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A six-volume collection of the scientific papers of Lord Kelvin (1824-1907), one of Britain's most eminent mathematical physicists.
The Handbook of Mathematical Fluid Dynamics is a compendium of essays that provides a survey of the major topics in the subject. Each article traces developments, surveys the results of the past decade, discusses the current state of knowledge and presents major future directions and open problems. Extensive bibliographic material is provided. The book is intended to be useful both to experts in the field and to mathematicians and other scientists who wish to learn about or begin research in mathematical fluid dynamics. The Handbook illuminates an exciting subject that involves rigorous mathematical theory applied to an important physical problem, namely the motion of fluids.
The Nobel Laureate's monumental study surveys hydrodynamic and hydromagnetic stability as a branch of experimental physics, surveying thermal instability of a layer of fluid heated from below, Benard problem, more.
Geared toward advanced undergraduate and graduate students in applied mathematics, engineering, and the physical sciences, this introductory text covers kinematics, momentum principle, Newtonian fluid, compressibility, and other subjects. 1971 edition.
The stability to small perturbations of shear layer and jet flows (z) in atmospheres with potential temperature (z) is investigated. The problem is reduced to a chardcteristic value problem for the dimensionless wave frequency v which appears in a second-order differential equation with the dependent variable being the horizontal and temporal Fourier transform amplitude of the vertical component of the perturbation momentum vector. Broken-line profiles of E(z) and (z) are used in the analysis of this problem. Integral equations, over the domain of the fluid, which contain both quadratic forms and interfacial contributions, are derived. The interfacial terms vanish for continuous flows, and the theorems of Synge, Howard, and Miles follow. A necessary and sufficient condition for instability is also obtained for continuous flows; however, its usefulness is compromised by integrands which depend on both the basic state flow and the dependent variable of the governing differential equation.