Lagrangian particle paths and ortho-normal quaternion frames

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.

9 pages, one figure, revised

References in corpus (1)

• Lagrangian dynamics and statistical geometric structure of turbulence

Cited by in corpus (2)

• Modeling the pressure Hessian and viscous Laplacian in Turbulence: comparisons with DNS and implications on velocity gradient dynamics
• Lagrangian analysis of alignment dynamics for isentropic compressible magnetohydrodynamics