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Pré-Publication, Document De Travail Année : 2021

A model of interacting Navier-Stokes singularities

Résumé

We introduce a model of interacting singularities of Navier-Stokes, named pinçons. They follow a Hamiltonian dynamics, obtained by the condition that the velocity field around these singularities obeys locally Navier-Stokes equations. This model can be seen of a generalization of the vorton model of Novikov [1], that was derived for the Euler equations. When immersed in a regular field, the pinçons are further transported and sheared by the regular field, while applying a stress onto the regular field, that becomes dominant at a scale that is smaller than the Kolmogorov length. We apply this model to compute the motion of a dipole of pinçons. When the initial relative orientation of the dipole is inside the interval [0, π/2], a dipole made of pinçon of same intensity exhibits a transient collapse stage, following a scaling with dipole radius tending to 0 like (tc − t) 0.63. For long time, the dynamics of the dipole is however repulsive, with both components running away from each other to infinity.
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hal-03184709 , version 1 (29-03-2021)

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  • HAL Id : hal-03184709 , version 1

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H Faller, D Geneste, B. Dubrulle. A model of interacting Navier-Stokes singularities. 2021. ⟨hal-03184709⟩
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