Mathematical Theory and Applications (Pt. 1) (Interdisciplinary Applied Mathematics) - Tapa dura

Joseph, Daniel D.; Renardy, Yuriko Y.

9780387979137: Mathematical Theory and Applications (Pt. 1) (Interdisciplinary Applied Mathematics)

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ISBN 10: 0387979131 ISBN 13: 9780387979137

Editorial: Springer-Verlag New York Inc., 1992

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Two-fluid dynamics is a challenging subject rich in physics and prac- tical applications. Many of the most interesting problems are tied to the loss of stability which is realized in preferential positioning and shaping of the interface, so that interfacial stability is a major player in this drama. Typically, solutions of equations governing the dynamics of two fluids are not uniquely determined by the boundary data and different configurations of flow are compatible with the same data. This is one reason why stability studies are important; we need to know which of the possible solutions are stable to predict what might be observed. When we started our studies in the early 1980's, it was not at all evident that stability theory could actu- ally work in the hostile environment of pervasive nonuniqueness. We were pleasantly surprised, even astounded, by the extent to which it does work. There are many simple solutions, called basic flows, which are never stable, but we may always compute growth rates and determine the wavelength and frequency of the unstable mode which grows the fastest. This proce- dure appears to work well even in deeply nonlinear regimes where linear theory is not strictly valid, just as Lord Rayleigh showed long ago in his calculation of the size of drops resulting from capillary-induced pinch-off of an inviscid jet.

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Rese�a del editor

Two-fluid dynamics is a challenging subject rich in physics and prac� tical applications. Many of the most interesting problems are tied to the loss of stability which is realized in preferential positioning and shaping of the interface, so that interfacial stability is a major player in this drama. Typically, solutions of equations governing the dynamics of two fluids are not uniquely determined by the boundary data and different configurations of flow are compatible with the same data. This is one reason why stability studies are important; we need to know which of the possible solutions are stable to predict what might be observed. When we started our studies in the early 1980's, it was not at all evident that stability theory could actu� ally work in the hostile environment of pervasive nonuniqueness. We were pleasantly surprised, even astounded, by the extent to which it does work. There are many simple solutions, called basic flows, which are never stable, but we may always compute growth rates and determine the wavelength and frequency of the unstable mode which grows the fastest. This proce� dure appears to work well even in deeply nonlinear regimes where linear theory is not strictly valid, just as Lord Rayleigh showed long ago in his calculation of the size of drops resulting from capillary-induced pinch-off of an inviscid jet.

Rese�a del editor

Two-fluid dynamics is a challenging subject rich in interdisciplinary science. Reporting from the forefront of research in this area, these volumes combine scientific, engineering, and technological results in a sound mathematical framework. The analytical techniques used throughout the books are rigorously derived in Part I, Mathematic Theory and Applications, making the books appropriate for graduate study. Rotating flows of two liquids, the two-layer Bernard problem, and plane channel flows are also thoroughly covered. In Part II, Lubricated Transport, Drops and Miscible Liquids, an extensive discussion of lubricated pipelining is given with the serious intention of advancing the technology. Core-annular flow, vortex rings in free fall, two-fluids with phase change, and miscible liquids are some of the topics presented in detail. Photographs, figures, graphs, and tables augment continuous comparison of theory and observations. These volumes are bound to become a standard source in a field which is attracting much scientific and industrial interest.

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