%0 Generic
%J Proceedings. Mathematical, physical and engineering sciences
%D 2009
%T A geometric interpretation of coherent structures in Navier–Stokes flows
%A Ian Roulstone
%A Bertrand Banos
%A Gibbon, J. D.
%A Vladimir Roubtsov
%K almost-complex
%K Navier–Stokes
%K three-forms
%K turbulence
%X The pressure in the incompressible three-dimensional Navier–Stokes and Euler equations is governed by Poisson'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—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'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.

%N 2107
%B Proceedings. Mathematical, physical and engineering sciences
%I Royal Society
%C London
%V 465
%P 2015 - 2021
%8 2009/08/07
%G eng
%U http://okina.univ-angers.fr/publications/ua191
%9 1
%4 http://dx.doi.org/10.1098/rspa.2008.0483
%R 10.1098/rspa.2008.0483