@article {ua191,
title = {A geometric interpretation of coherent structures in Navier{\textendash}Stokes flows},
journal = {Proceedings. Mathematical, physical and engineering sciences},
volume = {465},
number = {2107},
year = {2009},
month = {2009/08/07},
pages = {2015 - 2021},
publisher = {Royal Society},
type = {1},
address = {London},
abstract = {The pressure in the incompressible three-dimensional Navier{\textendash}Stokes and Euler equations is governed by Poisson{\textquoteright}s equation: this equation is studied using the geometry of three-forms in six dimensions. By studying the linear algebra of the vector space of three-forms *Λ*^{3}W* where *W* is a six-dimensional real vector space, we relate the characterization of non-degenerate elements of *Λ*^{3}W* to the sign of the Laplacian of the pressure{\textemdash}and hence to the balance between the vorticity and the rate of strain. When the Laplacian of the pressure, *Δp*, satisfies *Δp*\>0, the three-form associated with Poisson{\textquoteright}s equation is the real part of a decomposable complex form and an almost-complex structure can be identified. When *Δp*\<0, a real decomposable structure is identified. These results are discussed in the context of coherent structures in turbulence.

},
keywords = {almost-complex, Navier{\textendash}Stokes, three-forms, turbulence},
issn = {1471-2946},
doi = {10.1098/rspa.2008.0483},
url = {http://okina.univ-angers.fr/publications/ua191},
author = {Ian Roulstone and Bertrand Banos and Gibbon, J. D. and Vladimir Roubtsov}
}