Lagrangian diagnostics, such as the finite-time Lyapunov exponent and Lagrangian coherent structures, have become popular tools for analyzing unsteady fluid flows. These diagnostics can help illuminate regions where fluid parcels transported by a flow will converge to and diverge from. Unfortunately calculating Lagrangian diagnostics can be time consuming and computationally expensive. Recently new Eulerian diagnostics, such as objective Eulerian coherent structures and the trajectory divergence rate, have been developed which are faster and less expensive to compute. Because Eulerian diagnostics are so new, there is sill much about their connection to Lagrangian diagnostics that is unknown. This paper will provide a mathematical bridge between Lagrangian and Eulerian diagnostics. It will rigorously explore the deep mathematical relationship that exists between invariants of the Cauchy-Green strain tensor and the Eulerian rate-of-strain tensor in the infinitesimal time limit. Additionally, this paper will develop a new Eulerian diagnostic, infinitesimal-time Lagrangian coherent structures, and show its efficacy in predicting the Lagrangian transport of fluid parcels.
Comments: 30 Pages. In preparation for journal submission
Unique-IP document downloads: 32 times
Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.
Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.