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Stretching and folding diagnostics in solutions of the three-dimensional Euler and Navier-Stokes equations

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Title: Stretching and folding diagnostics in solutions of the three-dimensional Euler and Navier-Stokes equations
Authors: Gibbon, JD
Holm, DD
Item Type: Journal Article
Abstract: Stretching and folding dynamics in the incompressible, stratified 3D Euler and Navier-Stokes equations are reviewed in the context of the vector B = ∇q × ∇θ where, in atmospheric physics, θ is a temperature, q = ω · ∇θ is the potential vorticity, and ω = curl u is the vorticity. These ideas are then discussed in the context of the full compressible Navier-Stokes equations where q is taken in the form q = ω · ∇ f (ρ). In the two cases f = ρ and f = ln ρ, q is shown to satisfy the quasi-conservative relation ∂t q + div J = 0.
Issue Date: 17-Oct-2013
Date of Acceptance: 1-Oct-2013
URI: http://hdl.handle.net/10044/1/66551
DOI: https://dx.doi.org/10.1016/j.piutam.2013.09.004
ISSN: 2210-9838
Publisher: Elsevier
Start Page: 25
End Page: 31
Journal / Book Title: Procedia IUTAM
Volume: 9
Copyright Statement: © 2013 The Authors. Published by Elsevier Ltd. Open access under CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/3.0/).
Keywords: nlin.CD
math.AP
Publication Status: Published
Open Access location: https://doi.org/10.1016/j.piutam.2013.09.004
Online Publication Date: 2013-10-17
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics



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