Lagrangian particle paths and ortho-normal quaternion frames
Chaotic Dynamics
2009-11-11 v2
Abstract
Experimentalists now measure intense rotations of Lagrangian particles in turbulent flows by tracking their trajectories and Lagrangian-average velocity gradients at high Reynolds numbers. This paper formulates the dynamics of an orthonormal frame attached to each Lagrangian fluid particle undergoing three-axis rotations, by using quaternions in combination with Ertel's theorem for frozen-in vorticity. The method is applicable to a wide range of Lagrangian flows including the three-dimensional Euler equations and its variants such as ideal MHD. The applicability of the quaterionic frame description to Lagrangian averaged velocity gradient dynamics is also demonstrated.
Cite
@article{arxiv.nlin/0607020,
title = {Lagrangian particle paths and ortho-normal quaternion frames},
author = {J. D. Gibbon and D. D. Holm},
journal= {arXiv preprint arXiv:nlin/0607020},
year = {2009}
}
Comments
9 pages, one figure, revised