Gibbon, J. D., Holm, D. D., Kerr, Robert M. (Robert McDougall) and Roulstone, I. (2006) Quaternions and particle dynamics in the Euler fluid equations. Nonlinearity, Vol.19 (No.8). pp. 1969-1983. doi:10.1088/0951-7715/19/8/011

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Abstract

Vorticity dynamics of the three-dimensional incompressible Euler equations are cast into a quaternionic representation governed by the Lagrangian evolution of the tetrad consisting of the growth rate and rotation rate of the vorticity. In turn, the Lagrangian evolution of this tetrad is governed by another that depends on the pressure Hessian. Together these form the basis for a direction of vorticity theorem on Lagrangian trajectories. Moreover, in this representation, fluid particles carry ortho-normal frames whose Lagrangian evolution in time are shown to be directly related to the Frenet-Serret equations for a vortex line. The frame dynamics suggest an elegant Lagrangian relation similarly considered.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics Q Science > QC Physics
Divisions:	Faculty of Science > Mathematics Faculty of Science > Physics
Journal or Publication Title:	Nonlinearity
Publisher:	Institute of Physics Publishing Ltd.
ISSN:	0951-7715
Official Date:	August 2006
Dates:	Date Event August 2006 Published
Volume:	Vol.19
Number:	No.8
Number of Pages:	15
Page Range:	pp. 1969-1983
DOI:	10.1088/0951-7715/19/8/011
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access

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