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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.
It is pointed out that despite an abundance of investigations of hydromagnetic stability of toroidal plasma configurations, the problem still remains unsolved. In particular, the meaning of the general geometric Mercier criterion which plays an important role in modern calculations of stability of concrete systems remains unclear. A general theory of local instability is developed in the present paper from which it followed that the Mercier criterion is a necessary and sufficient condition for plasma stability with respect to a particular class of local perturbations, such as those for which the radial wavelength is small with respect to the wavelength along the small azimuth.
Instability of flows and their transition to turbulence are widespread phenomena in engineering and the natural environment, and are important in applied mathematics, astrophysics, biology, geophysics, meteorology, oceanography and physics as well as engineering. This is a textbook to introduce these phenomena at a level suitable for a graduate course, by modelling them mathematically, and describing numerical simulations and laboratory experiments. The visualization of instabilities is emphasized, with many figures, and in references to more still and moving pictures. The relation of chaos to transition is discussed at length. Many worked examples and exercises for students illustrate the ideas of the text. Readers are assumed to be fluent in linear algebra, advanced calculus, elementary theory of ordinary differential equations, complex variables and the elements of fluid mechanics. The book is aimed at graduate students but will also be very useful for specialists in other fields.