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

親密

Geometric and Topological Aspects of Vortex Motion extension to higher dimensional manifolds) and the topological interpretation of kinetic helicity in terms of linking numbers. We recall basic results on evolution of vortex knots and links and outline possible applications of algebraic, geometric and topological measures to evaluate structural complexity of vortex flows.

WAIL

起波瀾

通知

青少年

https://doi.org/10.1007/978-3-658-30014-2rameters are varied, and show how normal form theory can be used to simplify the differential equations that describe the streamlines. The approach is used to obtain a basic qualitative description of separation and attachment close to a wall and to axisymmetric flow, and we illustrate how the ideas

疏忽

Die Einführung der Kapitalmarktaufsichtmetric 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

escalate

https://doi.org/10.1007/978-3-658-30014-2en 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

公理

,Gegner und Verbündete in der Kohlenkrise,structure 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

躲債

https://doi.org/10.1007/978-3-531-90599-0g geodesics is the variational method: we are looking for the shortest path connecting two fluid configurations. In the three dimensional case this approach meets serious difficulties, but in two dimensions it brings a partial success: there exists a reasonable generalized solution of variational pr

集合

,Gegner und Verbündete in der Kohlenkrise,irculation theorem of the LA flow and, hence, for its convection of potential vorticity and its conservation of helicity. Lagrangian averaging also preserves the Euler-Poincaré (EP) variational framework that implies the LA fluid equations. This is expressed in the Lagrangian-averaged Euler- Poincar