Lagrangian particle paths and ortho-normal quaternion frames

Details Lagrangian particle paths and ortho-normal quaternion frames Lagrangian particle paths and ortho-normal quaternion frames

2006-07-11

arxiv.org/abs/nlin/0607020v2

Nonlinear Sciences

Chaotic Dynamics

9 pages, one figure, revised

Scientific paper

10.1088/0951-7715/20/7/010

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.

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