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The first to examine topological, group-theoretic and geometric problems of ideal hydrodynamics and magnetohydrodynamics from a unified viewpoint, this book describes preliminary notions in hydrodynamics and pure mathematics with numerous examples and figures.
This book develops the differential geometrical and topological points of view in hydrodynamics. It discusses interactions of hydrodynamics with a wide variety of mathematical domains such as theory of Lie groups, differential geometry, topology of knots, magnetic dynamo theory, calculus of variations and hamiltonian mechanics. The exposition contains extensive examples and figures, proofs of the main results, a survey of the recent achivements in (magneto) hydrodynamics and applications to hydrodynamic stability, dynamo theory and weather prediction.
The contents are accessible to graduate students as well as to both pure and applied mathematicians working in the fields of hydrodynamics, Lie groups, dynamical systems and differential geometry.
This book develops the differential geometrical and topological points of view in hydrodynamics. It discusses interactions of hydrodynamics with a wide variety of mathematical domains such as theory of Lie groups, differential geometry, topology of knots, magnetic dynamo theory, calculus of variations and hamiltonian mechanics. The exposition contains extensive examples and figures, proofs of the main results, a survey of the recent achivements in (magneto) hydrodynamics and applications to hydrodynamic stability, dynamo theory and weather prediction.
The contents are accessible to graduate students as well as to both pure and applied mathematicians working in the fields of hydrodynamics, Lie groups, dynamical systems and differential geometry.