account of the flow of inviscid incompressible fluids

This one-stop resource for students, instructors, and professionals goes beyond analytical solutions for irrotational fluids to provide practical answers to real-world problems involving complex boundaries. It offers extensive coverage of vorticity transport as well as computational methods for inviscid flows, and it provides a solid foundation for further studies in fluid dynamics.

Inviscid Incompressible Flow supplies a rigorous introduction to the continuum mechanics of fluid flows. It derives vector representation theorems, develops the vorticity transport theorem and related integral invariants, and presents theorems associated with the pressure field. This self-contained sourcebook describes both solution methods unique to two-dimensional flows and methods for axisymmetric and three-dimensional flows, many of which can be applied to two-dimensional flows as a special case. Finally, it examines perturbations of equilibrium solutions and ensuing stability issues.

Important features of this powerful, timely volume include:

• Focused, comprehensive coverage of inviscid incompressible fluids
• Four entire chapters devoted to vorticity transport and solution of vortical flows
• Theorems and computational methods for two-dimensional, axisymmetric, and three-dimensional flows
• A companion Web site containing subroutines for calculations in the book
• Clear, easy-to-follow presentation

Inviscid Incompressible Flow, the only all-in-one presentation available on this topic, is a first-rate teaching and learning tool for graduate- and senior undergraduate-level courses in inviscid fluid dynamics. It is also an excellent reference for professionals and researchers in engineering, physics, and applied mathematics.

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Inviscid Incompressible Flow

John Wiley & Sons

Chapter One

Earth, air, fire, and water-the four basic elements of the ancient Greek world-are each vital to human existence. Air is the medium by which oxygen is transported to our lungs, surging through our twisting pulmonary passageways with each gasped breath. Air is the domain of flight, of soaring birds and buzzing insects and the screaming vehicles of man. Air transports our words, allowing us to communicate with each other. Air and water together regulate the temperature of the earth's atmosphere, blocking out harmful solar emissions and surrounding us in blanketing warmth. They determine our weather, be it a tranquil summer day, a spring shower, a winter blizzard, or a roaring fall hurricane, and over time they control the climate in which we must strive to survive. Water is also vital to human life, transporting nourishment and waste products as it courses through our veins and regulating our body temperature as it evaporates from our skin. Much of the world depends upon oceans and rivers as a medium of transport for goods and a source of bounteous food. The ability to utilize fire is one of the major human characteristics distinguishing us from other animals. Fire cooks our food, warms our bodies, propels our vehicles, hardens and forms our metals. Even the earth is not stagnant and unmoving. Water percolates through its pores, providing us with drink and sustaining the plants that feed us and provide us with shelter. Oil gushes from its fissures, providing fuel for automobiles and engine lubrication. With too much water, the earth forms giant slides, burying houses and roads. Over geologic time scales the earth's motion forms our surroundings, be they from violent volcanic explosions to the subtle drifting of the earth's crust in response to the ever-present convective stirring of the mantle.

Nearly all human endeavors must in some way deal with restrictions imposed by fluid transport. This observation is obvious in the aerospace and marine transport industries, but equally true in other industries in which the importance of fluid flow may not be as apparent. For instance, the major limitation to the smallness, and hence speed, of modern computer chips is the restriction imposed by convective heat transfer in cooling electrical components. As computer chips become increasingly compact, the heating rates become higher and the passageways available for cooling become more confined. Biomedical applications must deal with a host of fluid transport issues, including oxygen supply to the lungs, pumping of blood and the associated transport of nutrients throughout the body, digestion of foods, and human reproduction. On a cellular level, transport of matter, such as viruses or nutrients, over cell boundaries controls the body's ability to fight diseases and heal wounds. Major medical crises, such as strokes and lung cancer, are related to transport of particulate matter either in the blood stream or in the pulmonary system, whereas other emergencies, such as heart attacks or hemorrhaging, are caused by inability to maintain a continual fluid flow. Agriculture must continually deal with fluid transport issues, such as water supply to crops, pesticide distribution, heating of livestock, and soil moisture during harvesting operations. Material processing, which is so vital for modern technological advances, deals with a host of fluid processes, ranging from metal casting to liquid spray coating.

Aside from its importance in diverse applications, fluid dynamics has had a central influence in development of much of modern science and mathematics. A fluid view of elementary matter dates back to ancient Greece, where Anaxagoras (500-428 BC) proposed that all matter consists of a fluid continuum whose basic component is a vortex. This continuum view competed with the atomic (or particulate) view of Democritus (460-370 BC), in which matter is formed of small particles immersed in a fluid and ordered by the action of vortices. The fluid theory of matter, again based on vortices, was later taken up by Descartes (1596-1650) to explain the suspension of celestial bodies and by Kelvin (1824-1907), who proposed that all matter is constructed of a set of "vortex atoms" that exist in the ether. Despite the errors that are now apparent in these concepts, the fluid/particle analogies of matter proposed by these early philosophers spurred development of the science of mechanics and of objective scientific processes to test these models. For instance, Kelvin's quest to uncover the structure of vortex atoms resulted in discovery of many of the basic laws and phenomena associated with vorticity transport in inviscid fluids. The wave/particle models used in modern physics to describe the theory of light and quantum models of elementary particles, as well as the quantum vortices in liquid helium II (London, 1954) and the "magnetic vortices" in high-temperature superconducting materials (Tinkham, 1975), have their base in the fluid/particle models of matter developed in ancient times.

Fluid dynamics has also had a large impact on development of modern applied mathematics. For instance, linear partial differential equations are usually categorized as hyperbolic, parabolic, or elliptic, where the classic examples for these three categories are the wave equation, the heat equation, and the Laplace equation, all of which play a prominent role in description of fluid systems. Two important paradigms for development of the theory of characteristics of nonlinear hyperbolic partial differential equations (Courant and Hilbert, 1962) are wave propagation in compressible gas dynamics and free-surface oscillations in shallow water layers. Kolmogorov's advancements in stochastic analysis found immediate application in his models of the energy cascade process of turbulent flows (Hunt et al., 1991). One of the earliest investigations of deterministic chaos was performed by Lorentz (1963) using a model of atmospheric transport, and further investigations into chaotic systems have been spurred by the need to formulate better models for turbulent flows. Fractal geometry is also commonly exhibited by fluid systems, as illustrated by many of the examples given in the book by Mandelbrot (1977).

Despite its importance to many fields, many centuries of study, and widespread use of advanced supercomputing systems, scientists and engineers specializing in fluid dynamics are still far from able to reliably predict most fluid flow problems. The principal difficulty lies in the inherent nonlinearity of the equations governing fluid flow. This nonlinearity arises from the fluid inertia and is responsible for instabilities and eventual transition of the flow to a turbulent state. Turbulent flows span an enormous range of length scales, with the ratio of the largest to the smallest scale exceeding a factor of [10.sup.5] in many marine and aerospace engineering applications and a factor of [10.sup.8] for flow in the earth's oceans and atmosphere. This wide range of length scales makes direct computational solution of the governing equations impossible for all but a few rather academic cases at low Reynolds numbers, thus requiring the use of models, often combined with empiricism, to truncate the mathematics to a manageable system. The situation is made yet more difficult by the fact that many natural and industrial processes involve particle or droplet transport, phase change, and chemical reactions that influence the fluid momentum...