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Bounds for Euler from vorticity moments and line divergence
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Kerr, Robert M. (Robert McDougall) (2013) Bounds for Euler from vorticity moments and line divergence. Journal of Fluid Mechanics, Volume 729 . doi:10.1017/jfm.2013.325 ISSN 0022-1120.
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Official URL: http://dx.doi.org/10.1017/jfm.2013.325
Abstract
The inviscid growth of a range of vorticity moments is compared using Euler
calculations of anti-parallel vortices with a new initial condition. The primary goal
is to understand the role of nonlinearity in the generation of a new hierarchy of
rescaled vorticity moments in Navier–Stokes calculations where the rescaled moments
obey Dm ≥ Dm+1, the reverse of the usual
Ωm+1 ≥ Ωm Hölder ordering of the original
moments. Two temporal phases have been identified for the Euler calculations. In the
first phase the 1 < m < ∞ vorticity moments are ordered in a manner consistent with
the new Navier–Stokes hierarchy and grow in a manner that skirts the lower edge of
possible singular growth with D2
m → � sup ӏωӏ ~ Am(Tc-t)-1 where the Am are nearly
independent of m. In the second phase, the new Dm ordering breaks down as the Ωm
converge towards the same super-exponential growth for all m. The transition is
identified using new inequalities for the upper bounds for the -dD-2m/dt that are based
solely upon the ratios Dm+1/Dm, and the convergent super-exponential growth is shown
by plotting log(d log Ωm/dt). Three-dimensional graphics show significant divergence
of the vortex lines during the second phase, which could be what inhibits the initial
power-law growth.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Navier-Stokes equations, Euler angles | ||||
Journal or Publication Title: | Journal of Fluid Mechanics | ||||
Publisher: | Cambridge University Press | ||||
ISSN: | 0022-1120 | ||||
Official Date: | August 2013 | ||||
Dates: |
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Volume: | Volume 729 | ||||
DOI: | 10.1017/jfm.2013.325 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Date of first compliant deposit: | 25 December 2015 | ||||
Date of first compliant Open Access: | 25 December 2015 |
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