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Quaternions and particle dynamics in the Euler fluid equations
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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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Official URL: http://dx.doi.org/10.1088/0951-7715/19/8/011
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 | ||||
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| Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics Faculty of Science, Engineering and Medicine > Science > Physics |
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| Journal or Publication Title: | Nonlinearity | ||||
| Publisher: | Institute of Physics Publishing Ltd. | ||||
| ISSN: | 0951-7715 | ||||
| Official Date: | August 2006 | ||||
| Dates: |
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| 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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