Lagrangian particle paths & ortho - normal quaternion frames
نویسندگان
چکیده
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.
منابع مشابه
ar X iv : n lin / 0 60 70 20 v 1 [ nl in . C D ] 1 1 Ju l 2 00 6 Lagrangian particle paths & ortho - normal quaternion frames
New optical methods now allow experimentalists to track the trajectories of Lagrangian tracer particles in fluid flows at high Reynolds numbers. Independently, quaternions are used in the aerospace and computer graphics industries to track the paths of objects undergoing three-axis rotations. It is shown here that quaternions are a natural way of selecting an appropriate ortho-normal quaternion...
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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 vo...
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