On the Geometric Structure of Flows I: The Referential Gradient. A Generally Covariant Measure of Flow Geometry

Autor:	Edmondson, J. K.
Rok vydání:	2014
Předmět:	Mathematical Physics Astrophysics - Solar and Stellar Astrophysics General Relativity and Quantum Cosmology Physics - Fluid Dynamics
Druh dokumentu:	Working Paper
Popis:	Assuming a-priori a smooth generating vector field, we introduce a generally covariant measure of the flow geometry called the referential gradient of the flow. The main result is the explicit relation between the referential gradient and the generating vector field, and is provided for from two equivalent perspectives: a Lagrangian specification with respect to a generalized parameter, and an Eulerian specification making explicit the evolution dynamics. Furthermore, we provide explicit non-trivial conditions which govern the transformation properties of the referential gradient object. Comment: Journal of Mathematical Fluid Mechanics. Submitted 17 Nov 2014
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1411.2283 Zobrazit plný text záznamu View this record from Arxiv