Titlebook: An Introduction to the Geometry and Topology of Fluid Flows; Renzo L. Ricca Book 2001 Springer Science+Business Media Dordrecht 2001 calcu

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An Introduction to the Geometry and Topology of Fluid Flows

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https://doi.org/10.1007/978-3-322-92509-1present geometrical formulations are successful for all the problems considered here and give insight into deep background common to the diverse physical systems. Further, the geometrical formulation opens a new approach to various dynamical systems.

Dedication

Elements of Classical Knot Theoryudy of knots in the usual 3D space .. or ... It also designates knot theory before 1984. In section 1 we describe the basic facts: curves in 3D space, isotopies, knots, links and knot types. We then proceed to knot diagrams and braids. Finally we introduce the useful notion of tangle due to John Con

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Introduction to a Geometrical Theory of Fluid Flows and Dynamical Systemsmely it is invariant under a group transformation, and further that the group manifold is endowed with a Riemannian metric. The basic ideas and tools are described, and application to various physical systems are considered: (i) free rotation of a rigid body; (ii) geodesic equation and KdV equation

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Topological Features Of Inviscid Flowsmetric properties of the fluid. Focusing first on steady Euler fields, we outline known results, giving special attention to the Beltrami fields and the contemporary topological techniques required to elucidate their dynamical features. We also propose a topological perspective for understanding the

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Geometric and Topological Aspects of Vortex Motionen fields and conservation laws, we discuss geometric aspects of vortex filament motion (intrinsic equations, connections with integrable dynamics and extension to higher dimensional manifolds) and the topological interpretation of kinetic helicity in terms of linking numbers. We recall basic result

Infraction

Measures of Topological Structure in Magnetic Fieldsstructure can be quantified using topological invariants. While topological quantities obey conservation laws in systems with no resistivity and simple boundary conditions, in more general circumstances they can change in time as the physical system evolves. Topological structure is often thought of

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