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Article Dans Une Revue Proceedings of Royal Society A Mathematical, physical and engineering sciences Année : 2009

A geometric interpretation of coherent structures in Navier–Stokes flows

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Résumé

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 Λ3W* where W is a six-dimensional real vector space, we relate the characterization of non-degenerate elements of Λ3W* 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.

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Dates et versions

hal-03054038 , version 1 (11-12-2020)

Identifiants

Citer

Ian Roulstone, Bertrand Banos, J. Gibbon, Vladimir Roubtsov. A geometric interpretation of coherent structures in Navier–Stokes flows. Proceedings of Royal Society A Mathematical, physical and engineering sciences, 2009, 465 (2107), pp.2015 - 2021. ⟨10.1098/rspa.2008.0483⟩. ⟨hal-03054038⟩
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